%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author-1        = "Norbert Juffa",
%%%     author-2        = "Nelson H. F. Beebe",
%%%     version         = "3.409",
%%%     date            = "04 December 2014",
%%%     time            = "11:11:20 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",
%%%     FAX-2           = "+1 801 581 4148",
%%%     URL-2           = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "49814 147832 659243 6684476",
%%%     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, floating-point
%%%                        arithmetic",
%%%     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 his 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 3.409, the year coverage looked
%%%                        like this:
%%%
%%%                             1837 (   1)    1897 (   1)    1957 (  13)
%%%                             1838 (   0)    1898 (   1)    1958 (  16)
%%%                             1839 (   0)    1899 (   0)    1959 (  24)
%%%                             1840 (   0)    1900 (   0)    1960 (  20)
%%%                             1841 (   0)    1901 (   0)    1961 (  30)
%%%                             1842 (   0)    1902 (   0)    1962 (  27)
%%%                             1843 (   0)    1903 (   0)    1963 (  24)
%%%                             1844 (   0)    1904 (   0)    1964 (  31)
%%%                             1845 (   0)    1905 (   0)    1965 (  53)
%%%                             1846 (   0)    1906 (   0)    1966 (  32)
%%%                             1847 (   0)    1907 (   0)    1967 (  42)
%%%                             1848 (   0)    1908 (   0)    1968 (  31)
%%%                             1849 (   0)    1909 (   1)    1969 (  46)
%%%                             1850 (   0)    1910 (   1)    1970 (  55)
%%%                             1851 (   0)    1911 (   0)    1971 (  55)
%%%                             1852 (   0)    1912 (   0)    1972 (  57)
%%%                             1853 (   0)    1913 (   0)    1973 (  76)
%%%                             1854 (   0)    1914 (   0)    1974 (  46)
%%%                             1855 (   0)    1915 (   1)    1975 (  94)
%%%                             1856 (   0)    1916 (   0)    1976 (  53)
%%%                             1857 (   0)    1917 (   0)    1977 (  69)
%%%                             1858 (   0)    1918 (   0)    1978 ( 100)
%%%                             1859 (   0)    1919 (   0)    1979 (  68)
%%%                             1860 (   0)    1920 (   0)    1980 ( 102)
%%%                             1861 (   0)    1921 (   0)    1981 ( 120)
%%%                             1862 (   0)    1922 (   0)    1982 (  79)
%%%                             1863 (   0)    1923 (   0)    1983 ( 143)
%%%                             1864 (   0)    1924 (   1)    1984 (  99)
%%%                             1865 (   0)    1925 (   1)    1985 ( 147)
%%%                             1866 (   0)    1926 (   0)    1986 (  96)
%%%                             1867 (   0)    1927 (   0)    1987 ( 134)
%%%                             1868 (   0)    1928 (   0)    1988 ( 151)
%%%                             1869 (   0)    1929 (   0)    1989 ( 187)
%%%                             1870 (   0)    1930 (   2)    1990 ( 144)
%%%                             1871 (   0)    1931 (   0)    1991 ( 219)
%%%                             1872 (   0)    1932 (   1)    1992 ( 174)
%%%                             1873 (   0)    1933 (   1)    1993 ( 189)
%%%                             1874 (   0)    1934 (   1)    1994 ( 173)
%%%                             1875 (   0)    1935 (   0)    1995 ( 157)
%%%                             1876 (   0)    1936 (   3)    1996 ( 175)
%%%                             1877 (   0)    1937 (   2)    1997 ( 128)
%%%                             1878 (   0)    1938 (   4)    1998 ( 126)
%%%                             1879 (   0)    1939 (   0)    1999 ( 187)
%%%                             1880 (   0)    1940 (   3)    2000 ( 140)
%%%                             1881 (   1)    1941 (   1)    2001 ( 204)
%%%                             1882 (   0)    1942 (   2)    2002 ( 156)
%%%                             1883 (   0)    1943 (   1)    2003 ( 143)
%%%                             1884 (   0)    1944 (   1)    2004 ( 165)
%%%                             1885 (   0)    1945 (   2)    2005 ( 164)
%%%                             1886 (   0)    1946 (   5)    2006 ( 120)
%%%                             1887 (   0)    1947 (   4)    2007 ( 130)
%%%                             1888 (   0)    1948 (   5)    2008 (  65)
%%%                             1889 (   0)    1949 (   3)    2009 ( 106)
%%%                             1890 (   0)    1950 (   3)    2010 (  73)
%%%                             1891 (   0)    1951 (   5)    2011 ( 124)
%%%                             1892 (   0)    1952 (   4)    2012 (  49)
%%%                             1893 (   2)    1953 (   1)    2013 (  30)
%%%                             1894 (   0)    1954 (   7)    2014 (  27)
%%%                             1895 (   0)    1955 (   7)    2015 (   1)
%%%                             1896 (   0)    1956 (   8)
%%%                             19xx (   2)
%%%                             20xx (   1)
%%%
%%%                             Article:       2838
%%%                             Book:           304
%%%                             InBook:           1
%%%                             InCollection:    59
%%%                             InProceedings: 1490
%%%                             Manual:          63
%%%                             MastersThesis:  144
%%%                             Misc:           141
%%%                             Periodical:       3
%%%                             PhdThesis:       69
%%%                             Proceedings:    356
%%%                             TechReport:     302
%%%                             Unpublished:      9
%%%
%%%                             Total entries: 5779
%%%
%%%                        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.

@Preamble{
  "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " #
  "\ifx \undefined \booktitle    \def \booktitle#1{{{\em #1}}} \fi" #
  "\ifx \undefined \circled      \def \circled #1{(#1)}\fi" #
  "\ifx \undefined \mathbb       \def \mathbb #1{{\bf #1}}\fi" #
  "\ifx \undefined \mathcal      \def \mathcal #1{{\cal #1}}\fi" #
  "\ifx \undefined \mathrm       \def \mathrm #1{{\rm #1}}\fi" #
  "\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}}\fi" #
  "\ifx \undefined \reg          \def \reg {\circled{R}}\fi" #
  "\ifx \undefined \texttt       \def \texttt #1{{\tt #1}}\fi" #
  "\ifx \undefined \TM           \def \TM {${}^{\sc TM}$} \fi" #
  "\hyphenation{
                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,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|http://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-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-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-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-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-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-ADA-LETT              = "Ada Letters"}

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

@String{j-ALGORITHMICA          = "Algorithmica"}

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

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

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

@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-STAT         = "Annals of Mathematical Statistics"}

@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-APP-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-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-BIT                   = "BIT (Nordisk tidskrift for
                                  informationsbehandling)"}

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

@String{j-COMM-STAT             = "Communications in Statistics"}

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

@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-ELECTR-ENG     = "Computers and Electrical Engineering"}

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

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

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

@String{j-EDN                   = "EDN"}

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

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

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

@String{j-HEWLETT-PACKARD-J     = "Hewlett--Packard 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-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-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-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-LETT = "IEEE signal processing letters"}

@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-2 = "IEEE transactions on circuits and
                                  systems. 2, Analog and digital signal
                                  processing"}

@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-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-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-SIG-PROC   = "IEEE Transactions on Signal Processing"}

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

@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-TSP              = "IEEE Transactions on Signal Processing"}

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

@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-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-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-ALG                 = "Journal of Algorithms"}

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

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

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

@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-APPL-MATH      = "Journal of Computational and Applied
                                  Mathematics"}

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

@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-INF-PROCESS         = "Journal of Information Processing"}

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

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

@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-KYBERNETIKA           = "Kybernetika"}

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

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

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

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

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

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

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

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

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

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

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

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

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

@String{j-MATH-COMP-SIM         = "Mathematics and Computers in Simulation"}

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

@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-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-MICROPROC-MICROPROG   = "Microprocessing and Microprogramming"}

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

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

@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-NEW-SCIENTIST         = "New Scientist"}

@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-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-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-PHYSICA-A             = "Physica A"}

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

@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-IEEE             = "Proceedings of the IEEE"}

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

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

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

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

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

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

@String{j-SUPERCOMPUTER         = "Supercomputer"}

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

@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-ZASTOS-MAT            = "Zastosowania Matematyki"}

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

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

@String{pub-A-K-PETERS          = "A. K. Peters, Ltd."}
@String{pub-A-K-PETERS:adr      = "Natick, MA, 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-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, 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-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-HAYDEN-BOOK         = "Hayden Book Co."}
@String{pub-HAYDEN-BOOK:adr     = "Rochelle Park, NJ, USA"}

@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-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-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-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-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-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-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-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-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-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-LNCS                = "Lecture Notes in Computer Science"}

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

@String{ser-LNM                 = "Lecture Notes in Mathematics"}

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

@String{ser-SIGPLAN             = "ACM SIG{\-}PLAN Notices"}

%%% ====================================================================
%%% Bibliography entries.
%%%
%%% 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.

@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 =    "http://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,
}

@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 =    "http://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",
  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{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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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 =    "http://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",
  ISSN-L =       "0035-8711",
  bibdate =      "Wed Oct 13 11:12:08 2010",
  bibsource =    "http://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",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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/page/journal/isis/about.html",
}

@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 =    "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =    "http://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",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "http://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",
  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 =    "http://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 =    "http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www2.research.att.com/~njas/doc/shannonbio.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Institute of Electrical
                 Engineers",
  journal-URL =  "http://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 ... a
                 landmark in that it helped to change digital circuit
                 design from an art to a science.''",
}

@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 =    "http://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 =    "http://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 =    "http://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 =    "http://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.",
}

@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 =    "http://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",
  bibsource =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =          "http://dx.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 =    "http://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 =       "??",
  pages =        "52--53",
  day =          "13",
  month =        jan,
  year =         "1945",
  CODEN =        "NATUAS",
  DOI =          "http://dx.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 =    "http://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;
                 http://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{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 =    "http://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)",
}

@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",
  bibdate =      "Wed Oct 13 08:17:48 2004",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
                 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/Theory/arith.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Report to the U.S. Army Ordnance Department. Reprinted
                 in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S
                 8.3]{Randell:1982:ODC}, and
                 \cite[pp.~97--146]{Aspray:1987:PJN}",
  acknowledgement = ack-nhfb,
  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 =    "http://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",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  note =         "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@TechReport{Goldstine:1947:PCP,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument",
  type =         "Technical report",
  number =       "1",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "69",
  day =          "1",
  month =        apr,
  year =         "1947",
  bibdate =      "Wed Jun 01 17:41:33 2005",
  bibsource =    "http://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:1997:SA} cites pp.~142--151 of this
                 report as the first published treatment of
                 double-precision arithmetic on digital computers.",
  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 =    "http://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 =    "http://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{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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
                 in \cite[v.~5, pp.~479--557]{Taub:1961:JNC}.",
  ZMnumber =     "0031.31402",
  acknowledgement = ack-nhfb # " and " # ack-jg,
  fjournal =     "Bulletin of the American Mathematical Society",
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  note =         "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  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",
  bibdate =      "Wed Oct 13 11:27:40 2010",
  bibsource =    "http://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",
}

@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 =    "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://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",
  ISSN-L =       "0033-5614",
  MRclass =      "65.0X",
  MRnumber =     "MR0028100 (10,405c)",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Sat Nov 19 12:09:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Turing:1992:PM} 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",
  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 =       "487",
  pages =        "??--??",
  year =         "1948",
  CODEN =        "NATUAS",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Oct 13 12:00:02 2010",
  bibsource =    "http://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/",
}

@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 =    "http://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 =       "??",
  pages =        "57--62",
  year =         "1949",
  CODEN =        "JRNBAG",
  ISSN =         "0091-0635",
  bibdate =      "Fri Aug 20 09:32:34 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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 =    "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@Article{Booth:1951:SBM,
  author =       "A. 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",
  ISSN =         "0033-5614",
  ISSN-L =       "0033-5614",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Cambridge Philosophical Society.
                 Mathematical and physical sciences",
  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 =    "http://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,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@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,
  pages =        "101--105",
  year =         "1952",
  DOI =          "http://dx.doi.org/10.1145/1434770.1434787",
  LCCN =         "????",
  bibdate =      "Fri Dec 03 09:17:58 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bookpages =    "vi + 114",
  keywords =     "Bell Laboratories Model 1--5 relay computers; complex
                 fixed-point decimal arithmetic; complex floating-point
                 decimal arithmetic",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Journal of the Acoustical Society of America",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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 Confer ence. {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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "http://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,
  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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Society for Industrial and Applied
                 Mathematics",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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",
  bibdate =      "Sun Jul 17 09:52:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "decimal floating-point arithmetic",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Mathematics",
  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 =    "http://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;
                 http://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;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Book{Richards:1955:AOD,
  author =       "R. K. 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 =    "http://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 =          "http://dx.doi.org/10.1109/IRETELC.1955.5407911",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:10:39 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1956.5219936",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:46:27 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1956.5219789",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:46:18 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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,
  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",
  bibdate =      "Fri Nov 09 19:14:45 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/TEC.1956.5219804",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:46:21 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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",
  bibdate =      "Fri Nov 09 19:38:57 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Ercoli:1960:LEE}.",
  acknowledgement = ack-nhfb,
  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 =    "http://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 =    "http://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 =          "http://dx.doi.org/10.1109/TEC.1957.5221576",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:27 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1957.5221579",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:27 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://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 =          "http://dx.doi.org/10.1109/TEC.1957.5222025",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:34 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  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 =    "http://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{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 =    "http://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 =    "http://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",
  bibdate =      "Thu Nov 06 05:53:55 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  keywords =     "negative base",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1957.5221558",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:23 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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",
  bibdate =      "Fri Nov 28 16:28:12 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  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",
  bibdate =      "Fri Nov 28 11:47:47 2003",
  bibsource =    "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  oldlabel =     "Ershov58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Ershov58",
}

@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;
                 http://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{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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://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 =        "????",
  year =         "1958",
  CODEN =        "IRELAO",
  DOI =          "http://dx.doi.org/10.1109/TEC.1958.5222657",
  ISSN =         "0367-9950",
  bibdate =      "Wed Feb 14 19:23:38 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  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",
  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",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1958.5222579",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:43 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1958.5222094",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:43 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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",
  ISSN-L =       "0033-5614",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
}

@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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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",
  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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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,
  year =         "1959",
  LCCN =         "TJ213 .G72",
  bibdate =      "Fri Aug 20 08:41:16 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Chapter 2.",
  acknowledgement = ack-nhfb,
  bookpages =    "????",
  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",
  bibdate =      "Thu Sep 08 08:14:00 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IRE Transactions on Electronic Computers",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =        "????",
  year =         "1959",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65.00",
  MRnumber =     "MR0099119 (20 \#5563)",
  bibdate =      "Tue Nov 22 09:08:17 MST 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1959.5222757",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:44 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1959.5219515",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:44 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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 =    "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://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 =          "http://dx.doi.org/10.1109/TEC.1959.5222057",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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 =    "http://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 =          "http://dx.doi.org/10.1109/TEC.1959.5219526",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1959.5219529",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219529",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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/;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://dx.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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
  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/",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =       "J. 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",
  ISSN =         "0367-9950",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:07 MDT 2000",
  bibsource =    "Compiler/semantics.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/",
  URL =          "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/",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "http://dx.doi.org/10.1109/TEC.1960.5219855",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:34:12 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219855",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1960.5219830",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:34:11 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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{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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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 =    "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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,
  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 =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
                 http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://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 =    "http://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 =          "http://dx.doi.org/10.1109/TEC.1961.5219227",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1961.5219154",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:02 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@Article{Cox:1961:NMP,
  author =       "A. G. Cox and H. A. Luther",
  title =        "A Note on Multiple Precision Arithmetic",
  journal =      j-CACM,
  volume =       "4",
  number =       "8",
  pages =        "353",
  month =        aug,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 15 18:36:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1961.5219286",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:05 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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",
  bibdate =      "Mon Sep 16 16:12:21 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IRE Proceedings",
  xxnote =       "Check author name: I have found this paper cited both
                 as Freiman and as Frieman?? Hennessy and Patterson
                 \cite{Hennessy:2002:CAQ} have Freiman.",
}

@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 =    "http://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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
                 http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://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 =          "http://doi.acm.org/10.1145/800029.808563",
  bibdate =      "Thu Aug 07 19:04:58 2008",
  bibsource =    "http://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 =          "http://dx.doi.org/10.1109/TEC.1961.5219198",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:03 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1961.5219240",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1961.5219274",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

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

@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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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",
  bibdate =      "Thu Feb 15 15:07:57 2007",
  bibsource =    "http://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",
  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 =       "P. Rabinowitz",
  title =        "Multiple-Precision Division",
  journal =      j-CACM,
  volume =       "4",
  number =       "2",
  pages =        "98--98",
  month =        feb,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 00:29:25 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1961.5219186",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:03 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Book{Taub:1961:JNC,
  editor =       "A. H. Taub",
  title =        "{John von Neumann}: Collected Works",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol.
                 4), ??? (vol. 5), ??? (vol. 6)",
  year =         "1961--1963",
  LCCN =         "????",
  bibdate =      "Wed Jun 01 16:58:29 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Six volumes. Volume I: Logic, Theory of Sets and
                 Quantum Mechanics (1961); Volume II: Operators, Ergodic
                 Theory and Almost Periodic Functions in a Group (1961);
                 Volume III: Rings of Operators (1961); Volume IV:
                 Continuous Geometry and Other Topics (1962); Volume V:
                 Design of Computers, Theory of Automata and Numerical
                 Analysis (1963); Volume VI: Theory of Games,
                 Astrophysics, Hydrodynamics and Meteorology (1963).",
  acknowledgement = ack-nhfb,
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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 =    "http://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 =          "http://dx.doi.org/10.1109/TEC.1961.5219271",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ibmjrd.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.",
  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, 9s in a decimal machine). Sow 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 waling 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,
  pages =        "92--121",
  year =         "1962",
  LCCN =         "QA76.8.I2 I5",
  bibdate =      "Wed Feb 14 17:24:27 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  bookpages =    "322",
  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 =          "http://dx.doi.org/10.1109/TEC.1962.5219348",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:49 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/TEC.1962.5219366",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:50 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://dx.doi.org/10.1109/TEC.1962.5219349",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:49 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii nauk SSSR",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1962.5219389",
  ISSN =         "0367-9950",
  MRclass =      "68.00",
  MRnumber =     "MR0150990 (27 \#976)",
  MRreviewer =   "N. H. Choksy",
  bibdate =      "Thu Jul 14 09:11:51 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@Article{Knuth:1962:EPC,
  author =       "D. E. Knuth",
  title =        "Evaluation of Polynomials By Computer",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "595--599",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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",
  bibdate =      "Sat Jul 16 20:52:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1962.5219460",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:53 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1962.5219391",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:51 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219391",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/TEC.1962.5219436",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:52 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219436",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@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",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
                 http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://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",
  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 =    "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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;
                 http://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 =          "http://dx.doi.org/10.1109/PGEC.1963.263644",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:42 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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 =          "http://dx.doi.org/10.1109/PGEC.1963.263391",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:36 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@Article{Eve:1963:SAI,
  author =       "J. Eve",
  title =        "Starting approximation for the iterative calculation
                 of square roots",
  journal =      j-COMP-J,
  volume =       "6",
  pages =        "274--276",
  year =         "1963",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 15 18:37:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://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)",
}

@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;
                 http://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 =    "http://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 =          "http://dx.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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =          "http://dx.doi.org/10.1109/PGEC.1963.263572",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:39 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =          "http://dx.doi.org/10.1109/PGEC.1963.263479",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:40 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =          "http://dx.doi.org/10.1109/PGEC.1963.263493",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:36 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754",
  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",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Apr 29 18:26:14 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@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 =          "http://dx.doi.org/10.1109/PGEC.1963.263593;
                 http://dx.doi.org/10.1109/PGEC.1963.263592",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:44 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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",
  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 =    "http://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 =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/",
  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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "A. S. Householder",
}

@Book{Wilkinson:1963:REA,
  author =       "James H. Wilkinson",
  title =        "Rounding Errors in Algebraic Processes",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "vi + 161",
  year =         "1963",
  LCCN =         "QA76.5 .W53 1964",
  bibdate =      "Thu Sep 08 13:29:45 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Aiken:1964:PAC,
  author =       "H. H. Aiken",
  title =        "Proposed automatic calculating machine",
  journal =      j-IEEE-SPECTRUM,
  volume =       "1",
  number =       "??",
  pages =        "62--69",
  month =        aug,
  year =         "1964",
  CODEN =        "IEESAM",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Oct 13 11:16:56 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Previously unpublished memorandum. Reprinted in
                 \cite[\S 5.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  remark =       "This article does not appear in the IEEE Xplore
                 database, and that source lists only volume 1, number
                 1, for 1964. I found multiple references to this paper
                 as the August 1964 issue, so perhaps IEEE Xplore is
                 missing early journal issues??",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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/;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://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/;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://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 =          "http://doi.acm.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;
                 http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://dx.doi.org/10.1109/PGEC.1964.263791",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:59 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://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 =       "R. E. Goldschmidt",
  title =        "Applications of division by convergence",
  type =         "Thesis ({M.S.})",
  school =       "Dept. of Electrical Engineering, Massachusetts
                 Institute of Technology",
  address =      "Cambridge, MA, USA",
  pages =        "44 (est.)",
  month =        jun,
  year =         "1964",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1964.263942",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:06 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =    "http://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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1964.263919",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:00 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =          "http://dx.doi.org/10.1109/PGEC.1964.263838",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:57 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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 =    "http://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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1964.263777;
                 http://dx.doi.org/10.1109/PGEC.1964.263776",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:58 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099",
  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/;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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;
                 http://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 =          "http://dx.doi.org/10.1109/PGEC.1964.263734",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:04 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1964.263830",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:56 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038071",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Wolfe:1964:RTE,
  author =       "J. M. Wolfe",
  title =        "Reducing Truncation Errors by Programming",
  journal =      j-CACM,
  volume =       "7",
  number =       "6",
  pages =        "355--356",
  month =        jun,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 00:17:16 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =  "http://www.jstor.org/page/journal/amermathmont/about.html",
  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 =    "http://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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1965.264145",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:33 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =          "http://dx.doi.org/10.1109/PGEC.1965.264080",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:41 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1965.264153",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:34 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1965.263975",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:23 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385",
  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 =          "http://dx.doi.org/10.1109/PGEC.1965.264031",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:40 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Hammer:1965:BRE,
  author =       "Preston C. Hammer",
  title =        "Book Review: {{\em 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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.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",
}

@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 =          "http://dx.doi.org/10.1109/PGEC.1965.264258",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  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 =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://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:FRR,
  author =       "W. Kahan",
  title =        "Further Remarks on Reducing Truncation Errors",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "40--40",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 00:18:17 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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}. Cited in
                 \cite{Sterbenz:1974:FPC}.",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://doi.acm.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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "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 =    "http://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 =    "http://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 =    "http://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;
                 http://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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://dx.doi.org/10.1109/PGEC.1965.264010",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:39 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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,
  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 =          "http://dx.doi.org/10.1109/PGEC.1965.263963",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://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",
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moller:1965:QDP}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01975722",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.80",
  MRnumber =     "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;
                 http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://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:FRR}. 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",
  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 =    "http://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,
  bookpages =    "????",
  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 =    "http://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{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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  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 =          "http://dx.doi.org/10.1109/PGEC.1965.264250",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1965.264051",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:20 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "accurate floating-point summation",
  sjb =          "Refers to \cite{Wolfe:cacm:196,Wilhelm:1977:GMPb}.",
}

@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 =          "http://dx.doi.org/10.1109/PGEC.1965.264066",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:21 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:42:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.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, is missing from
                 the PDF file.",
  xxmonth =      "(none)",
}

@Article{Winograd:1965:TRP,
  author =       "S. 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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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 =          "http://dx.doi.org/10.1109/PGEC.1966.264311",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:31 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/",
  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 =    "http://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 =    "http://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,
  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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/",
  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{Fike:1966:SAS,
  author =       "C. T. Fike",
  title =        "Starting Approximations for Square Root Calculation on
                 {IBM} System/360",
  journal =      j-CACM,
  volume =       "9",
  number =       "4",
  pages =        "297--299",
  month =        apr,
  year =         "1966",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
  remark =       "Probably November or December issue; missing from
                 amermathmonthly1960.bib.",
}

@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 =          "http://dx.doi.org/10.1109/PGEC.1966.264566",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:38 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038884",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@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 =          "http://dx.doi.org/10.1109/PGEC.1966.264312",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:31 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038726",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@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 =    "http://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 =    "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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 =    "http://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",
  year =         "1966",
  bibdate =      "Wed Nov 07 08:39:33 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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;
                 http://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 =    "http://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 =          "http://dx.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 =    "http://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",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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",
}

@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 =    "http://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 =    "http://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 =    "http://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",
}

@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;
                 http://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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
                 http://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 =       "A. {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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
                 http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://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 =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://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 =    "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Anderson:1967:ISM,
  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",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Sep 07 22:14:32 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "http://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",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  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 =      "Computer Design",
  volume =       "6",
  number =       "??",
  pages =        "52--63",
  month =        may,
  year =         "1967",
  bibdate =      "Thu Nov 06 06:07:24 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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 =          "http://dx.doi.org/10.1109/PGEC.1967.264580",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:02 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See correction \cite{Ferrari:1969:CDM}.",
  URL =          "http://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: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",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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 =          "http://dx.doi.org/10.1109/PGEC.1967.264752",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:06 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =    "http://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",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://doi.acm.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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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 =          "http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:01 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =          "http://dx.doi.org/10.1109/PGEC.1967.264730",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:03 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See comment \cite{Azgapetian:1968:CAP}.",
  URL =          "http://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 =    "http://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/;
                 http://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 =          "http://dx.doi.org/10.1109/PGEC.1967.264781",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:05 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  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 =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://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 =       "D. 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",
  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.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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;
                 http://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 =          "http://dx.doi.org/10.1109/PGEC.1967.264811",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:01 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039023;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4039015",
  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{}",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://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 =       "S. 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",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See \cite{Massell:1967:RAP}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687312",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "http://doi.acm.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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "cubical complexes; extremal; minimization; prime
                 implicants; switching function; ternary encoding",
}

@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;
                 http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Hart:1968:CA,
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted 1978 with corrections.",
  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 =    "http://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 =    "http://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 =    "http://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",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  bibdate =      "Fri Apr 21 07:26:39 2000",
  bibsource =    "http://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",
  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 =          "http://dx.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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@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 =    "http://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;
                 http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =          "http://dx.doi.org/10.1109/PGEC.1967.264810;
                 http://dx.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 =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687264;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35582",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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}.",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  reviewer =     "J. Kuntzmann",
}

@TechReport{Yohe:1968:CPA,
  author =       "J. M. 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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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,
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/T-C.1969.222658;
                 http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:18 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671251;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35034",
  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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
}

@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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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;
                 http://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;
                 http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See \cite{Ferrari:1967:DMU}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671148",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "http://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",
}

@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/",
  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;
                 http://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 =    "http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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",
  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/;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Argonne Nat. Lab., Argonne, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "$\sqrt(x)$; elementary functions; function evaluation;
                 iterative methods",
}

@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 =    "http://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 =      "Fri Mar 22 18:03:29 MST 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "RCA review",
}

@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 =    "http://ieeexplore.ieee.org/;
                 http://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 =  "http://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 =    "http://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 =    "http://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;
                 http://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 =    "http://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 =          "http://doi.acm.org/10.1145/356540.356543",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Mon Sep 19 18:18:44 1994",
  bibsource =    "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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,
  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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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/",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  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 =    "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@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 =    "http://ieeexplore.ieee.org/;
                 http://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 =  "http://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 =    "http://ieeexplore.ieee.org/;
                 http://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 =  "http://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",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See \cite{Atkins:1968:HRD}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671216",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://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,
  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 =    "http://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,
  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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://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 =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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",
  ISSN =         "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.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/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 include.",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://doi.acm.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;
                 http://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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 Univ., NY, USA",
  descriptors =  "Simulation; statistics; numeric calculation;",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://ieeexplore.ieee.org/;
                 http://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 =  "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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:AFA,
  author =       "Michael Malcolm",
  title =        "An algorithm for floating-point accumulation of sums
                 with small relative error",
  number =       "STAN-CS-70-163",
  institution =  "Computer Science Department, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "21",
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Algorithms.;
                 FORTRAN (Computer program language); Numerical
                 calculations --- Computer programs.",
  remark =       "Reproduced by National Technical Information Service.
                 AD 708 691.",
}

@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,
                 Dept. 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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Programming (Mathematics)",
}

@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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671610;
                 http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Matula.pdf",
  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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
                 database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Nagoya Univ., 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",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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;
                 http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671609;
                 http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Shively.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =        "181",
  year =         "1970",
  LCCN =         "TK7889.C6 T5 1970",
  bibdate =      "Wed Sep 14 22:45:51 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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 =    "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  journalabr =   "Commun ACM",
  keywords =     "CACMA; digital arithmetic; ele; iterative methods;
                 mathematics; numerical methods; optimisation",
}

@TechReport{Yohe:1970:ACB,
  author =       "J. M. 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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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. M. 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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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.",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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/page/journal/isis/about.html",
}

@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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Pawlak:1971:ACN,Wadel:1971:CNR}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671493",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
                 http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/",
  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 =    "http://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 =      "Honeywell Computer Journal",
  volume =       "5",
  number =       "3",
  pages =        "99--105",
  month =        "????",
  year =         "1971",
  bibdate =      "Thu Nov 25 09:37:15 2004",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01931808",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://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;
                 http://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 =          "http://doi.acm.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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  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;
                 http://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",
  year =         "1971",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "68A55",
  MRnumber =     "45 8056",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "accurate floating-point summation; balanced ternary",
  xxmonth =      "(none)",
}

@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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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 =          "http://doi.acm.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/;
                 http://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",
}

@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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM Algorithm 414.",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/",
  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/",
}

@InProceedings{Kahan:1971:SEA,
  author =       "W. Kahan",
  title =        "A survey of error analysis",
  crossref =     "Freiman:1971:PIC",
  pages =        "1214--1239",
  year =         "1971",
  bibdate =      "Tue Aug 28 05:24:53 2001",
  bibsource =    "http://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}.",
}

@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 =    "http://ieeexplore.ieee.org/;
                 http://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{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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671881",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Kulisch:1971:AAR,
  author =       "U. 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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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 =    "http://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",
}

@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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Stanford Univ., CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Wadel:1971:CNR,Zohar:1970:NRC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671894",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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 =          "http://dx.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;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671771",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "Check pages??",
  acknowledgement = ack-ec # " and " # ack-nhfb,
  affiliation =  "Univ., 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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Pawlak:1971:ACN,Zohar:1970:NRC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671893",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@InProceedings{Walther:1971:UAE,
  author =       "J. S. Walther",
  title =        "A unified algorithm for elementary functions",
  crossref =     "AFIPS:1971:ACP",
  volume =       "38",
  pages =        "379--385",
  year =         "1971",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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. M. 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 =    "http://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 =    "http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/",
  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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.doi.org/10.1109/T-C.1972.223499;
                 http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:48 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672092;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35066",
  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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}

@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;
                 http://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 =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://ieeexplore.ieee.org/;
                 http://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;
                 http://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;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://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 =    "http://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 .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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Heising:1972:MM,
  author =       "W. Heising and M. O. Rabin and S. 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;
                 http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@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 =    "http://ieeexplore.ieee.org/;
                 http://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;
                 http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Malcolm:1972:ARP,
  author =       "M. 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",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:14:16 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Gentleman:1974:MAR}.",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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 =          "http://dx.doi.org/10.1109/ARITH.1972.6153912",
  bibdate =      "Tue Mar 5 08:31:37 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@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/;
                 http://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",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  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 =    "http://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; 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 =          "http://dx.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;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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;
                 http://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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Numerical calculations.",
}

@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 =          "http://dx.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://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/",
  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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://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",
}

@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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
}

@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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009104;
                 http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Atkins.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =          "http://dx.doi.org/10.1109/T-C.1973.223711;
                 http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:18 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672304;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35074",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments
                 \cite{Blankenship:1974:CTC,Kroft:1974:CTC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672241",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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 =          "http://dx.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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Gardiner:1974:CAI}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672273",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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/;
                 http://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",
  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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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, Dept. of Computer Science",
  address =      "Helsinki",
  pages =        "ii + 20",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "http://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 =    "http://ieeexplore.ieee.org/;
                 http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/",
  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 =    "http://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{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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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 =    "http://ieeexplore.ieee.org/;
                 http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009117;
                 http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  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 =          "http://doi.acm.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;
                 http://www.math.utah.edu/pub/tex/bib/fparith.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,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  reviewer =     "V. V. Ivanov",
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/T-C.1973.223674;
                 http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672267;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35073",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://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{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 =    "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =    "http://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 =    "http://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 =    "http://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 =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://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:MAP,
  author =       "Michael A. Malcolm",
  title =        "A machine-independent {ALGOL} procedure for accurate
                 floating-point summation",
  type =         "Technical report",
  number =       "STAN-CS-73-374",
  institution =  "Stanford University, Computer Science Department",
  address =      "Stanford, CA, USA",
  pages =        "6",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ALGOL (Computer program language)",
}

@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 =       "Dept. of Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "ix + 129",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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",
  ISSN-L =       "0097-3165",
  MRclass =      "10A30 (02E10)",
  MRnumber =     "MR0321857 (48 \#222)",
  MRreviewer =   "R. L. Goodstein",
  bibdate =      "Thu Nov 8 14:50:22 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://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",
}

@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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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;
                 http://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 =    "http://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 =    "http://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;
                 http://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;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Sureshchander:1973:CDM}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 Univ., Dept. of Electrical Engineering",
  address =      "St. Louis, MO, USA",
  pages =        "vii + 111",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  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",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 08 08:17:30 1994",
  bibsource =    "http://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",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://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",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://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",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://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",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://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",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://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",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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/;
                 http://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 =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
  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",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://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\'olya 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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Roy:1973:ARC}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@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",
  ISSN-L =       "0373-6385",
  MRclass =      "65H10",
  MRnumber =     "48 1457",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "http://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",
}

@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 =    "http://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 =          "http://dx.doi.org/10.1109/T-C.1973.223594;
                 http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:11 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672187;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35069",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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. M. 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 =    "http://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. M. Yohe",
  title =        "Interval Bounds for Square Roots and Cube Roots",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "1",
  pages =        "51--57",
  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 =    "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009110;
                 http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Yohe.pdf",
  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,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009137",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  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 =          "http://dx.doi.org/10.1109/T-C.1974.223790;
                 http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:29 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672383;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.doi.org/10.1109/T-C.1974.224055;
                 http://dx.doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:35 MDT 2011",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672648;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35088",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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{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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Baugh:1973:TCP,Kroft:1974:CTC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672455",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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 =          "http://dx.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 =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://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;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",