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email: \path=norbert@iit.com="}†v…ˆcacknhfbNelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 841120090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, email: path beebe@math.utah.edu, path beebe@acm.org, path beebe@computer.org (Internet), URL: path http://www.math.utah.edu/~beebe/@String{acknhfb = "Nelson H. F. Beebe,
University of Utah,
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155 S 1400 E RM 233,
Salt Lake City, UT 841120090, USA,
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FAX: +1 801 581 4148,
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\pathbeebe@acm.org,
\pathbeebe@computer.org (Internet),
URL: \pathhttp://www.math.utah.edu/~beebe/"}ƒq‚W…ackmfcMichael F. Cowlishaw, IBM UK (MP5), PO Box 31, Birmingham Road, Warwick, CV34 5JL, UK, email: path mfc@uk.ibm.com, URL: path http://www2.hursley.ibm.com/decimal@String{ackmfc = "Michael F. Cowlishaw,
IBM UK (MP5),
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National Institute of Standards and Technology,
Building 820, Room 365,
Gaithersburg, MD 20899, USA,
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University of Utah,
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@Proceedings{Morris:1991:RWP,
editor = "Joseph M. Morris and Roger C. Shaw",
booktitle = "4th Refinement Workshop: proceedings of the 4th
Refinement Workshop, 911 January 1991, Cambridge",
title = "4th Refinement Workshop: proceedings of the 4th
Refinement Workshop, 911 January 1991, Cambridge",
publisher = pubSV,
address = pubSV:adr,
pages = "viii + 478",
year = "1991",
ISBN = "3540196579",
ISBN13 = "9783540196570",
LCCN = "????",
bibdate = "Sat Nov 29 09:29:05 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
confdate = "911 Jan. 1991",
conflocation = "Cambridge, UK",
pubcountry = "Germany",
}ôã‡<Žy
@InProceedings{Montuschi:1989:EIH,
author = "Paolo Montuschi and Luigi Cinimera",
title = "On the efficient implementation of higher radix square
root algorithms",
crossref = "Ercegovac:1989:PSC",
pages = "154161",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
acknowledgement = acknhfb,
keywords = "ARITH9",
summary = "Square root nonrestoring algorithms operating with a
radix higher than two (but power of 2) are discussed.
Formulas are derived delimiting the feasibility space
of the class of algorithms considered as a function of
the different parameters. This \ldots{}",
}æ
®…'ŠO
@Book{Hamacher:1984:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
edition = "Second",
pages = "xvi + 590",
year = "1984",
ISBN = "0070256837",
ISBN13 = "9780070256835",
LCCN = "QA76.9.A73 H351 1984",
bibdate = "Sat May 18 14:24:11 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGrawHill series in computer organization and
architecture",
acknowledgement = acknhfb,
}F*†dI
@Article{Pan:1981:BCA,
author = "V. Pan",
title = "The bitcomplexity of arithmetic algorithms",
journal = jJALG,
volume = "2",
number = "2",
pages = "144163",
month = jun,
year = "1981",
CODEN = "JOALDV",
DOI = "http://dx.doi.org/10.1016/01966774(81)90016X",
ISSN = "01966774 (print), 10902678 (electronic)",
ISSNL = "01966774",
bibdate = "Tue Dec 11 09:13:49 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/019667748190016X",
acknowledgement = acknhfb,
fjournal = "Journal of Algorithms",
journalURL = "http://www.sciencedirect.com/science/journal/01966774",
}0)ˆ
@Article{Gurzi:1960:HSM,
author = "Fred Gurzi",
title = "A HighSpeed Multiplication Process for Digital
Computers",
journal = jCACM,
volume = "3",
number = "4",
pages = "241245",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "htšce = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = acknhfb,
authordates = "Johan Vilhelm Nystr{\"o}m (18241885)",
subject = "Weights and measures; Numeration; base16 arithmetic;
hexadecimal arithmetic",
remark = "Thanks for Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicodecompatible fonts to represent the additional
digits needed by the system.",
}
: ƒ:ˆFW ##+u=m;a+iu‡q
unpublishedfparith.bibBabbage:1837:MPCCharles BabbageOn the mathematical powers of the calculating engine161173dec121837Wed Oct 13 11:09:59 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:09:59 ???Manuscript held by Museum of the History of Science, Oxford, UK. Reprinted in cite [ 2.1]Randell:1982:ODC.acknhfbCharles BabbageManuscript held by Museum of the History of Science, Oxford, UK. Reprinted in \cite[\S 2.1]{Randell:1982:ODC}.On the mathematical powers of the calculating engine
@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 = acknhfb,
}ŒzV #+3s?]7=m;y‚7sŽc
articlefparith.bibColson:1726:SANJohn Colson, F.R.S.A Short Account of NegativoAffirmative ArithmetickjPHILOSTRANSRSOCLOND343923981611731726PTRSAVhttp://dx.doi.org/10.1098/rstl.1726.003203702316 OR 03702316Tue Jul 28 14:21:05 2015http://www.math.utah.edu/pub/tex/bib/fparith.bib2015.07.28 14:21:05 ???http://arith22.gforge.inria.fr/slides/s2ercegovac.pdfPhilosophical transactions of the Royal Society of LondonEarly work on signeddigit arithmetic, reported by Milos Ercegovac in a talk at the ARITH'22 conference, Lyon, France, June 2015.acknhfbJohn {Colson, F.R.S.}A Short Account of NegativoAffirmative Arithmetick
@Article{Colson:1726:SAN,
author = "John {Colson, F.R.S.}",
title = "A Short Account of NegativoAffirmative Arithmetick",
journal = jPHILOSTRANSRSOCLOND,
volume = "34",
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bibdate = "Tue Jul 28 14:21:05 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith22.gforge.inria.fr/slides/s2ercegovac.pdf",
acknowledgement = acknhfb,
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conference, Lyon, France, June 2015.",
}
<<“A[ #I‚=7E%;e„O%QI‚•bookfparith.bibNystrom:1862:PNSJohn W. (John William) NystromProject of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the baseJ. B. Lippincott and Co.Philadelphia, PA, USA1061862QC96 .N95Sat Oct 29 10:28:27 MDT 2016http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2016.10.29 10:28:27 MDThttp://unifoundry.com/tonal/; https://catalog.hathitrust.org/Record/011602816; https://lccn.loc.gov/04025433Thanks for Paul Hardy of Unifoundry in San Diego, CA, USA, for information about Nystrom's promotion of hexadecimal arithmetic, and for creating a Web site about Nystrom's tonal system, as well as developing Unicodecompatible fonts to represent the additional digits needed by the system.Weights and measures; Numeration; base16 arithmetic; hexadecimal arithmeticacknhfbJohan Vilhelm Nystrom (18241885)John W. (John William) NystromProject of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the base
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title = "Project of a new system of arithmetic, weight, measure
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acknowledgement = acknhfb,
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remark = "Thanks for Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicodecompatible fonts to represent the additional
digits needed by the system.",
}
» C»X #1c!}57EU;K3]cŽOarticlefparith.bibAnonymous:1879:TRAAnonymousThree Rules for Abbreviating MultiplicationjSCIAMER411218418420sep91879SCAMAChttp://dx.doi.org/10.1038/scientificamerican0920187918400368733 (print), 19467087 (electronic) OR 00368733 (print), 19467087 (electronic)00368733 OR 00368733Fri May 17 10:36:54 MDT 2013http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/sciam1870.bib2013.05.17 10:36:54 MDThttp://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879184.pdfScientific Americanacknhfbhttp://www.nature.com/scientificamericanAnonymousThree Rules for Abbreviating Multiplication
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acknowledgement = acknhfb,
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URL = "http://links.jstor.org/sici?sici=00029327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2K",
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 = acknhfb,
fjournal = "American Journal of Mathematics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
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of numbers is such that all mantissas of their
logarithms are equally probable.''",
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3D"fUŠ,”Y
@Article{AMD:1988:IFP,
author = "{Advanced Micro Devices}",
title = "{IEEE} floatingpoint format",
journal = jMICROPROCMICROSYS,
volume = "12",
number = "1",
pages = "1323",
month = jan # "\slash " # feb,
year = "1988",
CODEN = "MIMID5",
ISSN = "01419331 (print), 18729436 (electronic)",
ISSNL = "01419331",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Co …i9
@Article{Acha:1992:LOF,
author = "J. I. Acha and J. Calvo",
title = "LowfrequencœO¹
@Article{Aamodt:2008:CTI,
author = "Tor M. Aamodt and Paul Chow",
title = "Compiletime and instructionset methods for improving
floating to fixedpoint conversion accuracy",
journal = jTECS,
volume = "7",
number = "3",
pages = "26:126:??",
month = apr,
year = "2008",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1347375.1347379",
ISSN = "15399087 (print), ðŠ=”{
@Article{Abdallah:2005:MRN,
author = "M. Abdallah and A. Skavantzos",
title = "On MultiModuli residue number systems with moduli of
forms $ r^a $, $ r^b  1 $, $ r^c + 1 $",
journal = "IEEE Transactions on Circuits and Systems I: Regular
Papers, [see also IEEE Transactions on Circuits and
Systems I: Fundamental Theory and Applications]",
volume = "52",
number = "7",
pages = "1253AŠ”
@Article{Aberbour:1998:PMF,
author = "M. Aberbour and A. Houelle and H. Mehrez and N.
Vaucher and A. Guyot",
title = "On portable macrocell {FPU} generators for division
and square root operators complying to the full
{IEEE754} standard",
journal = jIEEETRANSVLSISYST,
volume = "6",
number = "1",
pages = "114121",
month = mar,
year = "1998",
CODEN = °ŽI
@Article{Abbott:1999:ASS,
author = "P. H. Abbott and D. G. Brush and C. W. {Clark III} and
C. J. Crone and J. R. Ehrman and G. W. Ewart and C. A.
Goodrich and M. Hack and J. S. Kapernick and B. J.
Minchau and W. C. Shepard and R. M. {Smith, Sr.} and R.
Tallman and S. Walkowiak and A. Watanabe and W. R.
White",
title = "Architecture and software support in {IBM S/390
6ˆW‘/
@Article{Abbasbandy:2004:USA,
author = "S. Abbasbandy and M. A. Fariborzi Araghi",
title = "The use of the stochastic arithmetic to estimate the
value of interpolation polynomial with optimal degree",
journal = jAPPLNUMMATH,
volume = "50",
number = "34",
pages = "279290",
month = sep,
year = "2004",
CODEN = "ANMAEL",
DOI = "http://dx.doi.org/10.1016/j.apnum.2004.01.003"P’]¥;
@Article{Abbott:2012:TFA,
author = "John Abbott",
title = "Twinfloat arithmetic",
journal = jJSYMBOLICCOMP,
volume = "47",
number = "5",
pages = "536551",
month = may,
year = "2012",
CODEN = "JSYCEH",
DOI = "http://dx.doi.org/10.1016/j.jsc.2011.12.005",
ISSN = "07477171 (print), 1095855X (electronic)",
ISSNL = "07477171",
bibdate = "Sat Feb 25 10:12:47 MST 20e‰’'
@Article{Abdelmalek:1971:REA,
author = "Nabih N. Abdelmalek",
title = "Roundoff Error Analysis for {GramSchmidt} Method
and Solution of Linear Least Squares Problems",
journal = jBIT,
volume = "11",
number = "4",
pages = "345367",
month = dec,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01939404",
ISSN = "00063835 (print), 15725
5
"53äõ‡N
@Article{Adam:2012:FPD,
author = "Sanda Adam and Gheorghe Adam",
title = "Floating Point Degree of Precision in Numerical
Quadrature",
journal = jLECTNOTESCOMPSCI,
volume = "7125",
pages = "189194",
year = "2012",
CODEN = "LNCSD9",
DOI = "http://dx.doi.org/10.1007/9783642282126_19",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Wed Dec 19 15:24:39 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/lncs2012b.bib",
URL = "http://link.springer.com/chapter/10.1007/9783642282126_19/",
acknowledgement = acknhfb,
bookDOI = "http://dx.doi.org/10.1007/9783642282126",
bookURL = "http://www.springerlink.com/content/9783642282126",
fjournal = "Lecture Notes in Computer Science",
}£fÇM
@Article{Agarwal:1994:EFP,
author = "R. C. Agarwal and F. G. Gustavson and M. Zubair",
title = "Exploiting functional parallelism of {POWER2} to
design highperformance numerical algorithms",
journal = jIBMJRD,
volume = "38",
number = "5",
pages = "563576",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = "001Å™C³
@Article{Agarwal:1986:NSV,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "New Scalar and Vector Elementary Functions for the
{IBM System\slash 370}",
journal = jIBMJRD,
volume = "30",
number = "2",
pages = "126144",
month = mar,
year = "1986",
CODEN = "IBMe†M
@Article{Adikari:2011:HBT,
author = "Jithra Adikari and Vassil S. Dimitrov and Laurent
Imbert",
title = "Hybrid BinaryTernary Number System for Elliptic Curve
Cryptosystems",
journal = jIEEETRANSCOMPUT,
volume = "60",
number = "2",
pages = "254265",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2010.138",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}–ŒD™
@Article{Adams:1967:SCP,
author = "Duane A. Adams",
title = "A stopping criterion for polynomial root finding",
journal = jCACM,
volume = "10",
number = "10",
pages = "655658",
month = oct,
year = "1967",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "65.50",
MRnumber = "39\#2314",
bibdate = "Fri Nov 25 18:20o…\‹9
@Article{Acha:1992:LOF,
author = "J. I. Acha and J. Calvo",
title = "Lowfrequency oscillator for floatingpoint digital
signal processor chips",
journal = jELECTLETTERS,
volume = "28",
number = "17",
pages = "1582??",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "00135194 (print), 1350911X (electronic)",
ISSNL = "00135194",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Electronics Letters",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
v
÷÷–\ #'#57=m;A„[Ks‚„['•iarticlefparith.bibNewcomb:1881:NFUSimon NewcombNote on the frequency of use of the different digits in natural numbersjAMJMATH41/439401881AJMAAN00029327 (print), 10806377 (electronic) OR 00029327 (print), 10806377 (electronic)00029327 OR 00029327Thu Feb 15 16:35:24 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 16:35:24 ???http://links.jstor.org/sici?sici=00029327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2KThat 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.American Journal of MathematicsBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom p. 40: ``The law of probability of the occurrence of numbers is such that all mantissas of their logarithms are equally probable.''acknhfbThat 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.Simon NewcombNote on the frequency of use of the different digits in natural numbers
@Article{Newcomb:1881:NFU,
author = "Simon Newcomb",
title = "Note on the frequency of use of the different digits
in natural numbers",
journal = jAMJMATH,
volume = "4",
number = "1/4",
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year = "1881",
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URL = "http://links.jstor.org/sici?sici=00029327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2K",
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 = acknhfb,
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
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}
a ªaŒFX #%%7!57EU;M3]%7Ž!articlefparith.bibFelt:1893:MADorr E. FeltMechanical ArithmeticjSCIAMER692030931011nov111893SCAMAChttp://dx.doi.org/10.1038/scientificamerican11111893309b00368733 (print), 19467087 (electronic) OR 00368733 (print), 19467087 (electronic)00368733 OR 00368733Wed May 22 19:04:25 MDT 2013http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/sciam1890.bib2013.05.22 19:04:25 MDThttp://www.nature.com/scientificamerican/journal/v69/n20/pdf/scientificamerican11111893309b.pdfScientific Americanacknhfbhttp://www.nature.com/scientificamericanDorr E. FeltMechanical Arithmetic
@Article{Felt:1893:MA,
author = "Dorr E. Felt",
title = "Mechanical Arithmetic",
journal = jSCIAMER,
volume = "69",
number = "20",
pages = "309310",
day = "11",
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year = "1893",
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month = aug # "\slash " # sep,
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CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:37:08 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
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÷¨÷‰.U #'UE'77=m;_o'g]Šarticlefparith.bibBabbage:1910:BBAH. P. BabbageBabbage: Babbage's analytical enginejMONTHLYNOTROYASTRONSOC70517526, 6451910MNRAA400358711 OR 0035871100358711 OR 00358711Wed Oct 13 11:12:08 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:12:08 ???Reprinted in cite [ 2.3]Randell:1982:ODC.Monthly Notices of the Royal Astronomical SocietyacknhfbH. P. BabbageReprinted in \cite[\S 2.3]{Randell:1982:ODC}.{Babbage}: {Babbage}'s analytical engine
@Article{Babbage:1910:BBA,
author = "H. P. Babbage",
title = "{Babbage}: {Babbage}'s analytical engine",
journal = jMONTHLYNOTROYASTRONSOC,
volume = "70",
number = "??",
pages = "517526, 645",
year = "1910",
CODEN = "MNRAA4",
ISSN = "00358711",
ISSNL = "00358711",
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 = acknhfb,
fjournal = "Monthly Notices of the Royal Astronomical Society",
}ˆUU #'M?7=m;_q'gM‰3articlefparith.bibLudgate:1909:PAMP. E. LudgateOn a proposed analytical machinejSCIPROCROYDUBLINSOC12977911909SPRDAP03712303 OR 03712303Wed Oct 13 11:14:08 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:14:08 ???Reprinted in cite [ 2.4]Randell:1982:ODC.Scientific proceedings of the Royal Dublin SocietyacknhfbP. E. LudgateReprinted in \cite[\S 2.4]{Randell:1982:ODC}.On a proposed analytical machine
@Article{Ludgate:1909:PAM,
author = "P. E. Ludgate",
title = "On a proposed analytical machine",
journal = jSCIPROCROYDUBLINSOC,
volume = "12",
number = "9",
pages = "7791",
year = "1909",
CODEN = "SPRDAP",
ISSN = "03712303",
bibdate = "Wed Oct 13 11:14:08 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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acknowledgement = acknhfb,
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@Article{Aiken:1964:PAC,
author = "H. H. Aiken",
title = "Proposed automatic calculating machine",
journal = jIEEESPECTRUM,
volume = "1",
number = "??",
pages = "6269",
month = aug,
year = "1964",
CODEN = "IEESAM",
ISSN = "00189235 (print), 19399340 (electronic)",
ISSNL = "00189235",
bibdate = "Wed Oct 13 11:16:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/ˆ
@Article{Agrawal:1977:CNB,
author = "D. P. Agrawal",
title = "Comments on {``A Note on Base$2$ Arithmetic
Logic''}",
journal = jIEEETRANSCOMPUT,
volume = "C26",
number = "5",
pages = "511511",
month = may,
year = "1977",
CODEN = "ITCOB4",
DOI = ‡3Žg
@Article{Agrawal:1979:HSA,
author = "D. P. Agrawal",
title = "HighSpeed Arithmetic Arrays",
journal = jIEEETRANSCOMPUT,
volume = "C28",
number = "3",
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month = mar,
year = "1979",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1979.1675322",
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bibdate = "Mon Jul 11 06:49:36 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.‡<Žy
@Article{Agou:2003:SPR,
author = "Simon Joseph Agou and Marc Del{\'e}glise and
JeanLouis Nicolas",
title = "Short Polynomial Representations for Square Roots
Modulo $p$",
journal = jDESIGNSCODESCRYPTOGR,
volume = "28",
number = "1",
pages = "3344",
month = jan,
year = "2003",
CODEN = "DCCREC",
ISSN = "09251022 (print), 15737586 (electronic)",
ISSNL = "09251022",
bibdate = "Thu Dec 11 06:27:20 MST 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
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acknowledgement = acknhfb,
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@Article{Aggarwal:1979:REM,
author = "Vijay B. Aggarwal and James W. Burgmeier",
title = "A roundoff error model with applications to
arithmetic expressions",
journal = jSIAMJCOMPUT,
volume = "8",
number = "1",
pages = "6072",
month = "????",
year = "1979",
CODEN = "SMJCAT",
ISSN = "00975397 (print), 10957111 (electronic)",
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MRclass = "68C01 (65G05)",
MRnumber = "81b:68031",
bibdate = "Mon Nov 29 10:58:59 MST 2010",
bibsource = "http://epubs.siam.org/sambin/dbq/toclist/SICOMP/8/1;
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acknowledgement = acknhfb,
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title = "Negabinary carrylookahead adder and fast
multiplier",
journal = jELECTLETTERS,
volume = "10",
number = "??",
pages = "312313",
month = jul,
year = "1974",
CODEN = "ELLEAK",
ISSN = "00135194 (print), 1350911X (electronic)",
ISSNL = "00135194",
bibdate = "Thu Nov 06 06:16:38 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Electronics Letters",
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@Article{Barrow:1924:QDD,
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title = "Questions and Discussions: Discussions: On Taking
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journal = jAMERMATHMONTHLY,
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number = "10",
pages = "482484",
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CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
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@Article{TorresyQuevedo:1915:EAS,
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of its applications]",
journal = jREVGENSCIPURESAPPL,
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number = "??",
pages = "601611",
day = "15",
month = nov,
year = "1915",
ISSN = "03707431",
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}.
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acknowledgement = acknhfb,
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• ©•†U #/;?9/=m;;?†OÓbookfparith.bibKarpinski:1925:HALouis Charles KarpinskiThe History of ArithmeticRand McNally & CompanyNew York, NY, USAxi + 2001925Fri Nov 28 18:09:05 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:09:05 ???ackmfcLouis Charles KarpinskiThe History of Arithmetic
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bibdate = "Fri Nov 28 18:09:05 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
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@Article{Smith:1924:FPA,
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title = "The First Printed Arithmetic ({Treviso}, 1478)",
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@Article{Agrawal:1984:ACB,
author = "V. K. Agrawal and S. Murugesan",
title = "Algorithm converts {BCD} fractions to binary",
journal = jEDN,
volume = "29",
number = "13",
pages = "278280",
month = jun,
year = "1984",
CODEN = "EDNSBH",
ISSN = "00127515, 03646637",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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acknowledgement = acknj,
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@Article{Agrawal:1983:ICA,
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title = "Introduction: Computer Arithmetic",
journal = jIEEETRANSCOMPUT,
volume = "C32",
number = "4",
pages = "329330",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1983.1676232",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}ž‡wo
@Article{Agrawal:1980:NBA,
author = "D. P. Agrawal",
title = "On NegabinaryBinary Arithmetic Relationships and
Their Hardware Reciprocity",
journal = jIEEETRANSCOMPUT,
volume = "C29",
number = "11",
pages = "10321035",
month = nov,
year = "1980",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1980.1675502",
ISSN = "00189340 (print), 15579956 (electron7‡3Žg
@Article{Agrawal:1979:HSA,
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DOI = "http://dx.doi.org/10.1109/TC.1979.1675322",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Mon Jul 11 06:49:36 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/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675322",
acknowledgement = acknhfb,
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@Article{Agrawal:1977:CNB,
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title = "Comments on {``A Note on Base$2$ Arithmetic
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journal = jIEEETRANSCOMPUT,
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number = "5",
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CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1977.1674869",
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@Article{Smith:1926:FGC,
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÷ ±÷‹7Y ##;357E
;GIŒ9articlefparith.bibJ:1930:RPRbR. A. J.Recent Publications: Reviews: em Standard Table of Square Roots, by L. M. MilneThomsonjAMERMATHMONTHLY376314314jun61930AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:35:55 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:35:55 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlR. A. J.Recent Publications: Reviews: {{\em Standard Table of Square Roots}}, by {L. M. MilneThomson}
@Article{J:1930:RPRb,
author = "R. A. J.",
title = "Recent Publications: Reviews: {{\em Standard Table of
Square Roots}}, by {L. M. MilneThomson}",
journal = jAMERMATHMONTHLY,
volume = "37",
number = "6",
pages = "314314",
month = jun # "\slash " # jul,
year = "1930",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:35:55 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}ŒLW #+)e57Eƒ;Qo)iŽarticlefparith.bibCajori:1927:EAPFlorian CajoriThe Earliest Arithmetic Published in AmericajISIS93391401dec121927ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:57:45 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i214411; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1920.bib2013.07.30 21:57:45 MDThttp://www.jstor.org/stable/330806Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlFlorian CajoriThe Earliest Arithmetic Published in {America}
@Article{Cajori:1927:EAP,
author = "Florian Cajori",
title = "The Earliest Arithmetic Published in {America}",
journal = jISIS,
volume = "9",
number = "3",
pages = "391401",
month = dec,
year = "1927",
CODEN = "ISISA4",
ISSN = "00211753 (print), 15456994 (electronic)",
ISSNL = "00211753",
bibdate = "Tue Jul 30 21:57:45 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i214411;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/330806",
acknowledgement = acknhfb,
fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}
À ‹Y #)+357E
;G)+Œ
articlefparith.bibGarver:1932:QDNbRaymond GarverQuestions, Discussions, and Notes: a Square Root Method and Continued FractionsjAMERMATHMONTHLY399533535nov111932AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:36:47 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:36:47 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlRaymond GarverQuestions, Discussions, and Notes: a Square Root Method and Continued Fractions
@Article{Garver:1932:QDNb,
author = "Raymond Garver",
title = "Questions, Discussions, and Notes: a Square Root
Method and Continued Fractions",
journal = jAMERMATHMONTHLY,
volume = "39",
number = "9",
pages = "533535",
month = nov,
year = "1932",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:36:47 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}Š=W #//e357E
;G/e‹Qarticlefparith.bibLaughlin:1930:LNDHarry H. LaughlinLargeNumber Division by Calculating MachinejAMERMATHMONTHLY376287293jun61930AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:35:55 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:35:55 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlHarry H. LaughlinLargeNumber Division by Calculating Machine
@Article{Laughlin:1930:LND,
author = "Harry H. Laughlin",
title = "LargeNumber Division by Calculating Machine",
journal = jAMERMATHMONTHLY,
volume = "37",
number = "6",
pages = "287293",
month = jun # "\slash " # jul,
year = "1930",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:35:55 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
»Ì
Ms‡H
@Article{Carter:1990:STA,
author = "T. M. Carter and J. E. Robertson",
title = "The set theory of arithmetic decomposition",
journal = jIEEETRANSCOMPUT,
volume = "39",
number = "8",
pages = "9931005",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.57037",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Jul 7 14:20:03 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/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57037",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
} ,ŸU¿+
@Article{Carr:1994:IRM,
author = "S. Carr and K. Kennedy",
title = "Improving the Ratio of Memory Operations in
FloatingPoint Operations in Loops",
journal = jTOPLAS,
volume = "16",
number = "6",
pages = "17681810",
month = nov,
year = "1994",
CODEN = "ATPSDT",
ISSN = "01640925 (print), 15584593 (electronic)",
ISSNL = "01640925",
bibdate = "Sat Feb 24 15:Ü’!
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = jCACM,
volume = "2",
number = "5",
pages = "1015",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}†‡B
@Article{Carter:1990:RSD,
author = "T. M. Carter and J. E. Robertson",
title = "Radix$ 16 $ signeddigit division",
journal = jIEEETRANSCOMPUT,
volume = "39",
number = "12",
pages = "14241433",
month = dec,
year = "1990",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.61063",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Jul 7 14:20:05 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/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61063",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
} +‰,’Y
@Article{Carta:1974:HLR,
author = "David G. Carta",
title = "Help!!: {The} Lost Reference: ({A} Modified {Newton}
Method for Square Roots)",
journal = jSIGNUM,
volume = "9",
number = "4",
pages = "99",
month = oct,
year = "1974",
CODEN = "SNEWD6",
DOI = "http://doi.acm.org/10.1145/1206085.1206086",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL =
¯‹Y #/)!357E
;G)!Œarticlefparith.bibKalbfell:1934:QDND. C. KalbfellQuestions, Discussions and Notes: On a Method for Calculating Square RootsjAMERMATHMONTHLY418504506oct101934AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:37:31 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:37:31 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlD. C. KalbfellQuestions, Discussions and Notes: On a Method for Calculating Square Roots
@Article{Kalbfell:1934:QDN,
author = "D. C. Kalbfell",
title = "Questions, Discussions and Notes: On a Method for
Calculating Square Roots",
journal = jAMERMATHMONTHLY,
volume = "41",
number = "8",
pages = "504506",
month = oct,
year = "1934",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:37:31 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}ŠNY #3'‚'=m;''/‚Š
bookfparith.bibCouffignal:1933:MCLL. CouffignalLes machines a calculer, leurs principes, leur evolution. (French) [Calculating machines, their principles, their evolution]GauthierVillarsParis, France5335351933Wed Oct 13 11:19:11 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:19:11 ???Extracts reprinted in cite [ 3.2]Randell:1982:ODC. Translated by Mr. R. Basu.FrenchacknhfbL. CouffignalExtracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}. Translated by Mr. R. Basu.Les machines {\`a} calculer, leurs principes, leur {\'e}volution. ({French}) [{Calculating} machines, their principles, their evolution]
@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 = "GauthierVillars",
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 = acknhfb,
language = "French",
}
‰
z‰K Ž\ð„v‰m
@Article{Dunham:1991:ABA,
author = "C. Dunham",
title = "Applications of Best Approximation",
journal = jSIGNUM,
volume = "26",
number = "2",
pages = "210",
month = apr,
year = "1991",
CODEN = "SNEWD6",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "ACM SIGNUM Newsletter",
} ×[
@Article{Duprat:1991:WND,
author = "J. Duprat and J.M. Muller",
title = "Writing numbers differently for faster calculation",
journal = jTECHNIQUESCIINFORMATIQUES,
volume = "10",
number = "3",
pages = "211224",
month = "????",
year = "1991",
CODEN = "TTSIDJ‹#–G
@Article{Duprat:1988:HPE,
author = "Jean Duprat and JeanMichel Muller",
title = "Hardwired polynomial evaluation",
journal = jJPARDISTCOMP,
volume = "5",
number = "3",
pages = "291309",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "07437315 (print), 10960848 (electronic)",
ISSNL = "07437315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex¡†A
@Article{Dunham:1992:SFW,
author = "Charles B. Dunham",
title = "{Surveyor's Forum}: ``{What} Every Computer Scientist
Should Know About FloatingPoint Arithmetic''",
journal = jCOMPSURV,
volume = "24",
number = "3",
pages = "319319",
month = sep,
year = "1992",
CODEN = "CMSVAN",
ISSN = "03600300 (print), 15577341 (electronic)",
ISSNL = "03600300",
bibdate = "Sun Sep 25 10:14:37 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Wichmann:1992:SFW}.",
acknowledgement = acknhfb,
fjournal = "ACM Computing Surveys",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
“‡jU
@Article{Dunworth:1969:ECB,
author = "A. Dunworth and J. I. Roche",
title = "The Error Characteristics of the Binary Rate
Multiplier",
journal = jIEEETRANSCOMPUT,
volume = "C18",
number = "8",
pages = "741745",
month = aug,
year = "1969",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1969.222757",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
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 = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}¼…Š
@Article{Dunham:1990:FFE,
author = "C. B. Dunham",
title = "Feasibility of `Perfect' Function Evaluation",
journal = jSIGNUM,
volume = "25",
number = "4",
pages = "2526",
month = oct,
year = "1990",
CODEN = "SNEWD6",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "ACM SIGNUM Newsletter",
} 7mf
S`m‡<Žy
@Article{Agou:2003:SPR,
author = "Simon Joseph Agou and Marc Del{\'e}glise and
JeanLouis Nicolas",
title = "Short Polynomial Representations for Square Roots
¥eËK
@Article{Agarwal:2002:FPN,
author = "R. C. Agarwal and R. F. Enenkel and F. G. Gustavson
and A. Kothari and M. Zubair",
title = "Fast pseudorandomnumber generators with modulus $ 2^k
…ŠA
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = jELECTRóˆ>}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken",
title = "Proposed automatic calculating machine",
journal = jIEEESPECTRUM,
volume = "1",
number = "??",
pages = "6269",
month = aug,
year = "1964",
CODEN = "IEESAM",
ISSN = "00189235 (print), 19399340 (electronic)",
ISSNL = "00189235",
bibdate = "Wed Oct 13 11:16:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/ˆ%
@Article{Aharony:2012:IFP,
author = "Merav Aharony and Emanuel Gofman and Elena Guralnik
and Anatoly Koyfman",
title = "Injecting FloatingPoint Testing Knowledge into Test
Generators",
journal = jLECTNOTESCOMPSCI,
volume = "7261",
pages = "234241",
year = "2012",
CODEN = "LNCSD9",
DOI = "http://dx.doi.org/10.1007/9783642341885_20",
ISSN = "03029743 (printi‡A
@Article{Agrawal:1975:AAN,
author = "D. P. Agrawal",
title = "Arithmetic Algorithms in a Negative Base",
journal = jIEEETRANSCOMPUT,
volume = "C24",
number = "10",
pages = "9981000",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1975.224109",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Tue Jul 12 07:57:57 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/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}¥eËK
@Article{Agarwal:2002:FPN,
author = "R. C. Agarwal and R. F. Enenkel and F. G. Gustavson
and A. Kothari and M. Zubair",
title = "Fast pseudorandomnumber generators with modulus $ 2^k
$ or $ 2^{k  1} $ using fused multiplyadd",
journal = jIBMJRD,
volume = "46",
number = "1",
pages = "97116",
month = jan,
year = "2002",
CODEN = "IBMJAE",
DOI = "http://dx.doi.org/10.1147/rd.461.0097",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = "00188646",
bibdate = "Mon Mar 18 17:27:08 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ä
ˆg‘O
@Article{AbuElHaija:1979:AER,
author = "A. AbuElHaija and A. Peterson",
title = "An approach to eliminate roundoff errors in digital
filters",
journal = jIEEETRANSACOUSTSPEECH,
volume = "27",
number = "2",
pages = "195198",
month = apr,
year = "1979",
CODEN = "IETABA",
ISSN = "00963518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexpçsŒ7`
mŒ1(ˆq‘c
@Article{An:1988:CRE,
author = "S. H. An and K. Yao",
title = "Convergent and roundoff error properties of reflection
coefficients in adaptive spatial recursive least
squares lattice algorithm",
journal = jIEEETRANSCIRCUITSSYST,
volume = "35",
number = "2",
pages = "241246",
month = feb,
year = "1988",
CODEN = "ICSYBT",
ISSN = "00984094 (print), 1558127 ‡7†U+
@Article{Ambikairajah:1980:TPM,
author = "E. Ambikairajah and M. J. Carey",
title =Q…m‹[
@Article{Alsup:1990:MFA,
author = "M. Alsup",
title = "{Motorola}'s 88000 Family Architecture",
journal = jIEEEMICRO,
volume = "10",
number = "3",
pages = "4866",
month = jun,
year = "1990",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/40.56325",
ISSN = "02721732 (print), 19374143 (electronic)",
ISSNL = "02721732",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEEE Micro",
journalURL = "http://www.computer.org/csdl/mags/mi/index.html",
} l…n‹]
@Article{Alt:1988:FEP,
author = "Ren{\'e} Alt",
title = "Floatingpoint error propagation in iterative methods.
Stochastic methods in roundoff error analysis",
journal = jMATHCOMPSIM,
volume = "30",
number = "6",
pages = "505517",
year = "1988",
CODEN = "MCSIDR",
ISSN = "03784754 (print), 18727166 (electronic)",
ISSNL = "03784754",
MRclass = "65G05 (65F10)",
MRnumber = "90f:65067",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Mathematics and Computers in Simulation",
reviewer = "D. Bini",
}çú‡2Že
@Article{Alia:1991:VMM,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} modulo $m$ multiplier",
journal = jIEEETRANSCOMPUT,
volume = "40",
number = "7",
pages = "873878",
month = jul,
year = "1991",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.83626",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Jul 7 12:52:22 MDT ŠK•
@Article{Alia:1984:VAD,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} algorithm for direct and reverse conversion
from weighted binary number system to residue number
system",
journal = jIEEETRANSCIRCUITSSYST,
volume = "31",
number = "12",
pages = "10331039",
month = dec,
year = "1984",
CODEN = "ICSYBT",
DOI = "http://dx.doi.org/10.1109/TC.1984+$‡Ž5
@Article{AlTwaijry:1998:SPB,
author = "H. A. AlTwaijry and S. F. Oberman and S. T. Fu and M.
J. Flynn",
title = "The {SNAP} Project: Building Validated Floating
Point",
journal = jJUCS,
volume = "4",
number = "2",
pages = "99109",
day = "28",
month = feb,
year = "1998",
CODEN = "????",
ISSN = "09486968",
ISSNL = "09486968",
bibdate = "Wed Mar 4 15:32:49 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://medoc.springer.de:8000/jucs/jucs_4_2/the_snap_project_building;
http://www.jucs.org/jucs_4_2/the_snap_project_building/Al_twaijry_H_A.pdf",
acknowledgement = acknhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journalURL = "http://www.jucs.org/jucs",
}
@ ´@ŠqW #'‚c=m;_Og‚wŠ?#miscfparith.bibZuse:1936:VSDK. ZuseVerfahren zur selbsttatigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen. (German) [Procedure for automatic execution of calculations by calculating machines]18722111apr41936Wed Oct 13 11:22:03 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:22:03 ???Reprinted in cite [ 4.1]Randell:1982:ODC.GermanacknhfbGerman patent application Z23624.K. ZuseReprinted in \cite[\S 4.1]{Randell:1982:ODC}.{Verfahren zur selbstt{\"a}tigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen}. ({German}) [{Procedure} for automatic execution of calculations by calculating machines]
@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 = acknhfb,
language = "German",
}‡iU #)117=m;_W)g1ˆA#articlefparith.bibPhillips:1936:BCE. W. PhillipsBinary calculationjJINSTACTUARIES67187221193600202681 OR 00202681Wed Oct 13 11:33:16 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:33:16 ???Reprinted in cite [ 7.1]Randell:1982:ODC.Journal of the Institute of ActuariesacknhfbE. W. PhillipsReprinted in \cite[\S 7.1]{Randell:1982:ODC}.Binary calculation
@Article{Phillips:1936:BC,
author = "E. W. Phillips",
title = "Binary calculation",
journal = jJINSTACTUARIES,
volume = "67",
number = "??",
pages = "187221",
year = "1936",
ISSN = "00202681",
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 = acknhfb,
fjournal = "Journal of the Institute of Actuaries",
}Œ]W #'s57Eƒ;Qo'sŽarticlefparith.bibCalvert:1936:DDSH. R. CalvertDecimal Division of Scales before the Metric SystemjISIS252433436sep91936ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:21:25 MDT 2013http://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.bib2013.07.30 21:21:25 MDThttp://www.jstor.org/stable/225380Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlH. R. CalvertDecimal Division of Scales before the Metric System
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division of Scales before the Metric System",
journal = jISIS,
volume = "25",
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pages = "433436",
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bibdate = "Tue Jul 30 21:21:25 MDT 2013",
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URL = "http://www.jstor.org/stable/225380",
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;G%%Œarticlefparith.bibEscott:1937:QDNE. B. EscottQuestions, Discussions, and Notes: Rapid Method for Extracting a Square RootjAMERMATHMONTHLY4410644646dec121937AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:38:44 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:38:44 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlE. B. EscottQuestions, Discussions, and Notes: Rapid Method for Extracting a Square Root
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = jAMERMATHMONTHLY,
volume = "44",
number = "10",
pages = "644646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}rith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = acknhfb,
authordates = "April 30, 1916February 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 twentyone and published
when he was twentytwo, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 5961 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 6268,
``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.''",
}
::CW '#7s/_1=m;=
=O7=s¡%mastersthesisfparith.bibShannon:1937:SARClaude Elwood ShannonA Symbolic Analysis of Relay and Switching CircuitsMaster of ScienceDepartment of Electrical Engineering, MITCambridge, MA, USA7210aug81937Thu Nov 18 10:35:20 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 10:35:20 ???Not submitted until 1940http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdfSmiley 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 twentyone and published when he was twentytwo, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 5961 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 6268, ``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.''acknhfbApril 30, 1916February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@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 = acknhfb,
authordates = "April 30, 1916February 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 twentyone and published
when he was twentytwo, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 5961 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 6268,
``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.''",
}umbers 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 lawhence 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 multidigit 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 = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573585 (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.",
}
¨
‡UD‡Ž
@Article{Akishita:2001:FSS,
author = "Toru Akishita",
title = "Fast Simultaneous Scalar Multiplication on Elliptic
Curve with {Montgomery} Form",
journal = jLECTNOTESCOMPSCI,
volume = "2259",
pages = "255??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Sat Feb 2 13:07:44 MST 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2259.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/2259/22590255.htm;
http://link.springerny.com/link/service/series/0558/papers/2259/22590255.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}¼ 35
@Article{AlTwaijry:1998:SPB,
author = "H. A. AlTwaijry and S. F. Oberman and S. T. Fu and M.
J. Flynn",
title = "The {SNAP} Project: Building Validated Floating
Point",
journal = jJUCS,
volume = "4",
number = "2",
pages = "99109",
day = "28",
month = feb,
year = "1998",
CODEN = "????",
ISSN ‹q—c
@Article{AlMohy:2012:MAB,
author = "Awad H. AlMohy",
title = "A more accurate {Briggs} method for the logarithm",
journal = jNUMERALGORITHMS,
volume = "59",
number = "??",
pages = "????",
month = "????",
year = "2012",
CODEN = "NUALEG",
DOI = "http://dx.doi.org/10.1007/s110750119496z",
ISSN = "10171398 (print), 15729265 (electronic)",
ISSNL = "10171398",
bibdatkŽ
@Article{AlMouhamed:1995:ELF,
author = "Mayez AlMouhamed and Lubomir Bic",
title = "Effects of Loop Fusion and Statement Migration on the
Speedup of Vector Multiprocessors",
journal = jJPARDISTCOMP,
volume = "31",
number = "1",
pages = "5664",
day = "15",
month = nov,
year = "1995",
CODEN = "JPDCER",
DOI = "http://dx.doi.org/10.1006/jpdc.1995.1144",
ISSN =ÎT
@Article{Alam:1993:RTO,
author = "M. S. Alam and M. A. Karim",
title = ‡O
@Article{AlTwaijry:1998:TSE,
author = "H. A. AlTwaijry and M. J. Flynn",
title = "Technology scaling effects on multipliers",
journal = jIEEETRANSCOMPUT,
volume = "47",
number = "11",
pages = ‡Ž
@Article{Akleylek:2012:MRR,
author = "Sedat Akleylek and Ferruh Ozbudak",
title = "Modified Redundant Representation for Designing
Arithmetic Circuits with Small Complexity",
journal = jIEEETRANSCOMPUT,
volume = "61",
number = "3",
pages = "427432",
month = mar,
year = "2012",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2011.29",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Fri Feb 3 07:35:03 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}ˆK‘
@Article{Akbarpour:2010:VSI,
author = "Behzad Akbarpour and Amr T. AbdelHamid and
Sofi{\`e}ne Tahar and John Harrison",
title = "Verifying a Synthesized Implementation of {IEEE754}
FloatingPoint Exponential Function using {HOL}",
journal = jCOMPJ,
volume = "53",
number = "4",
pages = "465488",
month = may,
year = "2010",
CODEN = "CMPJA6",
DOI = "http://&&e Law of Anomalous Numbers is thus a general probability law of widespread application.Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledgeBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom 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), 573585 (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.acknhfbhttp://www.jstor.org/journal/procamerphilsociIt 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 lawhence 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 multidigit 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.Frank BenfordThe Law of Anomalous Numbers
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = jPROCAMERPHILSOC,
volume = "78",
number = "4",
pages = "551572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003049X (print), 23269243 (electronic)",
ISSNL = "0003049X",
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=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2G",
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 lawhence 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 multidigit 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 = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573585 (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.",
}
qqÓ[ #'E557=m;CŸ]WsŽEgŸe'EÌSarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous NumbersjPROCAMERPHILSOC784551572mar31938PAPCAA0003049X (print), 23269243 (electronic) OR 0003049X (print), 23269243 (electronic)0003049X OR 0003049XThu Feb 15 16:28:28 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 16:28:28 ???http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2GIt 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 lawhence 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 multidigit 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. Th%
Y Y‡9 W#)]!)!=m;]‡I£bookfparith.bibHardy:1938:ITNG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of NumberspubOXFORDpubOXFORD:adrxvi + 4031938QA241 .H28Fri Nov 30 06:49:15 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.30 06:49:15 ???acknhfbG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numbers
@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 = pubOXFORD,
address = pubOXFORD: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 = acknhfb,
}hY #3'ƒ7G'=m;''/ƒ_ phdthesisfparith.bibCouffignal:1938:AMAL. CouffignalSur l'analyse mecanique. Application aux machines a calculer et aux calculs de la mecanique celeste. (French) [On mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]GauthierVillarsFaculte des Sciences de ParisParis, France5515721938Wed Oct 13 11:17:22 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:17:22 ???Extracts reprinted in cite [ 2.7]Randell:1982:ODC. Translated by Mr. R. Basu.FrenchacknhfbL. CouffignalExtracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.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]
@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 = "GauthierVillars",
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 = acknhfb,
language = "French",
} http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = acknhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journalURL = "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.''",
}!
ùù”!Y #/sA7=]; ‡}/s–Uarticlefparith.bibShannon:1938:SARClaude E. ShannonA Symbolic Analysis of Relay and Switching CircuitsjTRANSAMERINSTELECENG57713723dec121938TAEEA500963860 OR 00963860Sat Nov 20 08:54:12 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www2.research.att.com/~njas/doc/shannonbio.html2010.11.20 08:54:12 ???Transactions of the American Institute of Electrical EngineersThis 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.''acknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714Claude E. ShannonA Symbolic Analysis of Relay and Switching Circuits
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
journal = jTRANSAMERINSTELECENG,
volume = "57",
number = "??",
pages = "713723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "00963860",
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 = acknhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journalURL = "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.''",
}
¼ ¼ŠW#X ##
)OE‚#;S]Œarticlefparith.bibK:1939:BRBdM. G. K.Book Review: booktitle Duodecimal Arithmetic, by George S. TerryjJRSTATSOC10222993001939http://dx.doi.org/10.2307/2980013Sat Jan 24 11:18:08 MST 2015http://www.jstor.org/stable/i349540; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrssa1930.bib2015.01.24 11:18:08 MSThttp://www.jstor.org/stable/2980013Journal of the Royal Statistical SocietyacknhfbM. G. K.Book Review: {{\booktitle{Duodecimal Arithmetic}}, by George S. Terry}
@Article{K:1939:BRBd,
author = "M. G. K.",
title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
George S. Terry}",
journal = jJRSTATSOC,
volume = "102",
number = "2",
pages = "299300",
month = "????",
year = "1939",
DOI = "http://dx.doi.org/10.2307/2980013",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrssa1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = acknhfb,
fjournal = "Journal of the Royal Statistical Society",
}g"Y#)Q57Eƒ;QoQarticlefparith.bibJager:1939:AADRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of Robert Jager (London, 1651)jISIS3112531nov111939ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:26:49 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302217; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1930.bib2013.07.30 21:26:49 MDThttp://www.jstor.org/stable/226014Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = jISIS,
volume = "31",
number = "1",
pages = "2531",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "00211753 (print), 15456994 (electronic)",
ISSNL = "00211753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
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/226014",
acknowledgement = acknhfb,
fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}
Ê
Ëß¨¹Ê¦ˆ'
@Article{Galˆ'
@Article{Gallagher:2000:FTN,
author = "W. L. Gallagher and E. E. {Swartzlander, Jr.}",
title = "Faulttolerant {NewtonRaphson} and {Goldschmidt}
dividers using time shared {TMR}",
journal = jIEEETRANSCOMPUT,
volume = "49",
number = "6",
pages = "588595",
month = jun,
year = "2000",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.862218",
ISSN = "0018934^‰A“
@Article{Galbraith:2002:ASC,
author = "S. D. Galbraith and S. M. Paulus and N. P. Smart",
title = "Arithmetic on superelliptic curves",
journal = jMATHCOMPUT,
volume = "71",
number = "237",
pages = "393405",
month = jan,
year = "2002",
CODEN = "MCMPAF",
ISSN = "00255718 (paper), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Thu Jan 31 06:16:28 MST 2002",
bibsou„5ˆk
@Article{Galand:1983:FD,
author = "C. Galand",
title = "Fast Division",
journal = jIBMTDB,
volume = "26",
number = "3B",
pages = "15371539",
month = aug,
year = "1983",
CODEN = "IBMTAA",
ISSN = "00188689",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IBM Technical Disclosure Bulletin",
}Å‡jU
@Article{GalanSimon:2001:MLD,
author = "F. Javier Gal{\'a}nSim{\'o}n and Edgar
Mart{\'\i}nezMoro and Juan G. TenaAyuso",
title = "MajorityLogicDecodable Cyclic ArithmeticModular
{AN}Codes in $1$, $2$, and {$L$} Steps",
journal = jLECTNOTESCOMPSCI,
volume = "2260",
pages = "128??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Sat Feb 2 13:07:45 MST 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2260.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/2260/22600128.htm;
http://link.springerny.com/link/service/series/0558/papers/2260/22600128.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}ô†D
@Article{Galal:2011:EEF,
author = "Sameh Galal and Mark Horowitz",
title = "EnergyEfficient FloatingPoint Unit Design",
journal = jIEEETRANSCOMPUT,
volume = "60",
number = "7",
pages = "913922",
month = jul,
year = "2011",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2010.121",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Wed Jun 29 10:26:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}Ã—'®O
@Article{Gal:1991:AEM,
author = "Shmuel Gal and Boris Bachelis",
title = "An Accurate Elementary Mathematical Library for the
{IEEE} Floating Point Standard",
journal = jTOMS,
volume = "17",
number = "1",
pages = "2645",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "00983500 (print), 15577295 (electronic)",
ISSNL = "00983500",
MRclass = "65D20 (65A
fŠÐVf x'V '#)7#1'=m;‡!7³kmastersthesisfparith.bibBerry:1941:DEDClifford Edward BerryDesign of electrical data recording and reading mechanismM.S. thesisIowa State CollegeAmes, IA, USA321941Thu Nov 18 11:18:18 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 11:18:18 ???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 o/†w&U !#)'9C/=m;_'g‡techreportfparith.bibStibitz:1940:CG. R. StibitzComputerUnpublished memorandumBell Telephone LaboratoriesNew York, NY, USA2993001940Wed Oct 13 11:30:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:30:38 ???Reprinted in cite [ 6.1]Randell:1982:ODC.acknhfbG. R. StibitzReprinted in \cite[\S 6.1]{Randell:1982:ODC}.Computer
@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 = acknhfb,
}‰7%X #%5=m;‚#‚+5ˆ}miscfparith.bibBush:1940:AMV. BushArithmetical Machine2993001940Wed Oct 13 11:37:32 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:37:32 ???Reprinted in cite [ 7.3]Randell:1982:ODC. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.acknhfbVannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 19391940V. BushReprinted in \cite[\S 7.3]{Randell:1982:ODC}. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.Arithmetical Machine
@Misc{Bush:1940:AM,
author = "V. Bush",
title = "Arithmetical Machine",
howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 19391940",
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 = acknhfb,
}ˆs$W !#1+/91'=m;_+g/ˆqtechreportfparith.bibAtanasoff:1940:CMSJ. V. AtanasoffComputing machine for the solution of large systems of linear algebraic equationsUnpublished memorandumIowa State CollegeAmes, IA, USA299300aug81940Wed Oct 13 11:36:11 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:36:11 ???Reprinted in cite [ 7.2]Randell:1982:ODC.acknhfbJ. V. AtanasoffReprinted in \cite[\S 7.2]{Randell:1982:ODC}.Computing machine for the solution of large systems of linear algebraic equations
@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 = acknhfb,
}"19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.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 WisconsinMadison. 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 AtanasoffBerry 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 19671973. 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 AtanasoffBerry 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 oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (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 50bit word.",
}'neofakind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 19301966'', (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 50bit word.acknhfb19181963Clifford Edward BerryDesign of electrical data recording and reading mechanism
@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 = acknhfb,
authordates = "19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.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 WisconsinMadison. 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 AtanasoffBerry 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 19671973. 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 AtanasoffBerry 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 oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (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 50bit word.",
}
¦
*¦k…0Ša
@Article{Weber:1990:EHP,
author = ˆ‡Ž3
@Article{Walter:2001:PBM,
author = "Colin D. Walter",
title = "Precise Bounds for {Montgomery} Modular Multiplication
and Some Potentially Insecure {RSA} Moduli",
journal = jLECTNOTESCOMPSCI,
volume = "2271",
pages = "30??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Tue Sep 10 19:09:06 MDT 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2271.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/2271/22710030.htm;
http://link.springerny.com/link/service/series/0558/papers/2271/22710030.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}hˆ
@Article{Wang:1993:SAC,
author = "ChinLiang Wang and JungLung Lin",
title = "A systolic architecture for computing inverses and
divisions in finite fields {$ \mathrm {GF}(2^m) $}",
journal = jIEEETRANSCOMPUT,
volume = "42",
number = "9",
pages = "11411146",
month = sep,
year = "1993",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.241603",
ISSN = "0018³‡gO
@Article{Wang:1989:ADF,
author = "C. C. Wang",
title = "An algorithm to design finite field multipliers using
a selfdual normal basis",
journal = jIEEETRANSCOMPUT,
volume = "38",
number = "10",
pages = "14571460",
month = oct,
year = "1989",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.35840",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Fri Jul 8 19:00:42 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/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=35840",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
} …"ŠE
@Article{Wang:1978:EPF,
author = "J. Y. Wang",
title = "The Evaluation of Periodic Functions with Large Input
Arguments",
journal = jSIGNUM,
volume = "13",
number = "4",
pages = "79",
month = dec,
year = "1978",
CODEN = "SNEWD6",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "ACM SIGNUM Newsletter",
}3†X1
@Article{Walter:2001:DIH,
author = "Colin D. Walter",
title = "Data Integrity in Hardware for Modular Arithmetic",
journal = jLECTNOTESCOMPSCI,
volume = "1965",
pages = "204??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Sat Feb 2 13:02:57 MST 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t1965.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/1965/19650204.htm;
http://link.springerny.com/link/service/series/0558/papers/1965/19650204.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}g
: W¡:ˆd*X!#/k +m_kg ˆQtechreportfparith.bibRajchman:1942:REPJ. A. Rajchman and G. A. Morton and A. W. VanceReport on Electronic Predictors for AntiAircraft Fire ControlResearch Laboratories, R. C. A. Manufacturing Company, Inc.Camden, NJ, USA112115apr41942http://www.math.utah.edu/pub/tex/bib/fparith.bibReprinted in cite [ 7.4]Randell:1982:ODC.acknhfbJ. A. Rajchman and G. A. Morton and A. W. VanceReprinted in \cite[\S 7.4]{Randell:1982:ODC}.Report on Electronic Predictors for AntiAircraft Fire Control
@TechReport{Rajchman:1942:REP,
author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
title = "Report on Electronic Predictors for AntiAircraft 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 = acknhfb,
}‰3)V !#'K7=m;_'g‰]techreportfparith.bibMauchly:1942:UHSJ. W. MauchlyThe use of high speed vacuum tube devices for calculatingPrivately circulated memorandumMoore School of Electrical Engineering, University of PennsylvaniaPhiladelphia, PA, USA112115aug81942Wed Oct 13 11:52:54 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:52:54 ???Reprinted in cite [ 7.6]Randell:1982:ODC.acknhfbJ. W. MauchlyReprinted in \cite[\S 7.6]{Randell:1982:ODC}.The use of high speed vacuum tube devices for calculating
@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 = acknhfb,
}&(W #1/i/57Eƒ;SkW/iŽ]articlefparith.bibLancaster:1942:MMEOtis E. LancasterMachine Method for the Extraction of Cube RootjJAMSTATASSOC37217112115mar31942JSTNAL01621459 (print), 1537274X (electronic) OR 01621459 (print), 1537274X (electronic)01621459 OR 01621459Wed Jan 25 08:05:24 MST 2012http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314096; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib2012.01.25 08:05:24 MSThttp://www.jstor.org/stable/2279437Journal of the American Statistical Associationacknhfbhttp://www.tandfonline.com/loi/uasa20Otis E. LancasterMachine Method for the Extraction of Cube Root
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = jJAMSTATASSOC,
volume = "37",
number = "217",
pages = "112115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "01621459 (print), 1537274X (electronic)",
ISSNL = "01621459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = acknhfb,
fjournal = "Journal of the American Statistical Association",
journalURL = "http://www.tandfonline.com/loi/uasa20",
}
0
’0”_,Y#/IuQ57=m;
„ysW„yIu”?articlefparith.bibGoudsmit:1944:SFNS. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical TablesjNATURE154392180080123dec121944NATUAShttp://dx.doi.org/10.1038/154800a000280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Sun Sep 18 11:57:19 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:57:19 ???http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdfA 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.NatureBenford's Law; Law of Anomalous Numbers; Zipf's Lawacknhfbhttp://www.nature.com/nature/archive/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.S. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical Tables
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
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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 = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}Šk+Y #//357E
;G/‹marticlefparith.bibCrawford:1943:DNSW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of CosinesjAMERMATHMONTHLY503190191mar31943AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:36:57 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:36:57 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of Cosines
@Article{Crawford:1943:DNS,
author = "W. S. H. Crawford",
title = "Discussions and Notes: Square Roots from a Table of
Cosines",
journal = jAMERMATHMONTHLY,
volume = "50",
number = "3",
pages = "190191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
} "00280836",
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 = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
},
B ŒBŽG.W !#3UA=‚ ;_‚ugY‘utechreportfparith.bibvonNeumann:1945:FDRJohn von NeumannFirst Draft of a Report on the EDVACUniversity of Pennsylvania525330jun61945Mon Jun 06 19:17:03 2005ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.06 19:17:03 ???Reprinted in cite [ 8.2]Randell:1982:ODC.This is the report that got von Neumann's name associated with the serial, storedprogram, general purpose, digital architecture upon which 99.99% of all computers today are based.acknhfbJohn von NeumannReprinted in \cite[\S 8.2]{Randell:1982:ODC}.First Draft of a Report on the {EDVAC}
@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 = acknhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, storedprogram, 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 W670ORD4926. Reprinted in
\cite[pp.~177246]{Stern:1981:EUA},
\cite[pp.~399413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}ŒqY#)GQ57=m;
sWGŽ'articlefparith.bibFurry:1945:DNDW. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant FiguresjNATURE155525313jan11945NATUAShttp://dx.doi.org/10.1038/155052a000280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Sun Sep 18 11:51:37 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:51:37 ???http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdfNatureBenford's Law; Law of Anomalous Numbers; Zipf's Lawacknhfbhttp://www.nature.com/nature/archive/W. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant Figures
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = jNATURE,
volume = "155",
number = "??",
pages = "5253",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "00280836",
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 = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}n \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, storedprogram, 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 W670ORD4926. Reprinted in
\cite[pp.~177246]{Stern:1981:EUA},
\cite[pp.~399413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}.
xix‡n1U #+!917=m;_=!g9ˆ[articlefparith.bibCesareo:1946:RIO. CesareoThe Relay InterpolatorjBELLLABSRECORD234574601946BLRCAB00058564 OR 00058564Wed Oct 13 11:31:47 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:31:47 ???Reprinted in cite [ 6.2]Randell:1982:ODC.Bell Laboratories RecordacknhfbO. CesareoReprinted in \cite[\S 6.2]{Randell:1982:ODC}.The Relay Interpolator
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = jBELLLABSRECORD,
volume = "23",
number = "??",
pages = "457460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "00058564",
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 = acknhfb,
fjournal = "Bell Laboratories Record",
}«0]!#)13;=„q;‚Y•U‚i1®]techreportfparith.bibBurks:1946:PDLArthur W. Burks and Herman H. Goldstine and John von NeumannPreliminary discussion of the logical design of an electronic computing instrumentinstINSTADVSTUDYinstINSTADVSTUDY:adr4228jun61946Wed Oct 13 08:17:48 2004ftp://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.bib2004.10.13 08:17:48 ???Report to the U.S. Army Ordnance Department. Reprinted in cite [pp.~221259]Swartzlander:1976:CDD, cite [ 8.3]Randell:1982:ODC, and cite [pp.~97146]Aspray:1987:PJNDiscusses floatingpoint versus fixedpoint computation, and concludes that floatingpoint 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'  multipl8‰m/V#)Ee%E7=m;_EgiŠAarticlefparith.bibAiken:1946:ASCH. H. Aiken and G. M. HopperThe Automatic Sequence Controlled CalculatorjELECTRENG65384391, 449454, 5225281946ELENAC00959197 OR 00959197Wed Oct 13 11:26:29 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:26:29 ???Reprinted in cite [ 5.2]Randell:1982:ODC.Electrical Engineering (American Institute of Electrical Engineers)acknhfbH. H. Aiken and G. M. HopperReprinted in \cite[\S 5.2]{Randell:1982:ODC}.The {Automatic Sequence Controlled Calculator}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = jELECTRENG,
volume = "65",
number = "??",
pages = "384391, 449454, 522528",
year = "1946",
CODEN = "ELENAC",
ISSN = "00959197",
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 = acknhfb,
fjournal = "Electrical Engineering (American Institute of
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}p://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.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint 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.''",
}0icative 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.''acknhfbArthur W. Burks and Herman H. Goldstine and John von NeumannReport to the U.S. Army Ordnance Department. Reprinted in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S 8.3]{Randell:1982:ODC}, and \cite[pp.~97146]{Aspray:1987:PJN}Preliminary discussion of the logical design of an electronic computing instrument
@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 = instINSTADVSTUDY,
address = instINSTADVSTUDY: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.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint 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.''",
}
!Ã!‹3W#1S}K7E
;_o=SgŒarticlefparith.bibGoldstine:1946:ENIH. H. Goldstine and Adele GoldstineThe Electronic Numerical Integrator and Computer (ENIAC)jMATHTABLESOTHERAIDSCOMPUT21597110jul71946MTTCAS08916837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 7.7]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationacknhfbhttp://www.ams.org/mcom/H. H. Goldstine and Adele GoldstineReprinted in \cite[\S 7.7]{Randell:1982:ODC}.The {Electronic Numerical Integrator and Computer (ENIAC)}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "2",
number = "15",
pages = "97110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "08916837",
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 = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
}Ž:2Y!#+Cƒ;=m;'C/ƒŽ#techreportfparith.bibDreyer:1946:REMH.J. Dreyer and A. WaltherDer Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945. (German) [The Ipm Calculator. The development of mathematical instruments in Germany 19391945]BerichtA3Institut fur Praktische Mathematik, Technische HochschuleDarmstadt, West Germany45746019aug81946Wed Oct 13 11:20:15 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:20:15 ???Reprinted in cite [ 3.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. JonesGermanacknhfbH.J. Dreyer and A. WaltherReprinted in \cite[\S 3.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones{Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945}. ({German}) [{The} {Ipm} Calculator. {The} development of mathematical instruments in {Germany} 19391945]
@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} 19391945]",
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 = acknhfb,
language = "German",
}
ú‡\5U #'917=m;_=g9ˆKarticlefparith.bibJuley:1947:BCJ. JuleyThe Ballistic ComputerjBELLLABSRECORD24591947BLRCAB00058564 OR 00058564Wed Oct 13 11:32:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:32:38 ???Reprinted in cite [ 6.3]Randell:1982:ODC.Bell Laboratories RecordacknhfbJ. JuleyReprinted in \cite[\S 6.3]{Randell:1982:ODC}.The Ballistic Computer
@Article{Juley:1947:BC,
author = "J. Juley",
title = "The Ballistic Computer",
journal = jBELLLABSRECORD,
volume = "24",
number = "??",
pages = "59",
year = "1947",
CODEN = "BLRCAB",
ISSN = "00058564",
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 = acknhfb,
fjournal = "Bell Laboratories Record",
}4Y!#1]3;=m;„;]„Ctechreportfparith.bibGoldstine:1947:PCPHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrumentTechnical report1instINSTADVSTUDYinstINSTADVSTUDY:adr691apr41947Wed Jun 01 17:41:33 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 17:41:33 ???Report prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in cite [80151]Taub:1963:JNCa. Knuth cite [p.~278]Knuth:1997:SA cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.acknhfbHerman H. Goldstine and John von NeumannReport prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in \cite[80151]{Taub:1963:JNCa}. Knuth \cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.Planning and coding of problems for an electronic computing instrument
@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 = instINSTADVSTUDY,
address = instINSTADVSTUDY: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 W36034OKD7481. Reprinted in
\cite[80151]{Taub:1963:JNCa}. Knuth
\cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this
report as the first published treatment of
doubleprecision arithmetic on digital computers.",
acknowledgement = acknhfb,
}
l ³lŒD7W #/)[57Eƒ;Qo)_Ž
articlefparith.bibRicheson:1947:FAPA. W. RichesonThe First Arithmetic Printed in EnglishjISIS37124756may51947ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:27:09 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302230; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1940.bib2013.07.30 21:27:09 MDThttp://www.jstor.org/stable/226161Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlA. W. RichesonThe First Arithmetic Printed in {English}
@Article{Richeson:1947:FAP,
author = "A. W. Richeson",
title = "The First Arithmetic Printed in {English}",
journal = jISIS,
volume = "37",
number = "12",
pages = "4756",
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year = "1947",
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ISSN = "00211753 (print), 15456994 (electronic)",
ISSNL = "00211753",
bibdate = "Tue Jul 30 21:27:09 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302230;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1940.bib",
URL = "http://www.jstor.org/stable/226161",
acknowledgement = acknhfb,
fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}ŒJ6Y '#'Ck=1=m;‚''G‚;o‹?inproceedingsfparith.bibMauchly:1947:PPEJ. W. MauchlyProceedings of a Symposium on Large Scale Digital Calculating Machinery, 710 January 1947Preparation of problems for EDVACtype machinesHarvard University PressCambridge, MA, USA591947Wed Oct 13 11:55:58 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:55:58 ???Reprinted in em Annals of the Computation Laboratory of Harvard University, bf 16, 203207 (1948). Reprinted in cite [ 8.2]Randell:1982:ODC.acknhfbJ. W. Mauchly{Proceedings of a Symposium on Large Scale Digital Calculating Machinery, 710 January 1947}Reprinted in {\em Annals of the Computation Laboratory of Harvard University}, {\bf 16}, 203207 (1948). Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.Preparation of problems for {EDVAC}type machines
@InProceedings{Mauchly:1947:PPE,
author = "J. W. Mauchly",
booktitle = "{Proceedings of a Symposium on Large Scale Digital
Calculating Machinery, 710 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}, 203207 (1948).
Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}
ª™ª®ˆ
†Œ[
@Article{Mandelbaum:1972:ECR,
author = "David Mandelbaum",
title = "Error correction in residue arithmetic",
journal = jIEEETRANSCOMPUT,
volume = "C21",
pages = "538545",
year = "1972",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109ˆ‘y
@Article{Makino:1996:MBF,
author = "H. Makino and H. Suzuki and H. Morinaka and Y. Nakase
and K. Mashiko and T. Sumi",
title = "A {286 MHz} 64b floating point multiplier with
enhanced {CG} operation",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "31",
number = "4",
pages = "504513",
month = apr,
year = "1996",
CODEN = "IJSCBC",
ISSN = "00189200 (print)ê,žY
@Article{Makarenko:1987:VMM,
author = "Darrell Makarenko and Jonathan Schaeffer",
title = "A {VLSI} multiprecision matrix multiplier and
polynomial evaluator",
journal = jJPARDISTCOMP,
volume = "4",
number = "6",
pages = "619628",
month = dec,
year = "1987",
CODEN = "JPDCER",
ISSN = "07437315 (print), 10960848 (electronic)",
ISSNL = "07437315",
bibdate = 5†$ŒI
@Article{Malcolm:1972:ARP,
author = "M. A. Malcolm",
title = "Algorithms To Reveal Properties of FloatingPoint
Arithmetic",
journal = jCACM,
volume = "15",
number = "11",
pages = "949951",
month = nov,
year = "1972",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Gentleman:1974:MAR}.",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}i‹
–
@Article{Malcolm:1971:AFP,
author = "Michael A. Malcolm",
title = "On Accurate FloatingPoint Summation",
journal = jCACM,
volume = "14",
number = "11",
pages = "731736",
month = nov,
year = "1971",
CODEN = "CACMA2",
DOI = "http://dx.doi.org/10.1145/362854.362889",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "65G05 (68XX)",
W†re
@Article{Mandelbaum:1967:CLS,
author = "David Mandelbaum",
title = "A Comparison of Linear Sequential Circuits and
Arithmetic Sequences",
journal = jIEEETRANSELECCOMPUT,
volume = "EC16",
number = "2",
pages = "151157",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "03677508",
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 = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}†~›}
@Article{Mancino:1966:MPF,
author = "O. G. Mancino",
title = "Multiple precision floatingpoint conversion from
decimaltobinary and vice versa",
journal = jCACM,
volume = "9",
number = "5",
pages = "347348",
month = may,
year = "1966",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/355592.365635",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL^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.~479557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
acknowledgement = acknhfb # " and " # ackjg,
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 doubleprecision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~10351038, 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}.",
}8
DD—98Y#3]g!!571!;m;Gg‡m!]Ogš3Oarticlefparith.bibvonNeumann:1947:NIMJohn von Neumann and Herman H. GoldstineNumerical Inverting of Matrices of High OrderjBULLAMS531110211099nov111947BAMOAD00029904 (print), 1936881X (electronic) OR 00029904 (print), 1936881X (electronic)00029904 OR 0002990465.0XMR0024235 (9,471b)E. BodewigThu Nov 8 14:49:36 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:36 ???See cite Goldstine:1951:NIM for Part II. Reprinted in cite [v.~5, pp.~479557]Taub:1961:JNC.Bulletin of the American Mathematical SocietyThis may be the first journal publication about the use of doubleprecision arithmetic on computers, used for the accumulation of inner products and matrix products. On pp.~10351038, 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.0031.31402acknhfbJohn von Neumann and Herman H. GoldstineSee \cite{Goldstine:1951:NIM} for Part II. Reprinted in \cite[v.~5, pp.~479557]{Taub:1961:JNC}.Numerical Inverting of Matrices of High Order
@Article{vonNeumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
title = "Numerical Inverting of Matrices of High Order",
journal = jBULLAMS,
volume = "53",
number = "11",
pages = "10211099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "00029904 (print), 1936881X (electronic)",
ISSNL = "00029904",
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.~479557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
acknowledgement = acknhfb # " and " # ackjg,
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 doubleprecision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~10351038, 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}.",
}
/
arè/†\9
@Article{Balasubramaniam:2007:ECS,
author = "P. Balasubramaniam and E. Karthikeyan",
title = "Elliptic curve scalar multiplication algorithm using
complementary recoding",
journal = jAPPLMATHCOMP,
volume = "190",
number = "1",
pages = "5156",
day = "1",
month = jul,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "00963003 (print), 18735649 (electronic)",
ISSNL = "00963003",
bibdate = "Sat Jul 12 09:03:06 MDT 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = acknhfb,
fjournal = "Applied Mathematics and Computation",
journalURL = "http://www.sciencedirect.com/science/journal/00963003",
}/j›U
@Article{Bakhrakh:1993:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floatingpoint arithmetic
operations",
journal = jPROGCOMPSOFT,
volume = "18",
number = "6",
pages = "255258",
year = "1993",
CODEN = "PCSODA",
ISSN
è†jU
@Article{Bakhrakh:1992:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floatingpoint arithmetic
operations. ({Russian})",
journal = jPROGRAMMIROVANIE,
volume = "6",
pages = "1317",
year = "1992",
CODEN = "PROGD3",
ISSN = "01323474, 03617688",
MRclass = "65G05",
MRnumber = "1 227 941",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation appears in
\cite{Bakhrakh:1993:NIF}.",
acknowledgement = acknhfb,
fjournal = "Programmirovanie",
language = "Russian",
}
…Š
@Article{Baker:1997:LEP,
author = "Louis Baker",
title = "Letter to the {Editor}: {Pentium II} Math Bug",
journal = jDDJ,
volume = "22",
number = "10",
pages = "1010",
month = oct,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044789X",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Comments on the Ariane 5 missile failure mentioned in
\cite{Collins:1997:IPI}.",
acknowledgement = acknhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
¨ À
@Article{Baker:1993:SLR,
author = "Henry G. {Baker, Jr.}",
title = "Safe and leakproof resource management using {Ada83}
limited types",
journal = jSIGADALETTERS,
volume = "13",
number = "5",
pages = "3242",
month = sep # "\slash " # oct,
year = "1993",
CODEN = "AALEE5",
ISSN = "10943641 (print), 15579476 (electronic)",
ISSNL = "10943641",
bibdate = "Sat
ã…Š;
@Article{Baker:1992:LCE,
author = "H. G. Baker",
title = "Less Complex Elementary Functions",
journal = jSIGPLAN,
volume = "27",
number = "11",
pages = "1516",
month = nov,
year = "1992",
CODEN = "SINODQ",
ISSN = "03621340 (print), 15232867 (print), 15581160
(electronic)",
ISSNL = "03621340",
bibdate = "Thu Sep 08 08:11:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "ACM SIGPLAN Notices",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
~
k
»°kˆB;V !#)'S7)1=‚Q;'S‰3techreportfparith.bibTukey:1948:NSRJohn W. TukeyA note on the squareroot iterationSRG Memorandum report10instPRINCETONinstPRINCETON:adr181948Tue May 15 08:00:09 2012http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2012.05.15 08:00:09 ???acknhfbJohn W. TukeyA note on the squareroot iteration
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the squareroot iteration",
type = "SRG Memorandum report",
number = "10",
institution = instPRINCETON,
address = instPRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}ˆ:U #)%?'7=m;_9%g?ˆ articlefparith.bibEckert:1948:ECW. J. EckertElectrons and computationjSCIMONTHLY675315323nov111948SCMOAA00963771 OR 00963771Wed Oct 13 11:27:40 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:27:40 ???Reprinted in cite [ 5.3]Randell:1982:ODC.The Scientific MonthlyacknhfbW. J. EckertReprinted in \cite[\S 5.3]{Randell:1982:ODC}.Electrons and computation
@Article{Eckert:1948:EC,
author = "W. J. Eckert",
title = "Electrons and computation",
journal = jSCIMONTHLY,
volume = "67",
number = "5",
pages = "315323",
month = nov,
year = "1948",
CODEN = "SCMOAA",
ISSN = "00963771",
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 = acknhfb,
fjournal = "The Scientific Monthly",
}ŠB9V #'%uK7E
;_o=%g}‹U
articlefparith.bibAlt:1948:BTLaFranz L. AltA Bell Telephone Laboratories' Computing MachineIjMATHTABLESOTHERAIDSCOMPUT321113jan11948MTTCAS08916837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 6.4]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationacknhfbhttp://www.ams.org/mcom/Franz L. AltReprinted in \cite[\S 6.4]{Randell:1982:ODC}.A {Bell Telephone Laboratories}' Computing Machine{I}
@Article{Alt:1948:BTLa,
author = "Franz L. Alt",
title = "A {Bell Telephone Laboratories}' Computing
Machine{I}",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "3",
number = "21",
pages = "113",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "08916837",
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 = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
} 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/a/turingalanmathison.bib;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.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 = acknhfb,
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.",
}<
™‰y=V#/GE57=m;_WGgEŠIarticlefparith.bibWilliams:1948:EDCF. C. Williams and T. KilburnElectronic digital computersjNATURE162487????1948NATUAS00280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Wed Oct 13 12:00:02 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:02 ???Reprinted in cite [ 8.4]Randell:1982:ODC.Natureacknhfbhttp://www.nature.com/nature/archive/F. C. Williams and T. KilburnReprinted in \cite[\S 8.4]{Randell:1982:ODC}.Electronic digital computers
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = jNATURE,
volume = "162",
number = "487",
pages = "????",
year = "1948",
CODEN = "NATUAS",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "00280836",
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 = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
}’dW #S{=m;SˆIarticlefparith.bibHartree:1949:NSRDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical IntegrationJournal of Research of the National Bureau of Standards4262??1949Wed Feb 14 19:07:37 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:07:37 ???acknhfbDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical Integration
@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 = acknhfb,
}
Çö ‰SCW '#+'7;Q'=m;_';g?‰Uinproceedingsfparith.bibWorsley:1950:EDB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949The EDSAC demonstrationUniversity Mathematical LaboratoryCambridge, UK1216jan11950Wed Oct 13 11:39:09 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:39:09 ???Reprinted in cite [ 8.6]Randell:1982:ODC.acknhfbB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, {2225 June 1949}Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.The {EDSAC} demonstration
@InProceedings{Worsley:1950:ED,
author = "B. H. Worsley",
booktitle = "Report of a Conference on High Speed Automatic
Calculating Machines, {2225 June 1949}",
title = "The {EDSAC} demonstration",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "1216",
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 = acknhfb,
}‰NBW'#'C7Q'=m;_C;g#‰Oinproceedingsfparith.bibWilkes:1950:EM. V. Wilkes and W. RenwickReport of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949The EDSACUniversity Mathematical LaboratoryCambridge, UK911jan11950Wed Oct 13 12:00:41 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:41 ???Reprinted in cite [ 8.5]Randell:1982:ODC.acknhfbM. V. Wilkes and W. Renwick{Report of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949}Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.The {EDSAC}
@InProceedings{Wilkes:1950:E,
author = "M. V. Wilkes and W. Renwick",
booktitle = "{Report of a Conference on High Speed Automatic
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title = "The {EDSAC}",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "911",
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 = acknhfb,
}Œ6AW #1E+3!E%;„I5EŽÐbookfparith.bibStifler:1950:HSCW. W. Stifler, Jr.Highspeed computing devicespubMCGRAWHILLpubMCGRAWHILL:adrxiii + 4511950QA75 .E5Fri Aug 20 10:18:44 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:18:44 MDTSupervised 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 N6ONR240, Task 1. Cited in cite Sterbenz:1974:FPC.computersacknhfbW. W. {Stifler, Jr.}Highspeed computing devices
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "Highspeed computing devices",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "xiii + 451",
year = "1950",
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bibdate = "Fri Aug 20 10:18:44 MDT 2010",
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acknowledgement = acknhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
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report to the Office of Naval Research, prepared under
a provision of contract N6ONR240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
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articlefparith.bibGill:1951:PSSS. GillA process for the stepbystep integration of differential equations in an automatic digital computing machinejPROCCAMBRIDGEPHILSOC47961081951PCPSA400081981 OR 00081981Tue Aug 28 05:54:12 2001http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.08.28 05:54:12 ???Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciencesaccurate floatingpoint summation; floatingpoint arithmetic; rounding errorsHigham 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 RungeKutta code in a program library for the EDSAC computer.''acknhfbS. GillA process for the stepbystep integration of differential equations in an automatic digital computing machine
@Article{Gill:1951:PSS,
author = "S. Gill",
title = "A process for the stepbystep integration of
differential equations in an automatic digital
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journal = jPROCCAMBRIDGEPHILSOC,
volume = "47",
pages = "96108",
year = "1951",
CODEN = "PCPSA4",
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EDSAC computer.''",
}†(EU %#)#K5=m;g#O†Wincollectionfparith.bibBrown:1951:HRRG. W. BrownHistory of RAND's random digitsHouseholder:1951:MCM31321951Sun Sep 18 12:02:43 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:02:43 ???http://www.rand.org/pubs/papers/2008/P113.pdfacknhfbG. W. BrownHistory of {RAND}'s random digits
@InCollection{Brown:1951:HRR,
author = "G. W. Brown",
title = "History of {RAND}'s random digits",
crossref = "Householder:1951:MCM",
pages = "3132",
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 = acknhfb,
}ˆGDU #)#]C77;m;y#]‰{articlefparith.bibBooth:1951:SBMA. D. BoothA signed binary multiplication techniquejQUARTJMECHAPPLIEDMATH422362401951QJMMAV00335614 OR 0033561400335614 OR 00335614Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied MathematicsacksfoA. D. BoothA signed binary multiplication technique
@Article{Booth:1951:SBM,
author = "A. D. Booth",
title = "A signed binary multiplication technique",
journal = jQUARTJMECHAPPLIEDMATH,
volume = "4",
number = "2",
pages = "236240",
month = "????",
year = "1951",
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acknowledgement = acksfo # " and " # acknhfb,
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@Article{White:1994:PNG,
author = "S. W. White and S. Dhawan",
title = "{POWER2}: {Next} generation of the {RISC System\slash
6000} family",
journal = jIBMJRD,
volume = "38",
number = "5",
pages = "493502",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = †A
@Article{Wichmann:1992:SFW,
author = "Brian A. Wichmann",
title = "{Surveyor's Forum}: ``{What} Every Computer Scientist
Should Know About FloatingPoint Arithmetic''",
journal = jCOMPSURV,
volume = "24",
number = "3",
pages = "319319",
month = sep,
year = "1992",
CODEN = "CMSVAN",
ISSN = "03600300 (print), 15577341 (electronic)",
ISSNL = "03600300",
bibdate = "Sun Sep 25 10:14:37 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Dunham:1992:SFW}.",
acknowledgement = acknhfb,
fjournal = "ACM Computing Surveys",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}ŽE
@Article{Wichmann:1992:NUF,
author = "Brian A. Wichmann",
title = "A Note on the Use of Floating Point in Critical
Systems",
journal = jCOMPJ,
volume = "35",
number = "1",
pages = "4144",
month = feb,
year = "1992",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource
ÃR›%
@Article{Wichmann:1989:TFS,
author = "B. A. Wichmann",
title = "Towards a formal specification of floating point",
journal = jCOMPJ,
volume = "32",
number = "5",
pages = "432436",
month = oct,
year = "1989",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
MRclass = "65G99 (65Y10)",
MRnumber = "91b:65055",
bibdate = "Wed+“t§i
@Article{Wichmann:1989:SPI,
author = "B. A. Wichmann",
title = "Scientific processing in {ISOPascal}: a proposal to
get the benefits of mixed precision floatingpoint",
journal = jSIGPLAN,
volume = "24",
number = "6",
pages = "2022",
month = jun,
year = "1989",
CODEN = "SINODQ",
ISSN = "03621340 (print), 15232867 (print), 15581160
(electronic)",
ISSNL(‰s“g
@Article{Wichmann:1979:PCG,
author = "B. A. Wichmann and J. {Du Croz}",
title = "A program to calculate the {GAMM} measure",
journal = jCOMPJ,
volume = "22",
number = "4",
pages = "317322",
month = nov,
year = "1979",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compende2†.Œ]
@Article{Wichmann:1979:ID,
author = "B. A. Wichmann",
title = "Integer division",
journal = jSPE,
volume = "9",
number = "6",
pages = "507508",
month = jun,
year = "1979",
CODEN = "SPEXBL",
DOI = "http://dx.doi.org/10.1002/spe.4380090610",
ISSN = "00380644 (print), 1097024X (electronic)",
ISSNL = "00380644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = acknhfb,
fjournal = "Software  Practice and Experience",
journalURL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097024X",
onlinedate = "27 Oct 2006",
}yúÿ)
æòÿžµ‡qc
@Article{Anonymous:1982:ARBf,
author = "Anonymous",
title = "Article Review: {{\booktitle{Ada model arithmetic:
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Proc.E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
pp 7580}",
journal = jMICROPROCMICROSYS,
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number = "9",
pages = "497498",
month = nov,
year = "1982",
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@Article{Anonymous:1879:TRA,
author = "Anonymous",
title = "Three Rules for Abbreviating Multiplication",
journal = jSCIAMER,
volume = "41",
number = "12",
pages = "184184",
day = "20",
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year = "1879",
CODEN = "SCAMAC",
DOI = "http://dx.doi.org/10.1038/scientificamerican09201879184",
ISSN = "00368733 (print), 19467087 (electronic)",
ISSNL = "00368733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879184.pdf",
acknowledgement = acknhfb,
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@Article{Anonymous:1992:FPa,
author = "Anonymous",
title = "Floating Point",
journal = jCOMPUTAIDEDENG,
volume = "11",
number = "8",
pages = "58??",
month = aug,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "07333536",
ISSNL = "07333536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "OpenGL: The NeWs of 3D Graphics?",
acknowledgement = acknhfb,
fjournal = "Computeraided engineering: CAE",
}
wì„J‰
@Article{Anonymous:1996:IBT,
author = "Anonymous",
title = "Inquiry Board Traces {Ariane 5} Failure to Overflow
Error",
journal = jSIAMNEWS,
volume = "29",
number = "8",
pages = "1, 12, 13",
month = oct,
year = "1996",
ISSN = "00361437",
bibdate = "Sat Apr 28 18:48:53 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.si†!ŒC
@Article{Andrews:1982:MMS,
author = "M. Andrews",
title = "Mathematical Microprocessor Software: a $ \sqrt (x) $
Comparison",
journal = jIEEEMICRO,
volume = "2",
number = "3",
pages = "6379",
month = may,
year = "1982",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1982.290970",
ISSN = "02721732 (print), 19374143 (electronic)",
ISSNL = "02721732",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEEE Micro",
journalURL = "http://www.computer.org/csdl/mags/mi/index.html",
}T(ˆq‘c
@Article{An:1988:CRE,
author = "S. H. An and K. Yao",
title = "Convergent and roundoff error properties of reflection
coefficients in adaptive spatial recursive least
squares lattice algorithm",
journal = jIEEETRANSCIRCUITSSYST,
volume = "35",
number = "2",
pages = "241246",
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CODEN = "ICSYBT",
ISSN = "00984094 (print), 1558127 ‡b/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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[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 RungeKutta code in a program library for the
EDSAC computer.''",
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ÄÄŽ9GX#1]o1573%;m;Qym]YsŽ}articlefparith.bibGoldstine:1951:NIMHerman H. Goldstine and John von NeumannNumerical Inverting of Matrices of High Order. IIjPROCAMMATHSOC21882021951PAMYAR00029939 (print), 10886826 (electronic) OR 00029939 (print), 10886826 (electronic)00029939 OR 0002993965.0XMR0041539 (12,861b)F. J. MurrayThu Nov 8 14:49:46 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:46 ???See cite vonNeumann:1947:NIM for Part I. Reprinted in cite [Paper~15, pp.~558572]Taub:1963:JNCa.http://www.jstor.org/view/00029939/di970628/97p0185x/0Proceedings of the American Mathematical Society043.12301acknhfbHerman H. Goldstine and John von NeumannSee \cite{vonNeumann:1947:NIM} for Part I. Reprinted in \cite[Paper~15, pp.~558572]{Taub:1963:JNCa}.Numerical Inverting of Matrices of High Order. {II}
@Article{Goldstine:1951:NIM,
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title = "Numerical Inverting of Matrices of High Order. {II}",
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volume = "2",
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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.~558572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
acknowledgement = acknhfb,
fjournal = "Proceedings of the American Mathematical Society",
}arith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (15601621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = acknhfb,
fjournal = "American Journal of Physics",
journalURL = "http://scitation.aip.org/content/aapt/journal/ajp",
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title = "Seminumerical Algorithms",
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@Book{Knuth:1981:SA,
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@Book{Knuth:1969:SA,
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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@Book{Klatte:1993:CXC,
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Michael Rauch and Andreas Wiethoff",
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computing",
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@Book{Klatte:1992:PXP,
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Dietmar Ratz and Christian Ullrich",
title = "{PASCALXSC}: language reference with examples",
publisher = pubSV,
address = pubSV:adr,
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@Book{Klatte:1991:PXP,
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bibdate = "Thu Nov 8 14:50:35 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation of \cite{Klatte:1991:PSB}.",
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acknowledgement = acknhfb,
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ÐÐ”HY #+MS57m…{Co…{+Q“Yarticlefparith.bibShirley:1951:BNBJohn W. ShirleyBinary Numeration before LeibnizjAMERJPHYSICS1984524541951AJPIAShttp://dx.doi.org/10.1119/1.193304200029505 (print), 19432909 (electronic) OR 00029505 (print), 19432909 (electronic)00029505 OR 00029505http://www.math.utah.edu/pub/tex/bib/fparith.bibhttp://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042Though it is frequently stated that binary numeration was first formally proposed by Leibniz as an illustration of his dualistic philosophy, the mathematical papers of Thomas Hariot (15601621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.American Journal of Physicsacknhfbhttp://scitation.aip.org/content/aapt/journal/ajpThough it is frequently stated that binary numeration was first formally proposed by Leibniz as an illustration of his dualistic philosophy, the mathematical papers of Thomas Hariot (15601621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.John W. ShirleyBinary Numeration before {Leibniz}
@Article{Shirley:1951:BNB,
author = "John W. Shirley",
title = "Binary Numeration before {Leibniz}",
journal = jAMERJPHYSICS,
volume = "19",
number = "8",
pages = "452454",
year = "1951",
CODEN = "AJPIAS",
DOI = "http://dx.doi.org/10.1119/1.1933042",
ISSN = "00029505 (print), 19432909 (electronic)",
ISSNL = "00029505",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (15601621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = acknhfb,
fjournal = "American Journal of Physics",
journalURL = "http://scitation.aip.org/content/aapt/journal/ajp",
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pages = "101105",
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 = acknhfb,
bookpages = "vi + 114",
keywords = "Bell Laboratories Model 15 relay computers; complex
fixedpoint decimal arithmetic; complex floatingpoint
decimal arithmetic",
}I
ˆfJU#)]Y/77=m;e]Y‰earticlefparith.bibDavis:1952:ARSK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken DigitsjJACOUSTSOCAM246637642nov111952JASMAN00014966 OR 0001496600014966 OR 00014966Fri Nov 28 16:38:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 16:38:51 ???Journal of the Acoustical Society of AmericaackmfcK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken Digits
@Article{Davis:1952:ARS,
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ISSN = "00014966",
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bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
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#_=m;‚'ƒ+inproceedingsfparith.bibAndrews:1952:RBLE. G. AndrewsJ. C. McPhersonProceedings of the AIEEIRE '51: Papers and discussions presented at the December 1012, 1951, joint AIEEIRE computer conference, Philadelphia, PA: Review of electronic digital computersA review of the Bell Laboratories' digital computer developmentspubACMpubACM:adr1011051952http://dx.doi.org/10.1145/1434770.1434787Fri Dec 03 09:17:58 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.12.03 09:17:58 ???Bell Laboratories Model 15 relay computers; complex fixedpoint decimal arithmetic; complex floatingpoint decimal arithmeticacknhfbvi + 114E. G. AndrewsProceedings of the AIEEIRE '51: Papers and discussions presented at the December 1012, 1951, joint AIEEIRE computer conference, Philadelphia, PA: Review of electronic digital computersJ. C. McPhersonA review of the {Bell Laboratories}' digital computer developments
@InProceedings{Andrews:1952:RBL,
author = "E. G. Andrews",
editor = "J. C. McPherson",
booktitle = "Proceedings of the AIEEIRE '51: Papers and
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@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "2",
pages = "181185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.263963",
ISSN = "03677508",
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 = acknhfb,
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}:†hQ
@Article{Metze:1962:CBD,
author = "Gernot Metze",
title = "A Class of Binary Divisions Yielding Minimally
Represented Quotients",
journal = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "6",
pages = "761764",
month = dec,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219460",
ISSN = "03679950",
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 = acknhfb,
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}Ý‰1’c
@Article{Metropolis:1980:SIN,
author = "N. Metropolis",
title = "Summation of imprecise numbers",
journal = jCOMPMATHAPPL,
volume = "6",
number = "3",
pages = "297299",
year = "1980",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/08981221(80)900371",
ISSN = "08981221 (print), 18737668 (electronic)",
ISSNL = "08981221",
MRclass = "65U05",
MRnumber = "MR6040k‹–
@Article{Metropolis:1977:SAP,
author = "N. Metropolis and Stephen M. Tanny",
title = "Significance arithmetic: the probability of carrying",
journal = jCOMPMATHAPPL,
volume = "3",
number = "1",
pages = "7781",
year = "1977",
CODEN = "CMAPDK",
ISSN = "08869561",
ISSNL = "08981221",
MRclass = "65G05 (10A30 65C10)",
MRnumber = "MR0458846 (56 \#17046)",
MRreviewer = "Artenio?‹–1
@Article{Metropolis:1973:SAC,
author = "N. Metropolis and GianCarlo Rota and S. Tanny",
title = "Significance arithmetic: the carrying algorithm",
journal = jJCOMBTHEORYA,
volume = "14",
pages = "386421",
month = may,
year = "1973",
CODEN = "JCBTA7",
ISSN = "00973165",
ISSNL = "00973165",
MRclass = "10A30 (02E10)",
MRnumber = "MR0321857 (48 \#222)",
MRreviewer = "R. LæŽfM
@Article{Metropolis:1973:ABC,
author = "Nicholas C. Metropolis",
title = "Analyzed Binary Computing",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "6",
pages = "573576",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009109",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Wed Mä
*
g¦*ŠyMW'#AQga/=m;_AYgkŠIinproceedingsfparith.bibSheldon:1952:ICPJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint AIEEIRE Computer Confer ence. 1012 December 1951The IBM cardprogrammed electronic calculatorAmerican Institute of Electrical EngineersNew York, NY, USA30361952Wed Oct 13 11:28:45 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:28:45 ???Reprinted in cite [ 5.4]Randell:1982:ODC.acknhfbJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint {AIEEIRE} Computer Confer ence. {1012 December 1951}Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.The {IBM} cardprogrammed electronic calculator
@InProceedings{Sheldon:1952:ICP,
author = "J. W. Sheldon and L. Tatum",
booktitle = "Review of Electronic Digital Computers. Joint
{AIEEIRE} Computer Confer ence. {1012 December
1951}",
title = "The {IBM} cardprogrammed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "3036",
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 = acknhfb,
}‰>LW#EQQ=a;EQŠearticlefparith.bibMorrill:1952:SEMC. D. Morrill and R. V. BaumA Stabilized Electronic MultiplierjTRANSIREPROFGROUPELECCOMPUTEC15259dec121952Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic ComputersacknhfbC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplier
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC1",
number = "??",
pages = "5259",
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;
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@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = jINCSTAT,
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number = "1",
pages = "3540",
month = feb,
year = "1952",
CODEN = "????",
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bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
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acknowledgement = acknhfb,
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:â:™%OY #+%I57=m;'‰1e‰%M—Marticlefparith.bibBackus:1954:ISSJ. W. BackusThe IBM 701 Speedcoding SystemjJACM1146jan11954JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4backus.pdfThe IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a threeaddress 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 builtin checking.Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401The IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a threeaddress 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 builtin checking.J. W. BackusThe {IBM 701 Speedcoding} System
@Article{Backus:1954:ISS,
author = "J. W. Backus",
title = "The {IBM 701 Speedcoding} System",
journal = jJACM,
volume = "1",
number = "1",
pages = "46",
month = jan,
year = "1954",
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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/p4backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
threeaddress 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
builtin checking.",
acknowledgement = acknhfb,
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}†NW #%+#=m;/†7bookfparith.bibIBM:1953:POTIBM CorporationPrinciples of Operation: Type 701 and Associated EquipmentpubIBMpubIBM:adr1031953Wed Sep 14 23:17:49 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.14 23:17:49 ???acknhfb{IBM Corporation}Principles of Operation: Type 701 and Associated Equipment
@Book{IBM:1953:POT,
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title = "Principles of Operation: Type 701 and Associated
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publisher = pubIBM,
address = pubIBM:adr,
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
threeaddress 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
builtin checking.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}Ond 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.",
}P
W²WŒXQX#?WQ=a;‚[?[ŽEarticlefparith.bibFreeman:1954:TSAH. Freeman and E. ParsonsTimeSharing Analog Multiplier (TSAM)jTRANSIREPROFGROUPELECCOMPUTEC311117mar31954Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic ComputersCited 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.acknhfbH. Freeman and E. ParsonsTimeSharing Analog Multiplier ({TSAM})
@Article{Freeman:1954:TSA,
author = "H. Freeman and E. Parsons",
title = "TimeSharing Analog Multiplier ({TSAM})",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC3",
number = "1",
pages = "1117",
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 = acknhfb,
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.",
}ŽKPV #/Q1%/Em;3†WU1
manualfparith.bibBurroughs:1954:DHBurroughs Corporation. ElectroDataDatatron handbooksThe DivisionPasadena, CA, USA461954Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MST12 volumes in 1.Datatron (Computer)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.acknhfb{Burroughs Corporation. ElectroData}12 volumes in 1.Datatron handbooks
@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 = acknhfb,
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.",
}
ÑGÑ‰;TV#)g[;7=a;]g[Š'articlefparith.bibMayer:1954:ODFM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback dividerjIRETRANSELECCOMPUTEC311720mar31954IRELAO03679950 OR 03679950Sun Jul 17 09:52:58 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:52:58 ???IRE Transactions on Electronic ComputersacknhfbM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback divider
@Article{Mayer:1954:ODF,
author = "M. A. Mayer and B. M. Gordon and R. N. Nicola",
title = "An operational digital feedback divider",
journal = jIRETRANSELECCOMPUT,
volume = "EC3",
number = "1",
pages = "1720",
month = mar,
year = "1954",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Sun Jul 17 09:52:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‰5SW#+AQQ=a;AQŠ]articlefparith.bibKovach:1954:AMUL. D. Kovach and W. ComleyAn Analog Multiplier Using ThyritejTRANSIREPROFGROUPELECCOMPUTEC324245jun61954Sun Jul 17 09:57:13 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:57:13 ???Transactions of the I.R.E. Professional Group on Electronic ComputersacknhfbL. D. Kovach and W. ComleyAn Analog Multiplier Using Thyrite
@Article{Kovach:1954:AMU,
author = "L. D. Kovach and W. Comley",
title = "An Analog Multiplier Using Thyrite",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC3",
number = "2",
pages = "4245",
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 = acknhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
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}‰6RX #'y5E
;yŠ9
articlefparith.bibGorn:1954:AACSaul GornThe Automatic Analysis and Control of Computing ErrorsjJSIAM226981jun61954JSIMAV03684245 (print), 1095712X (electronic) OR 03684245 (print), 1095712X (electronic)Thu Oct 15 18:16:06 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.15 18:16:06 MDTJournal of the Society for Industrial and Applied MathematicsacknhfbSaul GornThe Automatic Analysis and Control of Computing Errors
@Article{Gorn:1954:AAC,
author = "Saul Gorn",
title = "The Automatic Analysis and Control of Computing
Errors",
journal = jJSIAM,
volume = "2",
number = "2",
pages = "6981",
month = jun,
year = "1954",
CODEN = "JSIMAV",
ISSN = "03684245 (print), 1095712X (electronic)",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
}
L2
CLT%'šO
@Article{Subramaniam:1993:PPP,
‡5Žk
@Article{Strzebonski:1999:RPD,
author = "A. Strzebonski",
title = "A Real Polynomial Decision Algorithm Using
ArbitraryPrecision Floating Point Arithmetic",
journal = jRELIABLECOMPUTING,
volume = "5",
number = "3",
pages = "337346",
year = "1999",
CODEN = "RCOMF8",
ISSN = "13853139 (print), 15731340 (electronic)",
ISSNL = "13853139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
acknowledgement = acknhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journalURL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}!†O
@Article{Stummel:1986:SOP,
author = "F. Stummel",
title = "Strict optimal a posteriori error and residual bounds
for {Gaussian} elimination in floatingpoint
arithmetic",
journal = jCOMPUTING,
volume = "37",
number = "2",
pages = "103124",
year = "1986",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
MRclass = "65F05 (65G05)",
MRnumber = "88b:65047",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journalURL = "http://link.springer.com/journal/607",
reviewer = "Alfonso Laratta",
}[Œi™S
@Article{Stummel:1985:FEA,
author = "Friedrich Stummel",
title = "Forward error analysis of {Gaussian} elimination. {I}.
Error and residual estimates",
journal = jNUMMATH,
volume = "46",
number = "3",
pages = "365395",
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
ISSNL = "0029599X",
MRclass = "65G05 (65F10)",
MRnumber = H‹–;
@Article{Stroud:1963:MPF,
author = "A. H. Stroud and D. Secrest",
title = "A multipleprecision floatingpoint interpretive
program for the {Control Data} 1604",
journal = jCOMPJ,
volume = "6",
number = "1",
pages = "6266",
month = apr,
year = "1963",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Fri Se‡L
@Article{Strader:1982:CBS,
author = "N. R. Strader and V. T. Rhyne",
title = "A Canonical BitSequential Multiplier",
journal = jIEEETRANSCOMPUT,
volume = "C31",
number = "8",
pages = "791795",
month = aug,
year = "1982",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1982.1676085",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Sun Jul 10 10:33:14 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/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
®
È,®Š{WX#+wM#E%;M!wMŒ bookfparith.bibEckert:1955:FFSW. J. (Wallace John) Eckert and Rebecca Bradley JonesFaster, faster; a simple description of a giant electronic calculator and the problems it solvespubIBMpubIBM:adr1601955QA76 .E25Fri Aug 20 08:57:56 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 08:57:56 MDTCited in cite Sterbenz:1974:FPC.Computersacknhfb19021971W. J. (Wallace John) Eckert and Rebecca Bradley JonesFaster, faster; a simple description of a giant electronic calculator and the problems it solves
@Book{Eckert:1955:FFS,
author = "W. J. (Wallace John) Eckert and Rebecca Bradley
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title = "Faster, faster; a simple description of a giant
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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 = acknhfb,
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Computers",
xxaddress = pubMCGRAWHILL:adr,
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}‰VV#/IM%57=m;IMIM‰{articlefparith.bibCrockett:1955:GMMJ. B. Crockett and H. ChernoffGradient Methods of MaximizationjPACJMATH533501955PJMAAI00308730 (print), 19455844 (electronic) OR 00308730 (print), 19455844 (electronic)00308730 OR 00308730Fri Aug 20 08:54:24 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 08:54:24 ???Pacific Journal of MathematicsCited in cite Sterbenz:1974:FPC.acknhfbJ. B. Crockett and H. ChernoffGradient Methods of Maximization
@Article{Crockett:1955:GMM,
author = "J. B. Crockett and H. Chernoff",
title = "Gradient Methods of Maximization",
journal = jPACJMATH,
volume = "5",
number = "??",
pages = "3350",
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CODEN = "PJMAAI",
ISSN = "00308730 (print), 19455844 (electronic)",
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bibdate = "Fri Aug 20 08:54:24 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Pacific Journal of Mathematics",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}Š5UX #%57=m;1Oe%‹=articlefparith.bibMoshman:1954:GPRJack MoshmanThe Generation of PseudoRandom Numbers on a Decimal CalculatorjJACM128891apr41954JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???Journal of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Jack MoshmanThe Generation of PseudoRandom Numbers on a Decimal Calculator
@Article{Moshman:1954:GPR,
author = "Jack Moshman",
title = "The Generation of PseudoRandom Numbers on a Decimal
Calculator",
journal = jJACM,
volume = "1",
number = "2",
pages = "8891",
month = apr,
year = "1954",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
}
n¾×nŠfZX #1W57=m;1e1W‹articlefparith.bibParsons:1955:SDCFrances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic OperationsjJACM23205207jul71955JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Wed Nov 09 01:00:34 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.09 01:00:34 ???Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Frances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic Operations
@Article{Parsons:1955:SDC,
author = "Frances L. Parsons",
title = "A Simple DeskCalculator Method for Checking Binary
Results of Digital Computer Arithmetic Operations",
journal = jJACM,
volume = "2",
number = "3",
pages = "205207",
month = jul,
year = "1955",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Wed Nov 09 01:00:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}‡dYV #/)=)7;K;9)=‰articlefparith.bibLenaerts:1955:ASRE. H. LenaertsAutomatic Square RootingjELECTRONENG27287289jul71955ELEGAP00134902 OR 00134902Thu Sep 1 10:15:41 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:41 ???Electronic EngineeringacknjE. H. LenaertsAutomatic Square Rooting
@Article{Lenaerts:1955:ASR,
author = "E. H. Lenaerts",
title = "Automatic Square Rooting",
journal = jELECTRONENG,
volume = "27",
number = "??",
pages = "287289",
month = jul,
year = "1955",
CODEN = "ELEGAP",
ISSN = "00134902",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Electronic Engineering",
}ˆ?XX#/U'/!=K;Uˆ_Ñbookfparith.bibHastings:1955:ADCCecil B. Hastings, Jr. and Jeanne T. Hayward and James P. Wong, Jr.Approximations for Digital ComputerspubPRINCETONpubPRINCETON:adrviii + 2011955QA76 .H33Mon Sep 30 14:51:50 1996ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.09.30 14:51:50 ???acknjCecil B. {Hastings, Jr.} and Jeanne T. Hayward and James P. {Wong, Jr.}Approximations for Digital Computers
@Book{Hastings:1955:ADC,
author = "Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and
James P. {Wong, Jr.}",
title = "Approximations for Digital Computers",
publisher = pubPRINCETON,
address = pubPRINCETON:adr,
pages = "viii + 201",
year = "1955",
LCCN = "QA76 .H33",
bibdate = "Mon Sep 30 14:51:50 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
}
Û"D¹Ê
3Û‰ ’A
@Article{Gibson:1988:GBA,
author = "J. K. Gibson",
title = "A generalisation of {Brickell}'s algorithm for fast
modular multiplication",
journal = jBIT,
volume = "28",
number = "4",
pages = "755763",
month = dec,
year = "1988",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01954895",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = ·Ž@
@Article{Ghosh:2012:FPR,
author = "Aniruddha Ghosh and Satrughna Singha and Amitabha
Sinha",
title = "{``Floating point RNS''}: a new concept for designing
the {MAC} unit of digital signal processor",
journal = jCOMPARCHNEWS,
volume = "40",
number = "2",
pages = "3943",
month = may,
year = "2012",
CODEN = "CANED2",
DOI = "http://dx.doi.org/10.1145/2234336’‡ Ž
@Article{Ghazi:2010:WHU,
author = "Kaveh R. Ghazi and Vincent Lefevre and Philippe
Theveny and Paul Zimmermann",
title = "Why and How to Use Arbitrary Precision",
journal = jCOMPUTSCIENG,
volume = "12",
number = "3",
pages = "5",
month = may # "\slash " # jun,
year = "2010",
CODEN = "CSENFA",
DOI = "http://dx.doi.org/10.1109/MCSE.2010.73",
ISSN = "07407475 (print), 15581918 (electronic)",
ISSNL = "15219615",
bibdate = "Thu May 13 11:08:14 2010",
bibsource = "http://www.computer.org/portal/web/csdl/magazines/cise;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Computing in Science and Engineering",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}]ˆ#
@Article{Geyer:2004:DFD,
author = "Christina Lynn Geyer and Patricia Pepple Williamson",
title = "Detecting fraud in data sets using {Benford's Law}",
journal = jCOMMUNSTATSIMULCOMPUT,
volume = "B33",
number = "1",
pages = "229246",
month = "????",
year = "2004",
CODEN = "CSSCDB",
DOI = "http://dx.doi.org/10.1081/SAC120028442",
ISSN = "03610918",
ISSNL = "03610918",±‡y
@Article{Gibson:1975:SCT,
author = "J. A. Gibson and R. W. Gibbard",
title = "Synthesis and Comparison of Two's Complement Parallel
Multipliers",
journal = jIEEETRANSCOMPUT,
volume = "C24",
number = "10",
pages = "10201027",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1975.224117",
ISSN = "00189340 (print), 15579956 (elep–_?
@Article{Gerwig:2004:IEZ,
author = "G. Gerwig and H. Wetter and E. M. Schwarz and J. Haess
and C. A. Krygowski and B. M. Fleischer and M.
Kroener",
title = "The {IBM eServer z990} floatingpoint unit",
journal = jIBMJRD,
volume = "48",
number = "3/4",
pages = "311322",
month = "????",
year = "2004",
CODEN = "IBMJAE",
DOI = "http://dx.doi.org/10.1147/rd.483ŒJ™
@Article{Gerrity:1982:CRR,
author = "G. W. Gerrity",
title = "Computer Representation of Real Numbers",
journal = jIEEETRANSCOMPUT,
volume = "C31",
number = "8",
pages = "709714",
month = aug,
year = "1982",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1982.1676076",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "SunK
ò¬Æò‹Q]W #+gc;a7Ea;]gcŒcarticlefparith.bibEstrin:1956:NHSG. Estrin and B. Gilchrist and J. H. PomereneA Note on HighSpeed Digital MultiplicationjIRETRANSELECCOMPUTEC53140140sep91956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.521993603679950 OR 03679950Thu Jun 30 15:46:27 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:27 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936IRE Transactions on Electronic ComputersacknhfbG. Estrin and B. Gilchrist and J. H. PomereneA Note on HighSpeed Digital Multiplication
@Article{Estrin:1956:NHS,
author = "G. Estrin and B. Gilchrist and J. H. Pomerene",
title = "A Note on HighSpeed Digital Multiplication",
journal = jIRETRANSELECCOMPUT,
volume = "EC5",
number = "3",
pages = "140140",
month = sep,
year = "1956",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1956.5219936",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‹c\Y #1+;i7Ea;]+ articlefparith.bibRobertson:1955:TCMJ. E. RobertsonTwo's Complement Multiplication in Binary Parallel Digital ComputersjIRETRANSELECCOMPUTEC43118119sep91955IRELAOhttp://dx.doi.org/10.1109/IRETELC.1955.540791103679950 OR 03679950Thu Jun 30 15:10:39 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:10:39 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911IRE Transactions on Electronic ComputersacknhfbJ. E. RobertsonTwo's Complement Multiplication in Binary Parallel Digital Computers
@Article{Robertson:1955:TCM,
author = "J. E. Robertson",
title = "Two's Complement Multiplication in Binary Parallel
Digital Computers",
journal = jIRETRANSELECCOMPUT,
volume = "EC4",
number = "3",
pages = "118119",
month = sep,
year = "1955",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/IRETELC.1955.5407911",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}†Q[U #/;a+/'=m;;a†}‘bookfparith.bibRichards:1955:AODRichard Kohler RichardsArithmetic Operations in Digital ComputersD. Van NostrandNew York, NY, USAiv + 3971955QA75 .R5 1955Fri Nov 28 18:46:37 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:46:37 ???acknhfbRichard Kohler RichardsArithmetic Operations in Digital Computers
@Book{Richards:1955:AOD,
author = "Richard Kohler Richards",
title = "Arithmetic Operations in Digital Computers",
publisher = "D. Van Nostrand",
address = "New York, NY, USA",
pages = "iv + 397",
year = "1955",
LCCN = "QA75 .R5 1955",
bibdate = "Fri Nov 28 18:46:37 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}
Ñ" ˜ž¯ÑÀ‰’9
@Article{He:2001:UAA,
author = "Yun He and Chris H. Q. Ding",
title = "Using Accurate Arithmetics to Improve Numerical
Reproducibility and Stability in Parallel
Applications",
journal = jJSUPERCOMPUTING,
volume = "18",
number = "3",
pages = "259277",
month = mar,
year = "2001",
CODEN = "JOSUED",
DOI = "http://dx.doi.org/10.1023/A:1008153532043",
ISSN = 4ˆK‘
@Article{Head:1980:MM,
author = "A. K. Head",
title = "Multiplication modulo $n$",
journal = jBIT,
volume = "20",
number = "1",
pages = "115116",
month = mar,
year = "1980",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01933594",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
MRclass = "6804 (65G10)",
MRnumber = "81g[‹n—]
@Article{Hayes:2001:TB,
author = "Brian Hayes",
title = "Third Base",
journal = jAMSCI,
volume = "89",
number = "6",
pages = "490495",
month = nov # "\slash " # dec,
year = "2001",
CODEN = "AMSCAC",
ISSN = "00030996 (print), 15452786 (electronic)",
ISSNL = "00030996",
bibdate = "Tue Nov 08 08:06:17 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib"2…x‹q
@Article{Haviland:1980:CAP,
author = "G. L. Haviland and A. A. Tuszynski",
title = "A {CORDIC} Arithmetic Processor Chip",
journal = jIEEETRANSCOMPUT,
volume = "C29",
number = "2",
pages = "6879",
month = feb,
year = "1980",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1980.1675529",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Sep 08 00:47:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
} …Š
@Article{Havender:1980:DBN,
author = "J. W. Havender",
title = "Decimaltobinary Number Conversion",
journal = jIBMTDB,
volume = "23",
number = "3",
pages = "11261127",
month = aug,
year = "1980",
CODEN = "IBMTAA",
ISSN = "00188689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floatingpoint arithmetic",
}Ÿˆv‘m
@Article{Havender:1980:DBF,
author = "J. W. Havender",
title = "Decimaltobinary floating point number conversion
mechanism",
journal = jIBMTDB,
volume = "23",
number = "2",
pages = "706708",
month = jul,
year = "1980",
CODEN = "IBMTAA",
ISSN = "00188689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
X›@·
@Article{Hauser:1996:HFE,
author = "John R. Hauser",
title = "Handling floatingpoint exceptions in numeric
programs",
journal = jTOPLAS,
volume = "18",
number = "2",
pages = "139174",
month = mar,
year = "1996",
CODEN = "ATPSDT",
ISSN = "01640925 (print), 15584593 (electronic)",
ISSNL = "01640925",
bibdate = "Tue Aug 13 11:46:35 MDT 1996",
bibsource = º
ÓÃÓ¢`X #)?57=m;Ž1OqeŽ)Gžgarticlefparith.bibPerkins:1956:EPCRobert PerkinsEASIAC, A PseudoComputerjJACM326572apr41956JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 23:46:26 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 23:46:26 ???One of the primary functions of the MIDAC installation at the University of Michigan is the instru^ŠJ_W #//A;a7Ea;]/AŒ articlefparith.bibLilamand:1956:TDMM. Lejet LilamandA TimeDivision MultiplierjIRETRANSELECCOMPUTEC512634mar31956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.521978903679950 OR 03679950Thu Jun 30 15:46:18 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:18 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789IRE Transactions on Electronic ComputersacknhfbM. Lejet LilamandA TimeDivision Multiplier
@Article{Lilamand:1956:TDM,
author = "M. Lejet Lilamand",
title = "A TimeDivision Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC5",
number = "1",
pages = "2634",
month = mar,
year = "1956",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1956.5219789",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‰m^W #3AQ+3E%;u1AQŠ}bookfparith.bibHildebrand:1956:INAFrancis Begnaud HildebrandIntroduction to numerical analysispubMCGRAWHILLpubMCGRAWHILL:adr5111956QA300 .H5Fri Aug 20 09:19:58 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 09:19:58 MDTInternational series in pure and applied mathematicsSee also second edition cite Hildebrand:1974:INA,Hildebrand:1987:INA.Numerical analysisacknhfbFrancis Begnaud HildebrandIntroduction to numerical analysis
@Book{Hildebrand:1956:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL: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 = acknhfb,
remark = "See also second edition
\cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
subject = "Numerical analysis",
}ib",
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 manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}`ction 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 manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Journal of the ACMdecimal floatingpoint arithmeticEarly example of a decimal floatingpoint machine.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401One 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 manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Robert Perkins{EASIAC}, {A} PseudoComputer
@Article{Perkins:1956:EPC,
author = "Robert Perkins",
title = "{EASIAC}, {A} PseudoComputer",
journal = jJACM,
volume = "3",
number = "2",
pages = "6572",
month = apr,
year = "1956",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
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 manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}
F`FŒcY#+k;a7Ea;]k%articlefparith.bibSydnor:1956:AMSR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid ModulatorjIRETRANSELECCOMPUTEC528285jun61956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.521980403679950 OR 03679950Thu Jun 30 15:46:21 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:21 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804IRE Transactions on Electronic ComputersacknhfbR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulator
@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 = jIRETRANSELECCOMPUT,
volume = "EC5",
number = "2",
pages = "8285",
month = jun,
year = "1956",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1956.5219804",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‡8bV#)W;=m;MW;‡{
articlefparith.bibStegun:1956:PCIrene A. Stegun and Milton AbramowitzPitfalls in computationJournal of the Society for Industrial and Applied Mathematics42072191956Tue Aug 28 06:16:28 2001http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.08.28 06:16:28 ???Cited in cite Sterbenz:1974:FPC.acknhfbIrene A. Stegun and Milton AbramowitzPitfalls in computation
@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 = "207219",
year = "1956",
bibdate = "Tue Aug 28 06:16:28 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}‡baU #1+[;7=m;]+[ˆ_ articlefparith.bibRobertson:1956:NCDJ. E. RobertsonA new class of digital division methodsjIRETRANSELECCOMPUTEC56573jun61956IRELAO03679950 OR 03679950Fri Nov 09 19:14:45 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 19:14:45 ???IRE Transactions on Electronic ComputersacknhfbJ. E. RobertsonA new class of digital division methods
@Article{Robertson:1956:NCD,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = jIRETRANSELECCOMPUT,
volume = "EC5",
number = "??",
pages = "6573",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Fri Nov 09 19:14:45 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}æù,æ
9FÌÙ
B‹z—u
@Article{Bauer:1977:CFP,
author = "Henry R. Bauer",
title = "Comments on {``On the Floating Point Representation of
Complex Numbers''}",
journal = jIEEETRANSCOMPUT,
volume = "C26",
number = "2",
pages = "191191",
month = feb,
year = "1977",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1977.5009301",
ISSN = "00189340 (print), 15579956 (electronic)",
0ˆ*U
@Article{Berger:2011:FSM,
author = "Arno Berger and Theodore P. Hill and Bahar Kaynar and
Ad Ridder",
title = "Finitestate {Markov} Chains Obey {Benford's Law}",
journal = jSIAMJMATANAAPPL,
volume = "32",
number = "3",
pages = "665684",
month = "????",
year = "2011",
CODEN = "SJMAEL",
DOI = "http://dx.doi.org/10.1137/100789890",
ISSN = "08954798 (print), 109ÍÔ†ti
@Article{Bemer:1963:NRT,
author = "R. W. Bemer",
title = "A Note on Range Transformations for Square Root and
Logarithm",
journal = jCACM,
volume = "6",
number = "6",
pages = "306307",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\log(x)$; $\sqrt(x)$; elementary functions",
}å
VŠf•M
@Article{Beckmann:1993:FFTb,
author = "P. E. Beckmann and B. R. Musicus",
title = "Fast faulttolerant digital convolution using a
polynomial residue number system",
journal = jIEEETRANSSIGPROC,
volume = "41",
number = "7",
pages = "23002313",
month = jul,
year = "1993",
CODEN = "ITPRED",
DOI = "http://dx.doi.org/10.1109/78.224241",
ISSN = "1053587X (print), 1
ïøz›u
@Article{Bayoumi:1986:LBV,
author = "Magdy A. Bayoumi",
title = "Lower bounds for {VLSI} implementation of residue
number system architectures",
journal = jINTEGRATIONVLSIJ,
volume = "4",
number = "3",
pages = "263269",
month = sep,
year = "1986",
CODEN = "IVJODL",
DOI = "http://dx.doi.org/10.1016/01679260(86)900040",
ISSN = "01679260",
ISSNL = "0167i™‡N
@Article{Bashagha:2001:NRS,
author = "A. E. Bashagha",
title = "Novel radix$2$ $k$ square root module",
journal = "Circuits, Devices and Systems, IEE Proceedings [see
also IEE Proceedings G Circuits, Devices and
Systems]",
volume = "148",
number = "4",
pages = "190196",
month = aug,
year = "2001",
CODEN = "????",
ISSN = "????",
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 = acknhfb,
summary = "The conventional two's complement radix$2$ k square
root algorithm requires a set of 2 k full precision
comparisons to generate all the 2 k possible values of
the partial remainder. The correct remainder is the
minimum \ldots{}",
}Ì
Z³ZŒVeX#+IO57=m;M1SeIQSarticlefparith.bibErcoli:1957:EDOPaolo Ercoli and Roberto VaccaErrors Due to Overflow in Arithmetic Operations Particularly as Regards FINAC Electronic ComputerjJACM44450455oct101957JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Thu Dec 08 09:28:48 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.12.08 09:28:48 ???See letter cite Ercoli:1960:LEE.Journal of the ACMfloatingpoint arithmetic; overflowacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Paolo Ercoli and Roberto VaccaSee letter \cite{Ercoli:1960:LEE}.Errors Due to Overflow in Arithmetic Operations Particularly as Regards {FINAC} Electronic Computer
@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 = jJACM,
volume = "4",
number = "4",
pages = "450455",
month = oct,
year = "1957",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
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 = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "floatingpoint arithmetic; overflow",
}ˆJdU#3Gw;7=m;]Gw‰; articlefparith.bibWeinberger:1956:OMAA. Weinberger and J. L. SmithA OneMicrosecond Adder Using OneMegacycle CircuitryjIRETRANSELECCOMPUTEC56573jun61956IRELAO03679950 OR 03679950Fri Nov 09 19:38:57 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 19:38:57 ???IRE Transactions on Electronic ComputersacknhfbA. Weinberger and J. L. SmithA OneMicrosecond Adder Using OneMegacycle Circuitry
@Article{Weinberger:1956:OMA,
author = "A. Weinberger and J. L. Smith",
title = "A OneMicrosecond Adder Using OneMegacycle
Circuitry",
journal = jIRETRANSELECCOMPUT,
volume = "EC5",
number = "??",
pages = "6573",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Fri Nov 09 19:38:57 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
J
ˆJŠ;gX #+%‚=m;s%‚Šwarticlefparith.bibHerzel:1957:SDDAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. (Italian) [On the frequency of initial digits of statistical numbers]Atti dell XV e XVII Riunione, Societa Italiana di Statistica????1957Sun Sep 18 12:00:07 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:00:07 ???Benford's Law; Law of Anomalous Numbers; Zipf's LawItalianacknhfbAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]
@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 = acknhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}ŠufW #'%‚C=m;cs%c‚‹%articlefparith.bibGini:1957:SFDCorrado GiniSulla frequenza delle cifre iniziali dei numeri osservati. (Italian) [On the frequency of initial digits of observed numbers]Bull. Inst. Internat. Stat.3557761957Sun Sep 18 11:54:25 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:54:25 ???29th session, 2nd delivery, Rio de Janerio.Benford's Law; Law of Anomalous Numbers; Zipf's LawItalianacknhfbCorrado Gini29th session, 2nd delivery, Rio de Janerio.Sulla frequenza delle cifre iniziali dei numeri osservati. (Italian) [{On} the frequency of initial digits of observed numbers]
@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 = "5776",
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 = acknhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
ðŠ]iW #//K;a7Ea;]/KŒarticlefparith.bibKalbfell:1957:EAMDavid C. KalbfellAn Electronic Analog MultiplierjIRETRANSELECCOMPUTEC62100103jun61957IRELAOhttp://dx.doi.org/10.1109/TEC.1957.522157903679950 OR 03679950Thu Jun 30 16:07:27 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:27 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579IRE Transactions on Electronic ComputersacknhfbDavid C. KalbfellAn Electronic Analog Multiplier
@Article{Kalbfell:1957:EAM,
author = "David C. Kalbfell",
title = "An Electronic Analog Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC6",
number = "2",
pages = "100103",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1957.5221579",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Œ
hY#'E%;a7Ea;]E%articlefparith.bibHowe:1957:TRAR. M. Howe and E. G. GilbertTrigonometric Resolution in Analog Computers by Means of Multiplier ElementsjIRETRANSELECCOMPUTEC628692jun61957IRELAOhttp://dx.doi.org/10.1109/TEC.1957.522157603679950 OR 03679950Thu Jun 30 16:07:27 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:27 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576IRE Transactions on Electronic ComputersacknhfbR. M. Howe and E. G. GilbertTrigonometric Resolution in Analog Computers by Means of Multiplier Elements
@Article{Howe:1957:TRA,
author = "R. M. Howe and E. G. Gilbert",
title = "Trigonometric Resolution in Analog Computers by Means
of Multiplier Elements",
journal = jIRETRANSELECCOMPUT,
volume = "EC6",
number = "2",
pages = "8692",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1957.5221576",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
¹¨"¹
3‡xq
@Article{Namin:2008:NFF,
author = "A. H. Namin and Huapeng Wu and M. Ahmadi",
title = "A New FiniteField Multiplier Using Redundant
Representation",
journal = jIEEETRANSCOMPUT,
volume = "57",
number = "5",
pages = "716720",
month = may,
year = "2008",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2007.70834",
ISSN = "00189340 (print), 15579956 (electr2†^=
@Article{Nakano:1992:FPB,
author = "H. Nakano and M. Nakajima and Y. Nakakura and T.
Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
Kishida and H. Kadota",
title = "An 80{FLOPS} (Peak) 64b Microprocessor for Parallel
Computer",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "27",
number = "3",
pages = "365372",
month = mar,
year = "1992",
CODEN = "IJSCBC",
ISSN = "00189200 (print), 1558173X (electronic)",
ISSNL = "00189200",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEEE Journal of SolidState Circuits",
}
Ö†)ŒS
@Article{Nandi:1967:STD,
author = "Salil K. Nandi and E. V. Krishnamurthy",
title = "A simple technique for digital division",
journal = jCACM,
volume = "10",
number = "5",
pages = "299301",
month = may,
year = "1967",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}‘P£!
@Article{Nance:1975:IFR,
author = "Richard E. Nance and Claude {Overstreet, Jr.}",
title = "Implementation of {Fortran} Random Number Generators
on Computers with One's Complement Arithmetic",
journal = jJSTATCOMPUTSIMUL,
volume = "4",
number = "3",
pages = "235243",
month = "????",
year = "1975",
CODEN = "JSCSAJ",
DOI = "http://dx.doi.org/10.1080/00949657508810126",
I«Š”5
@Article{Nakayama:1989:MFPb,
author = "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
and H. Igarashi and T. Toba and Y. Yamagami and Y.
Yano",
title = "A 6.7{MFLOPS} FloatingPoint Coprocessor with
Vector\slash Matrix Instructions",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "24",
number = "5",
pages = "13241330",
month = oct,
year = "1989",
ô–¬;
@Article{Nakayama:1989:FCV,
author = "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
and H. Igarashi and T. Toba and Y. Yamagami and Y.
Yano",
title = "A 6.7{MFLOPS} floatingpoint coprocessor with
vector\slash matrix instructions",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "24",
number = "5",
pages = "13241330",
month = oct,
year = "1989",
C
ð
º
ºŠGkW #+O;a7Ea;]OŒarticlefparith.bibLehman:1957:HSDM. LehmanHighSpeed Digital MultiplicationjIRETRANSELECCOMPUTEC63204205sep91957IRELAOhttp://dx.doi.org/10.1109/TEC.1957.522202503679950 OR 03679950Thu Jun 30 16:07:34 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:34 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025IRE Transactions on Electronic ComputersacknhfbM. LehmanHighSpeed Digital Multiplication
@Article{Lehman:1957:HSD,
author = "M. Lehman",
title = "HighSpeed Digital Multiplication",
journal = jIRETRANSELECCOMPUT,
volume = "EC6",
number = "3",
pages = "204205",
month = sep,
year = "1957",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1957.5222025",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‹yjZ #71/57=K;[13Œcarticlefparith.bibKogbetliantz:1957:CENE. G. KogbetliantzComputation of $ e^n $ for $  infty < n < + infty $ Using an Electronic ComputerjIBMJRD12110115apr41957IBMJAE00188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Tue Sep 06 18:04:49 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.06 18:04:49 ???IBM Journal of Research and Developmentacknjhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520E. G. KogbetliantzComputation of $ e^n $ for $  \infty < n < + \infty $ Using an Electronic Computer
@Article{Kogbetliantz:1957:CEN,
author = "E. G. Kogbetliantz",
title = "Computation of $ e^n $ for $  \infty < n < + \infty $
Using an Electronic Computer",
journal = jIBMJRD,
volume = "1",
number = "2",
pages = "110115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = "00188646",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IBM Journal of Research and Development",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
{0{‹2mX !#)Cs+=m;‚cCŒ+techreportfparith.bibMetze:1957:SPOG. MetzeA Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow StorageReport81Digital Computer Laboratory, University of IllinoisUrbana, IL, USA771957Thu Nov 18 09:07:07 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:07:07 ???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.acknhfbG. MetzeA Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow Storage
@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 = acknhfb,
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.",
}‰MlV #'!mK7;K;o=!y‹articlefparith.bibLuke:1957:CLZY. L. LukeOn the Computation of $ log Z $ and $ arctan Z $jMATHTABLESOTHERAIDSCOMPUT1116181957MTTCAS08916837 OR 08916837Thu Sep 1 10:16:09 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:16:09 ???Mathematical Tables and Other Aids to Computationacknjhttp://www.ams.org/mcom/Y. L. LukeOn the Computation of $ \log {Z} $ and $ \arctan {Z} $
@Article{Luke:1957:CLZ,
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http://www.research.ibm.com/journal/",
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steps and imply the feasibility of constructing less
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acknowledgement = acknhfb,
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articlefparith.bibMurphy:1957:PIAR. W. MurphyA PositiveInteger Arithmetic for Data ProcessingjIBMJRD12158170apr41957IBMJAEhttp://dx.doi.org/10.1147/rd.12.015800188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 0018864668.0X18,939dTue Sep 11 15:35:33 MDT 2012http://ieeexplore.ieee.org/servlet/opac?punumber=5288520; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; http://www.research.ibm.com/journal/2012.09.11 15:35:33 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735; http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdfIt is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield nonnegative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex dataprocessing machines.IBM Journal of Research and Developmentacknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520C. C. GotliebIt is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield nonnegative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex dataprocessing machines.R. W. MurphyA PositiveInteger Arithmetic for Data Processing
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abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
nonnegative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex dataprocessing machines.",
acknowledgement = acknhfb,
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<<‡]qU #)#E;7=m;]'#Eˆarticlefparith.bibWadel:1957:NBNL. B. WadelNegative base number systemsjIRETRANSELECCOMPUTEC6123??jun61957IRELAO03679950 OR 03679950Thu Nov 06 05:53:55 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:53:55 ???IRE Transactions on Electronic Computersnegative baseacknhfbL. B. WadelNegative base number systems
@Article{Wadel:1957:NBN,
author = "L. B. Wadel",
title = "Negative base number systems",
journal = jIRETRANSELECCOMPUT,
volume = "EC6",
number = "??",
pages = "123??",
month = jun,
year = "1957",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Nov 06 05:53:55 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "negative base",
}ppZ !#++‚u/Em;‚E7‚+‚mtechreportfparith.bibTaylor:1957:CCAW. Bruce TaylorCOIN (CompileInterpreter): an automatic programming, fixed and floatingpoint library of subroutines for the ERA 1103 computerOperations Research Office, Johns Hopkins UniversityBethesda, MD, USA431957Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTStaff paper / Johns Hopkins University, Operations Research Office; OROSP32 Staff paper (Johns Hopkins University. Operations Research Office); OROSP32.Military art and science  Data processing.; Military research  Data processing.Cover title. ``Operating under contract with the Department of the Army.'' ``Project COMPLAB.'' ``October 1957.'' OROSP32acknhfbW. Bruce Taylor{COIN} (CompileInterpreter): an automatic programming, fixed and floatingpoint library of subroutines for the {ERA} 1103 computer
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}‡noW #+/Y=m;'/ˆAarticlefparith.bibPawlak:1957:UENZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computerBull. Acad. Pol. Sci., Ser. Sci. Tech.52322361957Thu Nov 06 05:56:32 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:56:32 ???negative baseacknhfbZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computer
@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 = "232236",
month = "????",
year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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}k{k
v‡˜e†Œ
@Article{Timmermann:1993:GFR,
author = "D. Timmermann and B. Rix and B. Hosticka",
title = "{Gleitkommaprozessor f{\"u}r rechenintensive
Echtzeitanwendungen} \toenglish {Floatingpoint
Processor for Computationally Intensive RealTime Use}
\endtoenglish",
journal = jELECTRONIK,
volume = "20",
number = "??",
pages = "142146",
month = "????",
year = "1993",
CODEN = "EKRKAR",
ISSN = "00135658",
bibdate = "Fri Dec 08 13:05:00 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
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}´†Œ
@Article{Timmermann:1992:LLT,
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title = "Low Latency Time {CORDIC} Algorithms",
journal = jIEEETRANSCOMPUT,
volume = "41",
number = "8",
pages = "10101015",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.156543",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Sep 08 00:52:02 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}[
@Article{Tienari:197ˆx‘q
@Article{Tisseur:2001:NMF,
author = "Fran{\c{c}}oise Tisseur",
title = "{Newton}'s Method in Floating Point Arithmetic and
Iterative Refinement of Generalized Eigenvalue
Problems",
journal = jSIAMJMATANAAPPL,
volume = "22",
number = "4",
pages = "10381057",
month = "????",
year = "2001",
CODEN = "SJMAEL",
DOI = "http://dx.doi.org/10.1137/S08954798993598§‘8¢q
@Article{Timmermann:1994:CFV,
author = "D. Timmermann and B. Rix and H. Hahn and B. J.
Hosticka",
title = "A {CMOS} floatingpoint vectorarithmetic unit",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "29",
number = "5",
pages = "634639",
month = may,
year = "1994",
CODEN = "IJSCBC",
ISSN = "00189200 (print), 1558173X (electronic)",
ISSNL = "00189200",
bibd›‰’#
@Article{Timmermann:1994:CFP,
author = "D. Timmermann and B. Rix and H. Hahn and B. J.
Hosticka",
title = "A {CMOS} FloatingPoint VectorArithmetic Unit",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "29",
number = "5",
pages = "634639",
month = may,
year = "1994",
CODEN = "IJSCBC",
ISSN = "00189200 (print), 1558173X (electronic)",
ISSNL = "00189200",
bibdš‡Ž3
@Article{Tiwari:1993:NCP,
author = "Neeraj Tiwari and A. K. Nigam",
title = "A note on constructive procedure for unbiased
controlled rounding",
journal = jSTATPROBLETT,
volume = "18",
number = "5",
pages = "415420",
day = "2",
month = dec,
year = "1993",
CODEN = "SPLTDC",
ISSN = "01677152 (print), 18792103 (electronic)",
ISSNL = "01677152",
bibdate = "Sun Jun 1 11:14:48 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/statproblett1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/016771529390036I",
acknowledgement = acknhfb,
fjournal = "Statistics \& Probability Letters",
journalURL = "http://www.sciencedirect.com/science/journal/01677152",
}µic)",
ISSNL = "00188646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://ieeexplore.ieee.org/servlet/opac?punumber=5288520;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50megacycle
pulserepetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phaselocked frequency divider which
provides a 3.125megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a highspeed shift register, a
highspeed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variablephase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of highspeed computing and measurements
applications.",
acknowledgement = acknhfb,
bookURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
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}r used advantageously to provide features such as the variablephase clock system used in the arithmetic unit.\par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of highspeed computing and measurements applications.R. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50Megacycle Arithmetic Unit
@Article{Walker:1957:EMA,
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abstract = "An experimental 50megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50megacycle
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arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phaselocked frequency divider which
provides a 3.125megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a highspeed shift register, a
highspeed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
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variablephase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of highspeed computing and measurements
applications.",
acknowledgement = acknhfb,
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^^½r^#+eU57Eƒ;‚™S[™Ye¶Yarticlefparith.bibWalker:1957:EMAR. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50Megacycle Arithmetic UnitjIBMJRD13257278jul71957IBMJAEhttp://dx.doi.org/10.1147/rd.13.025700188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Tue Sep 11 15:35:35 MDT 2012http://ieeexplore.ieee.org/servlet/opac?punumber=5288520; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; http://www.research.ibm.com/journal/2012.09.11 15:35:35 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687; http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdfAn experimental 50megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50megacycle pulserepetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phaselocked frequency divider which provides a 3.125megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a highspeed shift register, a highspeed indicator register, and a binary word generator.par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.par In a 50megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may be used advantageously to provide features such as the variablephase clock system used in the arithmetic unit.par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of highspeed computing and measurements applications.IBM Journal of Research and Developmentacknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520An experimental 50megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50megacycle pulserepetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phaselocked frequency divider which provides a 3.125megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a highspeed shift register, a highspeed indicator register, and a binary word generator.\par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.\par In a 50megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may bem
Š uW #)+e57=K;?c+e‹
articlefparith.bibBemer:1958:MMSRobert W. BemerA Machine Method for SquareRoot ComputationjCACM1167jan11958CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 15 18:35:46 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:35:46 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79Robert W. BemerA Machine Method for SquareRoot Computation
@Article{Bemer:1958:MMS,
author = "Robert W. Bemer",
title = "A Machine Method for SquareRoot Computation",
journal = jCACM,
volume = "1",
number = "1",
pages = "67",
month = jan,
year = "1958",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 15 18:35:46 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}ˆ_tV !#1U+1Em;eUŠtechreportfparith.bibAnonymous:1958:ARMAnonymousAnalysis and research memorandum 294AR Memo294 (AD 207929)Massachusetts Institute of Technology, Naval Supersonic LaboratoryCambridge, MA, USA723oct101958Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTError functions.; Floatingpoint arithmetic.acknhfbAnonymousAnalysis and research memorandum 294
@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
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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 = acknhfb,
keywords = "Error functions.; Floatingpoint arithmetic.",
}ŠsW #++i;a7Ea;]+iŒ)articlefparith.bibWeibel:1957:EAMErich S. WeibelAn Electronic Analog Multiplier Using CarriersjIRETRANSELECCOMPUTEC613034mar31957IRELAOhttp://dx.doi.org/10.1109/TEC.1957.522155803679950 OR 03679950Thu Jun 30 16:07:23 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:23 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558IRE Transactions on Electronic ComputersacknhfbErich S. WeibelAn Electronic Analog Multiplier Using Carriers
@Article{Weibel:1957:EAM,
author = "Erich S. Weibel",
title = "An Electronic Analog Multiplier Using Carriers",
journal = jIRETRANSELECCOMPUT,
volume = "EC6",
number = "1",
pages = "3034",
month = mar,
year = "1957",
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DOI = "http://dx.doi.org/10.1109/TEC.1957.5221558",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
àž ¯J¡²àƒP‡!
@InProceedings{Dimitrova:1996:NAS,
author = "N. S. Dimitrova",
title = "On a Numerical Approach for Solving a Class of
Nonlinear Systems",
crossref = "Alefeld:1996:SCV",
pages = "147153",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
acknowledgement = acknhfb,
}
&Œ˜%
@InProceedings{Dimitrov:2007:MCS,
author = "Vassil Dimitrov and Laurent Imbert and Andrew
Zakaluzny",
title = "Multiplication by a Constant is Sublinear",
crossref = "Kornerup:2007:PIS",
pages = "261268",
year = "2007",
DOI = "http://dx.doi.org/10.1109/ARITH.2007.24",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/te8…'ŠO
@InProceedings{Dimitrov:2001:UMD,
author = "V. S. Dimitrov and J. Eskritt and L. Imbert and G. A.
Jullien and W. C. Miller",
title = "The Use of the MultiDimensional Logarithmic Number
System in {DSP} Applications",
crossref = "Burgess:2001:ISC",
pages = "247256",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
URL = "http://www.acsellab.com/arithmetic/arith15/papers/ARITH15_Dimitrov.pdf",
acknowledgement = acknhfb,
keywords = "ARITH15",
}ð„c‰G
@InProceedings{Dimitrov:1997:TAD,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "Theory and Applications for a DoubleBase Number
System",
crossref = "Lang:1997:ISC",
pages = "4453",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
URL = "http://www.acsellab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_theory.pdf",
acknowledgement = acknhfb,
keywords = "ARITH13",
}
¹‰
’
@InProceedings{Dimitrov:1997:ERN,
author = "V. Dimitrov and G. A. Jullien and W. C. Miller",
booktitle = "Proceedings of the 40th Midwest Symposium on Circuits
and Systems, 1997",
title = "{Eisenstein} residue number system with applications
to {DSP}",
volume = "2",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "675678",
year = "1997",
CODEN = "????",
DOI = ?„q‰c
@InProceedings{Dimitrov:1997:AME,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "Algorithms for MultiExponentiation Based on Complex
Arithmetic",
crossref = "Lang:1997:ISC",
pages = "208217",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
URL = "http://www.acsellab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_algorithms.pdf",
acknowledgement = acknhfb,
keywords = "ARITH13",
}
·ˆ+W
@InProceedings{Dimitrov:2013:ALI,
author = "Vassil Dimitrov and Kimmo J{\"a}rvinen",
title = "Another Look at Inversions over Binary Fields",
crossref = "IEEE:2013:PIS",
pages = "211218",
year = "2013",
DOI = "http://dx.doi.org/10.1109/ARITH.2013.25",
ISSN = "10636889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
ke
""
æ
ð 'y†Œ
@Article{Chabert:2009:PEA,
author = "Gilles Chabert and Luc Jaulin",
title = "A Priori Error Analysis and Spring Arithmetic",
journal = jSIAMJSCICOMP,
volume = "31",
number = "3",
pages = "22142230",
month = "????",
year = "2009",
CODEN = "SJOCE3",
DOI = "",
ISSN = "10648275 (print), 10957197 (electronic)",
ISSNL = "10648275",
bibdate = "Wed May 19 10:44:16 MDT 2010",
bibsource = "http://epubs.siam.org/sambin/dbq/toc/SISC/31/3;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "SIAM Journal on Scientific Computing",
journalURL = "http://epubs.siam.org/sisc",
}øš
@Article{Chakraborti:1986:IMR,
author = "N. B. Chakraborti and J. S. Soundararajan and A. L. N.
Reddy",
title = "An Implementation of MixedRadix Conversion for
Residue Number Applications",
journal = jIEEETRANSCOMPUT,
volume = "C35",
number = "8",
pages = "762764",
month = aug,
year = "1986",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1986.16p‡iS
@Article{Chakrabarti:1974:DCA,
author = "S. Chakrabarti",
title = "DivideandCorrect Algorithm for Division in a
Negative Base",
journal = jIEEETRANSCOMPUT,
volume = "C23",
number = "9",
pages = "981983",
month = sep,
year = "1974",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1974.224066",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Tue Jul 12 11:27:35 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=1672659",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}ßŠ1”c
@Article{Chaitin:1988:RA,
author = "Gregory J. Chaitin",
title = "Randomness in Arithmetic",
journal = jSCIAMER,
volume = "259",
number = "1",
pages = "8085 (Intl. ed. 5257)",
month = jul,
year = "1988",
CODEN = "SCAMAC",
DOI = "http://dx.doi.org/10.1038/scientificamerican078880",
ISSN = "00368733 (print), 19467087 (electronic)",
ISSNL = "00368733",
bibdate = ¤…t‹i
@Article{ChaitinChatelin:1996:FPA,
author = "F. ChaitinChatelin",
title = "Is Finite Precision Arithmetic Useful For Physics?",
journal = jJUCS,
volume = "2",
number = "5",
pages = "380??",
day = "28",
month = may,
year = "1996",
CODEN = "????",
ISSN = "09486968",
ISSNL = "09486968",
bibdate = "Wed May 28 19:32:35 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/is_finite_precision_arithmetic_useful_for_physics",
acknowledgement = acknhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journalURL = "http://www.jucs.org/jucs",
}
„ˆ1
@Article{Chai:1991:MCF,
author = "P. Chai and T. Chuk and Y. H. Fong and L. Hu and K. Ng
and J. Prabhu and A. Quek and A. Samuels and J. Yeun",
title = "A 120 {MFLOPS CMOS} FloatingPoint Processor",
crossref = "IEEE:1991:PIC",
pages = "15.1/14",
year = "1991",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
} À
$
üŽ$†gxU #+U%7=m;;U‡9
articlefparith.bibDelury:1958:CANDaniel B. DeluryComputation with Approximate NumbersjMATHTEACH51521530nov11195800255769 OR 00255769Fri Nov 28 11:47:47 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 11:47:47 ???The Mathematics TeacheracknhfbDaniel B. DeluryComputation with Approximate Numbers
@Article{Delury:1958:CAN,
author = "Daniel B. Delury",
title = "Computation with Approximate Numbers",
journal = jMATHTEACH,
volume = "51",
pages = "521530",
month = nov,
year = "1958",
ISSN = "00255769",
bibdate = "Fri Nov 28 11:47:47 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "The Mathematics Teacher",
}ˆkwW #';7=m;]O' ‰earticlefparith.bibCouleur:1958:BBDJ. F. CouleurBIDEC  a BinarytoDecimal or DecimaltoBinary ConverterjIRETRANSELECCOMPUTEC73133161958IRELAO03679950 OR 03679950Fri Nov 28 16:28:12 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 16:28:12 ???IRE Transactions on Electronic Computersdecimal floatingpoint arithmeticackmfcJ. F. Couleur{BIDEC}  a BinarytoDecimal or DecimaltoBinary Converter
@Article{Couleur:1958:BBD,
author = "J. F. Couleur",
title = "{BIDEC}  a BinarytoDecimal or DecimaltoBinary
Converter",
journal = jIRETRANSELECCOMPUT,
volume = "EC7",
pages = "313316",
year = "1958",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Fri Nov 28 16:28:12 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floatingpoint arithmetic",
}ŠvW #)#i57;K;?c#i‹articlefparith.bibBemer:1958:SMCR. W. BemerA Subroutine Method for Calculating LogarithmsjCACM1557may51958CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:16:09 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:16:09 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79R. W. BemerA Subroutine Method for Calculating Logarithms
@Article{Bemer:1958:SMC,
author = "R. W. Bemer",
title = "A Subroutine Method for Calculating Logarithms",
journal = jCACM,
volume = "1",
number = "5",
pages = "57",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
‰zW #)#o57=K;5O#o‹articlefparith.bibGower:1958:NIMJ. C. GowerA Note on an Iterative Method for Root ExtractionjCOMPJ11421431958CMPJA600104620 (print), 14602067 (electronic) OR 00104620 (print), 14602067 (electronic)00104620 OR 00104620Thu Sep 15 18:36:55 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:36:55 ???The Computer Journalacknjhttp://comjnl.oxfordjournals.org/J. C. GowerA Note on an Iterative Method for Root Extraction
@Article{Gower:1958:NIM,
author = "J. C. Gower",
title = "A Note on an Iterative Method for Root Extraction",
journal = jCOMPJ,
volume = "1",
pages = "142143",
year = "1958",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Thu Sep 15 18:36:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "The Computer Journal",
journalURL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}‹wyW #+[57E‚;?c[Žarticlefparith.bibErshov:1958:PAOAndrei P. ErshovOn Programming of Arithmetic OperationsjCACM1836aug81958CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:21 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm1.html#Ershov58; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:21 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Andrei P. ErshovOn Programming of Arithmetic Operations
@Article{Ershov:1958:PAO,
author = "Andrei P. Ershov",
title = "On Programming of Arithmetic Operations",
journal = jCACM,
volume = "1",
number = "8",
pages = "36",
month = aug,
year = "1958",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Wed Jul 14 15:48:21 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm1.html#Ershov58;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Ershov58",
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›„z‰u
@Article{Krick:1999:AN,
author = "T. Krick and L. M. Pardo and M. Sombra",
title = "Arithmetic {Nullstellens{\"a}tze}",
journal = jSIGSAM,
volume = †~}
@Article{Kreifelts:1975:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine GleitkommaArithmetik
(Berichtigung)} \toenglish {Optimal Basis Choice for a
FloatingPoint Arithmetic (Correction)} \endtoenglish",
journal = jCOMPUTING,
volume = "14",
number = "??",
pages = "313314",
month =‰l“Y
@Article{Kramer:2012:MAP,
author = "Walter Kr{\"a}mer",
title = "Multiple\slash arbitrary precision interval
computations in {CXSC}",
journal = jCOMPUTING,
volume = "94",
number = "24",
pages = "229241",
month = mar,
year = "2012",
CODEN = "CMPTA2",
DOI = "http://dx.doi.org/10.1007/s0060701101748",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL£†eK
@Article{Kreifelts:1973:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
GleitkommaArithmetik} \toenglish {Optimal Choice of
Basis for a FloatingPoint Arithmetic} \endtoenglish",
journal = jCOMPUTING,
volume = "11",
number = "??",
pages = "353363",
month = "????",
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journalURL = "http://link.springer.com/journal/607",
}¤Š0”a
@Article{Kravchenko:1997:AEP,
author = "Yu. P. Kravchenko and M. A. Liberman",
title = "On the Application of Extended Precision Arithmetic to
Quantum Mechanical Calculations",
journal = jIJQC,
volume = "62",
number = "6",
pages = "593601",
month = "????",
year = "1997",
CODEN = "IJQCB2",
DOI = "http://dx.doi.org/10.1002/(SICI)1097461X(1997)62:6<593::AIDQUA3>3.0.CO;2R",
f‡B
@Article{Kramer:2001:AFE,
author = "Walter Kr{\"a}mer and Armin Bantle",
title = "Automatic forward error analysis for floating point
algorithms",
journal = jRELIABLECOMPUTING,
volume = "7",
number = "4",
pages = "321340",
year = "2001",
CODEN = "RCOMF8",
ISSN = "13853139 (print), 15731340 (electronic)",
ISSNL = "13853139",
MRclass = "65G40 (65G50)",
MRnumber = "MR1843023 (2002d:65046)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
authordates = "19522014 (WK)",
fjournal = "Reliable Computing. An International Journal Devoted
to Reliable Mathematical Computations Based on Finite
Representations and Guaranteed Accuracy",
journalURL = "http://link.springer.com/journal/11155",
}Ž4œi
@Article{Kramer:1998:PWC,
author = "W. Kramer",
title = "A priori worst case error bounds for floatingpoint
computations",
journal = jIEEETRANSCOMPUT,
volume = "47",
number = "7",
pages = "750756",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.709374",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "0018÷
÷‹bZ #9157;K;[1%ŒUarticlefparith.bibKogbetliantz:1958:CANbE. G. KogbetliantzComputation of Arcsin $N$ for $ 0 < N < 1 $ Using an Electronic ComputerjIBMJRD23218222jul71958IBMJAE00188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Thu Sep 1 10:16:10 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:16:10 ???IBM Journal of Research and Developmentacknjhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520E. G. KogbetliantzComputation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using an Electronic Computer
@Article{Kogbetliantz:1958:CANb,
author = "E. G. Kogbetliantz",
title = "Computation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using
an Electronic Computer",
journal = jIBMJRD,
volume = "2",
number = "3",
pages = "218222",
month = jul,
year = "1958",
CODEN = "IBMJAE",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = "00188646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IBM Journal of Research and Development",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}Œ{Z #91557;K;[1AŒmarticlefparith.bibKogbetliantz:1958:CANaE. G. KogbetliantzComputation of Arctan $N$ for $  infty < N < + infty $ Using an Electronic ComputerjIBMJRD214353jan11958IBMJAE00188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Thu Sep 1 10:16:10 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:16:10 ???IBM Journal of Research and Developmentacknjhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520E. G. KogbetliantzComputation of Arctan {$N$} for $  \infty < {N} < + \infty $ Using an Electronic Computer
@Article{Kogbetliantz:1958:CANa,
author = "E. G. Kogbetliantz",
title = "Computation of Arctan {$N$} for $  \infty < {N} < +
\infty $ Using an Electronic Computer",
journal = jIBMJRD,
volume = "2",
number = "1",
pages = "4353",
month = jan,
year = "1958",
CODEN = "IBMJAE",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = "00188646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IBM Journal of Research and Development",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}rce = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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••‡u~U #3+[;7;m;]+[‰articlefparith.bibRobertson:1958:NCDaJ. E. RobertsonA new class of digital division methodsjIRETRANSELECCOMPUTEC738892sep91958IRELAO03679950 OR 03679950Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???IRE Transactions on Electronic ComputersacksfoJ. E. RobertsonA new class of digital division methods
@Article{Robertson:1958:NCDa,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = jIRETRANSELECCOMPUT,
volume = "EC7",
number = "3",
pages = "8892",
month = sep,
year = "1958",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}’p}X#3QW;a7=‚o;„]M„QW’}articlefparith.bibMetropolis:1958:SDCN. Metropolis and R. L. AshenhurstSignificant Digit Computer ArithmeticjIRETRANSELECCOMPUTEC742652671958IRELAOhttp://dx.doi.org/10.1109/TEC.1958.522265703679950 OR 03679950Wed Feb 14 19:23:38 2007http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2007.02.14 19:23:38 ???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.IRE Transactions on Electronic ComputersCited in cite Sterbenz:1974:FPC.acknhfbThe 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.N. Metropolis and R. L. AshenhurstSignificant Digit Computer Arithmetic
@Article{Metropolis:1958:SDC,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Significant Digit Computer Arithmetic",
journal = jIRETRANSELECCOMPUT,
volume = "EC7",
number = "4",
pages = "265267",
month = "????",
year = "1958",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1958.5222657",
ISSN = "03679950",
bibdate = "Wed Feb 14 19:23:38 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
”D"Ä"3DˆB‘
@Article{Wong:1990:QNF,
author = "P. W. Wong",
title = "Quantization noise, fixedpoint multiplicative
roundoff noise, and dithering",
journal = jIEEETRANSACOUSTSPEECH,
volume = "38",
number = "2",
pages = "286300",
month = feb,
year = "1990",
CODEN = "IETABA",
ISSN = "00963518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.orà‰7’o
@Article{Wolrich:1984:HPF,
author = "G. Wolrich and E. McLellan and L. Harada and J.
Montanaro and R. A. J. Yodlowski",
title = "A High Performance Floating Point Coprocessor",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "SC19",
number = "5",
pages = "690696",
month = oct,
year = "1984",
CODEN = "IJSCBC",
ISSN = "00189200 (print), 1558173X (electronic)",
ISSNL = … ŠA
@Article{Wollenberg:1986:SRD,
author = "R. Wollenberg and R. Milnikel",
title = "{Schnelles Radizierverfahren durch Tabellenzugriff}
\toenglish {Fast Squarerooting Method by Means of
Table Lookup} \endtoenglish",
journal = jELECTRONIK,
volume = "6",
pages = "7982",
year = "1986",
CODEN = "EKRKAR",
ISSN = "00135658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Elektronik",
}f‡N
@Article{Wolfe:1964:RTE,
author = "Jack M. Wolfe",
title = "Reducing Truncation Errors by Programming",
journal = jCACM,
volume = "7",
number = "6",
pages = "355356",
month = jun,
year = "1964",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Fri Nov 25 18:19:54 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://portal.acm.org/;
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 = acknhfb # " and " # acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floatingpoint arithmetic; truncation errors",
}Ž/
@Article{Wlodarski:1971:FLN,
author = "J. Wlodarski",
title = "{Fibonacci} and {Lucas} Numbers Tend to Obey
{Benford's Law}",
journal = jFIBQUART,
volume = "9",
number = "1",
pages = "8788",
month = feb,
year = "1971",
CODEN = "FIBQAU",
ISSN = "00150517",
ISSNL = "0015051‰B“
@Article{Woehr:1997:CWK,
author = "Jack Woehr",
title = "A Conversation with {William Kahan}: How important is
numerical accuracy?",
journal = jDDJ,
volume = "22",
number = "11",
pages = "1820, 22, 24, 26, 30, 32",
month = nov,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044789X",
bibdate = "Fri Nov 28 17:28:03 MST 1997",
bibsource = "http://www.math.utah.edu/pub/ªˆ+
@Article{Wong:1992:DSR,
author = "W. F. Wong and E. Goto",
title = "Division and squarerooting using a split multiplier",
journal = jELECTLETTERS,
volume = "28",
number = "18",
pages = "17581759",
day = "27",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "00135194 (print), 1350911X (electronic)",
ISSNL = "00135194",
bibdate = "Sat Jul 16 15:28:13 MDT 20
Ë
Ý
6ÝŒUY #+)=;a7E‚;])=yarticlefparith.bibSchmid:1958:TFQHermann SchmidA Transistorized FourQuadrant TimeDivision Multiplier with an Accuracy of 0.1 Per CentjIRETRANSELECCOMPUTEC714147mar31958IRELAOhttp://dx.doi.org/10.1109/TEC.1958.522209403679950 OR 03679950Thu Jul 14 15:56:43 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:43 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094IRE Transactions on Electronic ComputersacknhfbHermann SchmidA Transistorized FourQuadrant TimeDivision Multiplier with an Accuracy of 0.1 Per Cent
@Article{Schmid:1958:TFQ,
author = "Hermann Schmid",
title = "A Transistorized FourQuadrant TimeDivision
Multiplier with an Accuracy of 0.1 Per Cent",
journal = jIRETRANSELECCOMPUT,
volume = "EC7",
number = "1",
pages = "4147",
month = mar,
year = "1958",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1958.5222094",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‹GW #31[;a7E‚;]1[ articlefparith.bibRobertson:1958:NCDbJames E. RobertsonA New Class of Digital Division MethodsjIRETRANSELECCOMPUTEC73218222sep91958IRELAOhttp://dx.doi.org/10.1109/TEC.1958.522257903679950 OR 03679950Thu Jul 14 15:56:43 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:43 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579IRE Transactions on Electronic ComputersacknhfbJames E. RobertsonA New Class of Digital Division Methods
@Article{Robertson:1958:NCDb,
author = "James E. Robertson",
title = "A New Class of Digital Division Methods",
journal = jIRETRANSELECCOMPUT,
volume = "EC7",
number = "3",
pages = "218222",
month = sep,
year = "1958",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1958.5222579",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}/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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Sisson58",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sisson58",
}
=N‡'ŽQ
@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 = jREVGENSCIPURESAPPL,
volume = "??",
number = "??",
pages = ŠA•
@Article{Toivonen:2006:VFF,
author = "T. Toivonen and J. Heikkila",
title = "Video filtering with {Fermat} number theoretic
transforms using residue number system",
journal = jIEEETRANSCIRCUITSSYSTVIDEOTECH,
volume = "16",
number = "1",
pages = "92101",
month = jan,
year = "2006",
CODEN = "ITCTEM",
DOI = "http://dx.doi.org/10.1109/TCSVT.2005.858612",
ISSN = "ì†G
@Article{Tornaria:2002:SRM,
author = "Gonzalo Tornar{\'\i}a",
title = "Square Roots Modulo $p$",
journal = jLECTNOTESCOMPSCI,
volume = "2286",
pages = "430??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Tue Sep 10 19:09:12 MDT 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2286.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/2286/22860430.htm;
http://link.springerny.com/link/service/series/0558/papers/2286/22860430.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}ü‰I“
@Article{Tong:2000:RPO,
author = "J. Y. F. Tong and D. Nagle and R. A. Rutenbar",
title = "Reducing power by optimizing the necessary
precision\slash range of floatingpoint arithmetic",
journal = jIEEETRANSVLSISYST,
volume = "8",
number = "3",
pages = "273286",
month = jun,
year = "2000",
CODEN = "IEVSE9",
DOI = "http://dx.doi.org/10.1109/92.845894",
ISSN = "1Ö…V‹
@Article{Tomasulo:1967:EAE,
author = "R. M. Tomasulo",
title = "An Efficient Algorithm for Exploiting Multiple
Arithmetic Units",
journal = jIBMJRD,
volume = "11",
number = "1",
pages = "2533",
month = jan,
year = "1967",
CODEN = "IBMJAE",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = "00188646",
bibdate = "Fri Aug 26 10:27:10 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IBM Journal of Research and Development",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}“‡iS
@Article{Toma:1975:CLA,
author = "C. I. Toma",
title = "Cellular Logic Array for HighSpeed Signed Binary
Number Multiplication",
journal = jIEEETRANSCOMPUT,
volume = "C24",
number = "9",
pages = "932935",
month = sep,
year = "1975",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1975.224340",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Tue Jul 12 07:57:57 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/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}S
ÂÂ–:Y #++U57Ek;†'?Oc†'+U–carticlefparith.bibSisson:1958:IDRRoger L. SissonAn Improved Decimal Redundancy CheckjCACM151012may51958CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Mon Jan 22 07:22:12 MST 2001http://dblp.unitrier.de/db/journals/cacm/cacm1.html#Sisson58; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 07:22:12 MSTAs 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.Communications of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79As 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.Roger L. SissonAn Improved Decimal Redundancy Check
@Article{Sisson:1958:IDR,
author = "Roger L. Sisson",
title = "An Improved Decimal Redundancy Check",
journal = jCACM,
volume = "1",
number = "5",
pages = "1012",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Mon Jan 22 07:22:12 MST 2001",
bibsource = "http://dblp.unitrier.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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Sisson58",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sisson58",
}
i;i‹NW #)#I57E‚;?c#I}articlefparith.bibWadey:1958:TSRW. G. WadeyTwo SquareRoot ApproximationsjCACM1111314nov111958CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm1.html#Wadey58; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79W. G. WadeyTwo SquareRoot Approximations
@Article{Wadey:1958:TSR,
author = "W. G. Wadey",
title = "Two SquareRoot Approximations",
journal = jCACM,
volume = "1",
number = "11",
pages = "1314",
month = nov,
year = "1958",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm1.html#Wadey58;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Wadey58",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}‰AW #+%C77;m;y%Šcarticlefparith.bibTocher:1958:TMDK. D. TocherTechniques of Multiplication and Division for Automatic Binary ComputersjQUARTJMECHAPPLIEDMATH1133643841958QJMMAV00335614 OR 0033561400335614 OR 00335614Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied MathematicsacksfoK. D. TocherTechniques of Multiplication and Division for Automatic Binary Computers
@Article{Tocher:1958:TMD,
author = "K. D. Tocher",
title = "Techniques of Multiplication and Division for
Automatic Binary Computers",
journal = jQUARTJMECHAPPLIEDMATH,
volume = "11",
number = "3",
pages = "364384",
month = "????",
year = "1958",
CODEN = "QJMMAV",
ISSN = "00335614",
ISSNL = "00335614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
}",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.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 onestage
error propagation is developed for each operation; a
suggested statistical model for longrun error
propagation is also set forth.",
acknowledgement = acknhfb,
fjournal = "Journal of the Association for Computing Machinery",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}„
*;Ó; >Â˜p±a
@Article{Clinger:2004:RHR,
author = "William D. Clinger",
title = "Retrospective: How to read floating point numbers
accurately",
journal = jSIGPLAN,
volume = "39",
number = "4",
pages = "360371",
month = apr,
year = "2004",
CODEN = "SINODQ",
DOI = "http://doi.acm.org/10.1145/989393.989430",
ISSN = "03621340 (print), 15232867 (print), 15581160
{©
@Article{Cluley:1980:DCB,
author = "J. C. Cluley",
title = "Digital Circuits for Binary Arithmetic",
journal = jCOMPJ,
volume = "23",
number = "3",
pages = "269269",
month = aug,
year = "1980",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/23.3.269",
ISSN = "00104620 (print), 14602067 (electronic)",
‰B“
@Article{Cleveland:2013:OIR,
author = "Mathew A. Cleveland and Thomas A. Brunner and Nicholas
A. Gentile and Jeffrey A. Keasler",
title = "Obtaining identical results with double precision
global accuracy on different numbers of processors in
parallel particle {Monte Carlo} simulations",
journal = jJCOMPUTPHYS,
volume = "251",
number = "??",
pages = "223236",
day = õ†zu
@Article{Cloutier:1983:PAR,
author = "Mark J. Cloutier and Matthew J. Friedman",
title = "Precision Averaging for RealTime Analysis",
journal = jCACM,
volume = "26",
number = "7",
pages = "525529",
year = "1983",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Mon Jan 22 06:31:47 MST 2001",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm26.html#CloutierF83;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "CloutierF83",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/CloutierF83",
}³ˆg‘O
@Article{Clouser:1999:MSF,
author = "J. Clouser and M. Matson and R. Badeau and R. Dupcak
and S. Samudrala and R. Allmon and N. Fairbanks",
title = "A {600MHz} superscalar floatingpoint processor",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "34",
number = "7",
pages = "10261029",
month = jul,
year = "1999",
CODEN = "IJSCBC",
ISSN = "00189200 (print), 1558173X (eleca…b‹E
@Article{Clinger:2004:HRF,
author = "William D. Clinger",
title = "How to read floating point numbers accurately",
journal = jSIGPLAN,
volume = "39",
number = "4",
pages = "360371",
month = apr,
year = "2004",
CODEN = "SINODQ",
ISSN = "03621340 (print), 15232867 (print), 15581160
(electronic)",
ISSNL = "03621340",
bibdate = "Tue Apr 12 09:38:13 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "ACM SIGPLAN Notices",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}¦£bÇE
@Article{Clinger:1990:HRF,
author = "William D. Clinger",
title = "How to Read Floating Point Numbers Accurately",
journal = jSIGPLAN,
volume = "25",
number = "6",
pages = "92101",
month = jun,
year = "1990",
CODEN = "SINODQ",
DOI = "http://dx.doi.org/10.1145/93548.93557",
ISBN = "0897913647",
ISBN13 = "9780897913645",
ISSN = "03621340 (print), 15232867 Kê¤vê ¯S`…†pa
@Article{Dumas:2014:NRI,
author = "JeanGuillaume Dumas",
title = "On {NewtonRaphson} Iteration for Multiplicative
Inverses Modulo Prime Powers",
journal = jIEEETRANSCOMPUT,
volume = "63",
number = "8",
pages = "21062109",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2013.94",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}®ŒJ™
@Article{Duprat:1991:WND,
author = "J. Duprat and J.M. Muller",
title = "Writing numbers differently for faster calculation",
journal = jTECHNIQUESCIINFORMATIQUES,
volume = "10",
number = "3",
pages = "211224",
month = "????",
year = "1991",
CODEN = "TTSIDJ",
ISSN = "07524072, 02647419",
ISSNL = "07524072",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "htt6¦„V‰
@Article{Dunham:1989:S,
author = "C. B. Dunham",
title = "Summation",
journal = jSIGNUM,
volume = "24",
number = "1",
pages = "1415",
month = jan,
year = "1989",
CODEN = "SNEWD6",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
bibdate = "Tue Sep 13 08:58:48 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "ACM SIGNUM Newsletter",
keywords = "accurate floatingpoint summation",
}•Ø…A‹
@Article{Dunham:1988:PMA,
author = "C. B. Dunham",
title = "Provably Monotone Approximations {III}",
journal = jSIGNUM,
volume = "23",
number = "1",
pages = "1010",
month = jan,
year = "1988",
CODEN = "SNEWD6",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
bibdate = "Tue Sep 13 09:05:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "ACM SIGNUM Newsletter",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
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}A‡Ž
@Article{Du:1973:CSS,
author = "MinWen Du and C. Dennis Weiss",
title = "Circuit Structure and Switching Function
Verification",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "6",
pages = "618625",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009116",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH2",
}•
00—LY#3eY577+={;†3q!e†3eY—articlefparith.bibAshenhurst:1959:UFPRobert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point ArithmeticjJACM63415428jul71959JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541168.00MR0105833 (21 \#4568)H. H. GoldstineFri Dec 08 13:06:24 1995http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:06:24 ???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 onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Journal of the Association for Computing Machinery0121.12102acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Algorithms 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 onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Robert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point Arithmetic
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = jJACM,
volume = "6",
number = "3",
pages = "415428",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
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/metropolisnicholas.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 onestage
error propagation is developed for each operation; a
suggested statistical model for longrun error
propagation is also set forth.",
acknowledgement = acknhfb,
fjournal = "Journal of the Association for Computing Machinery",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
} bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
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}…
ð÷ðŒW #'c57E‚;?c1cŽ!articlefparith.bibCarr:1959:EAFJohn W. Carr IIIError Analysis in Floating Point ArithmeticjCACM251015may51959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:23 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:23 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79John W. {Carr III}Error Analysis in Floating Point Arithmetic
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = jCACM,
volume = "2",
number = "5",
pages = "1015",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a;
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}ŽY #//57Eo;?Oc/‘ articlefparith.bibBuchholz:1959:FFCWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)jCACM2123111959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Mon Jan 22 06:28:45 MST 2001http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 06:28:45 MSTCommunications of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Wilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
title = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = jCACM,
volume = "2",
number = "12",
pages = "311",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.unitrier.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.",
}
0ˆ*U #'U;7=m;]O'Y‰?articlefparith.bibDaggett:1959:DBCD. H. DaggettDecimalBinary Conversions in CORDICjIRETRANSELECCOMPUTEC85335339sep91959IRELAO03679950 OR 03679950Thu Sep 08 08:14:00 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:00 ???IRE Transactions on Electronic Computersdecimal floatingpoint arithmeticacknjD. H. DaggettDecimalBinary Conversions in {CORDIC}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
title = "DecimalBinary Conversions in {CORDIC}",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "5",
pages = "335339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floatingpoint arithmetic",
}LW %#%ym9'!=%;!‚;{1my!9Ž[incollectionfparith.bibCarr:1959:PCJohn W. Carr IIIEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeHandbook of Automation, Computation, and ControlProgramming and CodingpubWILEYpubWILEY:adr10151959TJ213 .G72Fri Aug 20 08:41:16 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 08:41:16 ???Chapter 2.19581961: Volume 1. Control fundamentals. Volume 2. Computers and data processing. Volume 3. Systems and components. Cited in cite Sterbenz:1974:FPC.automation; mathematics; computers; operations researchacknhfbJohn W. {Carr III}Handbook of Automation, Computation, and ControlEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeChapter 2.Programming and Coding
@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 = pubWILEY,
address = pubWILEY: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 = acknhfb,
bookpages = "????",
remark = "19581961: 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",
}
kZk"d8I!šC
@Article{Jaime:2011:HSA,
author = "F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and
J. Villalba and E. L. Zapata",
title = "HighSpeed Algorithms and Architectures for Range
Reduction Computation",
journal = jIEEETRANSVLSISYST,
volume = "19",
number = "3",
pages = "512516",
month = "????",
year = "2011",
CODEN = "IEVSE9",
DOI = "http://dx.doi.org/10.Š/”_
@Article{Jager:2008:DAD,
author = "Hendrik Jager and Pierre Liardet",
title = "Distributions arithm{\'e}tiques des d{\'e}nominateurs
de convergents de fractions continues. ({French})
[Arithmetic distributions of the denominators of
continued fractions]",
journal = "Proceedings of the Koninklijke Nederlandse Akademie
van Wetenschappen, Series A, Indagationes
mathematicae",
š=´{
@Article{Jamieson:1989:SNR,
author = "M. J. Jamieson",
title = "Short Notes: Rapidly Converging Iterative Formulae for
Finding Square Roots and their Computational
Efficiencies",
journal = jCOMPJ,
volume = "32",
number = "1",
pages = "9394",
month = feb,
year = "1989",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/32.1.93",
ISSN = "00
¢„*ˆU
@Article{James:1983:RDB,
author = "F. V. James",
title = "An 8085 routine divides 32bit unsigned numbers",
journal = jELECTRONICS,
volume = "56",
number = "22",
pages = "163165",
month = nov,
year = "1983",
ISSN = "08834989",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Electronics",
}Õ‡<Žy
@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 = jMATHCOMPUT,
volume = "19",
number = "91",
pages = "497500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
garbo.uwasa.fi:/pc/docsoft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = acknj # " and " # acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}*™2²e
@Article{Jain:1991:CSN,
author = "Suneel Jain",
title = "Circular scheduling: a new technique to perform
software pipelining",
journal = jSIGPLAN,
volume = "26",
number = "6",
pages = "219228",
month = jun,
year = "1991",
CODEN = "SINODQ",
ISSN = "03621340 (print), 15232867 (print), 15581160
(electronic)",
ISSNL = "03621340",
bibdate = "S^š
@Article{Jahn:1993:LIF,
author = "K.U. Jahn",
title = "Loop Invariants in Floating Point Algorithms.
{SchleifenInvarianten in Gleitpunktalgorithmen}",
journal = jCOMPUTING,
volume = "50",
number = "3",
pages = "255264",
year = "1993",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
MRclass = "65G05 (65G10)",
MRnumber = 6
ß Vßs
W #/1]'O577E…I;#1!C%1]“Aarticlefparith.bibForsythe:1959:RNRGeorge E. ForsytheReprint of a Note on RoundingOff ErrorsjSIAMREVIEW1166671959SIREADhttp://dx.doi.org/10.1137/100101100361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 0036144565.00MR0099119 (20 \#5563)Thu Mar 27 09:04:24 MDT 2014http://epubs.siam.org/toc/siread/1/1; http://www.math.utah.edu/pub/bibnet/authors/f/forsythegeorgeelmer.bib; http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:04:24 MDTSIAM Reviewnumerical analysis0168.14002acknhfbhttp://epubs.siam.org/sirevJanuary 1959George E. ForsytheReprint of a Note on RoundingOff Errors
@Article{Forsythe:1959:RNR,
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title = "Reprint of a Note on RoundingOff Errors",
journal = jSIAMREVIEW,
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http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib;
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}& Y#+I!57E‚;?cI!)articlefparith.bibErcoli:1959:BADPaolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial ComputerjCACM241315apr41959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#ErcoliV59; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Paolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial Computer
@Article{Ercoli:1959:BAD,
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title = "Binary Arithmetic for Discretely Variable Word Length
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journal = jCACM,
volume = "2",
number = "4",
pages = "1315",
month = apr,
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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S æS‹W #+?;a7E‚;]?Œaarticlefparith.bibGarner:1959:RNSHarvey L. GarnerThe Residue Number SystemjIRETRANSELECCOMPUTEC82140147jun61959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.521951503679950 OR 03679950Thu Jul 14 15:56:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515IRE Transactions on Electronic ComputersacknhfbHarvey L. GarnerThe Residue Number System
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "2",
pages = "140147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5219515",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}ŒY #+;a7E‚;]Oarticlefparith.bibGarner:1959:RMSHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement CodesjIRETRANSELECCOMPUTEC812530mar31959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.522275703679950 OR 03679950Thu Jul 14 15:56:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757IRE Transactions on Electronic ComputersacknhfbHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement Codes
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "1",
pages = "2530",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5222757",
ISSN = "03679950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
ŒY '#''‚U=m;M''‚UŒinproceedingsfparith.bibHenrici:1959:TESPeter HenriciProceedings of the International Conference on Information Processing, UNESCOTheoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations36431959Fri Aug 20 09:11:32 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:11:32 ???Cited in cite Sterbenz:1974:FPC.acknhfbPeter HenriciProceedings of the International Conference on Information Processing, UNESCOTheoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations
@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 = "3643",
year = "1959",
LCCN = "????",
bibdate = "Fri Aug 20 09:11:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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Y'#'A7'%=m;A7‰einproceedingsfparith.bibGray:1959:NFPH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, MA, December 13, 1959Normalized floatingpoint arithmetic with an index of significance16pubAFIPSpubAFIPS:adr2442481959TK7885.A1 J6Tue Oct 09 09:43:31 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.10.09 09:43:31 ???acknhfbH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, MA, December 13, 1959Normalized floatingpoint arithmetic with an index of significance
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}ŒZ #71=57;K;[1QŒarticlefparith.bibKogbetliantz:1959:CSCE. G. KogbetliantzComputation of $ sin N $, $ cos N $, and $M$ th Root of $N$ Using an Electronic ComputerjIBMJRD32147152apr41959IBMJAE00188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Thu Sep 1 10:15:56 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:56 ???IBM Journal of Research and Developmentacknjhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520E. G. KogbetliantzComputation of $ \sin {N} $, $ \cos {N} $, and {$M$ th} Root of {$N$} Using an Electronic Computer
@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 = jIBMJRD,
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number = "2",
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CODEN = "IBMJAE",
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@Art—d¯I
@Article{Quinn:1990:REL,
author = "T. Quinn and S. Tremaine",
title = "Roundoff error in longterm planetary orbit
integrations",
journal = jASTRONJ,
volume = "99",
number = "3",
pages = "10161023",
month = mar,
year = "1990",
CODEN = "ANJOAA",
ISSN = "00046256",
ISSNL = "00046256",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "http://www.mat_›?
@Article{Quach:2004:SIR,
author = "N. T. Quach and N. Takagi and M. J. Flynn",
title = "Systematic {IEEE} rounding method for highspeed
floatingpoint multipliers",
journal = jIEEETRANSVLSISYST,
volume = "12",
number = "5",
pages = "511521",
month = may,
year = "2004",
CODEN = "IEVSE9",
DOI = "http://dx.doi.org/10.1109/TVLSI.2004.825860",
ISSN = "10638210 (prÿ…y‹s
@Article{Quach:1992:HSA,
author = "N. T. Quach and M. J. Flynn",
title = "Highspeed addition in {CMOS}",
journal = jIEEETRANSCOMPUT,
volume = "41",
number = "12",
pages = "16121615",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.214671",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
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@Article{Qian:2006:HMP,
author = "Jianbo Qian and Cao An Wang",
title = "How much precision is needed to compare two sums of
square roots of integers?",
journal = jINFOPROCLETT,
volume = "100",
number = "5",
pages = "194198",
day = "16",
month = dec,
year = "2006",
CODEN = "IFPLAT",
ISSN = "00200190 (print), 18726119 (electronic)",
ISSNL = "00200190",
bibdate = "Thu Mar 31 15:52:31 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = acknhfb,
fjournal = "Information Processing Letters",
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@Article{Putot:2004:SAB,
author = "Sylvie Putot and Eric Goubault and Matthieu Martel",
title = "Static AnalysisBased Validation of FloatingPoint
Computations",
journal = jLECTNOTESCOMPSCI,
volume = "2991",
pages = "306313",
year = "2004",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
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bibdate = "Wed Mar 10 06:51:00 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springeronline.com/3540212604",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
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@Article{Purtilo:1980:IAP,
author = "Jim Purtilo",
title = "On implementing arbitrary precision arithmetic in
{NIL}: an exercise in data abstraction",
journal = jSIGSAM,
volume = "14",
number = "1",
pages = "1418",
month = feb,
year = "1980",
CODEN = "SIGSBZ",
ISSN = "01635824 (print), 15579492 (electronic)",
ISSNL = "01635824",
bibdate = "Wed Oct 5 08:31:56 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "SIGSAM Bulletin",
issue = "??",
}À
/ å/‡2W #+Y=m;'ˆ
articlefparith.bibPawlak:1959:EDCZ. PawlakAn electronic digital computer based on the `$  2 $' system,Bull. Acad. Pol. Sci., Ser. Sci. Tech.77137221959Thu Nov 06 05:58:31 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:58:31 ???negative baseacknhfbZ. PawlakAn electronic digital computer based on the `$  2 $' system,
@Article{Pawlak:1959:EDC,
author = "Z. Pawlak",
title = "An electronic digital computer based on the `$  2 $'
system,",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "7",
number = "??",
pages = "713722",
month = "????",
year = "1959",
bibdate = "Thu Nov 06 05:58:31 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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}ŒY #+#57;u;1Me#9articlefparith.bibMuller:1959:CMGMervin E. MullerA Comparison of Methods for Generating Normal Deviates on Digital ComputersjJACM63376383jul71959JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Tue Nov 1 09:33:26 1994ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.01 09:33:26 ???Journal of the ACMCited in cite Sterbenz:1974:FPC.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Mervin E. MullerA Comparison of Methods for Generating Normal Deviates on Digital Computers
@Article{Muller:1959:CMG,
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title = "A Comparison of Methods for Generating Normal Deviates
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journal = jJACM,
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}Œ{Y #/M;a7E‚;]MŽarticlefparith.bibPfeiffer:1959:FQMPaul E. PfeifferA FourQuadrant Multiplier Using Triangular Waves, Diodes, Resistors, and Operational AmplifiersjIRETRANSELECCOMPUTEC82222227jun61959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.521952603679950 OR 03679950Thu Jul 14 15:56:45 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:45 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526IRE Transactions on Electronic ComputersacknhfbPaul E. PfeifferA FourQuadrant Multiplier Using Triangular Waves, Diodes, Resistors, and Operational Amplifiers
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title = "Binary Conversion, with Fixed Decimal Precision, of a
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8¨8’lX #'g57E‚;‡'5O'g”karticlefparith.bibWensley:1959:CNAJ. H. WensleyA Class of NonAnalytical Iterative ProcessesjCOMPJ14163167jan11959CMPJA600104620 (print), 14602067 (electronic) OR 00104620 (print), 14602067 (electronic)00104620 OR 00104620Fri Sep 29 08:55:07 MDT 2000Compiler/semantics.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/2000.09.29 08:55:07 MDThttp://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.tifThe Computer Journalacknhfbhttp://comjnl.oxfordjournals.org/J. H. WensleyA Class of NonAnalytical Iterative Processes
@Article{Wensley:1959:CNA,
author = "J. H. Wensley",
title = "A Class of NonAnalytical Iterative Processes",
journal = jCOMPJ,
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number = "4",
pages = "163167",
month = jan,
year = "1959",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
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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 = acknhfb,
fjournal = "The Computer Journal",
journalURL = "http://comjnl.oxfordjournals.org/",
}ˆTV #+%e;7;K;]%i‰]articlefparith.bibVolder:1959:CTCJ. E. VolderThe CORDIC Trigonometric Computing TechniquejIRETRANSELECCOMPUTEC85330334sep91959IRELAO03679950 OR 03679950Thu Sep 1 10:15:31 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:31 ???IRE Transactions on Electronic ComputersacknjJ. E. VolderThe {CORDIC} Trigonometric Computing Technique
@Article{Volder:1959:CTC,
author = "J. E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "5",
pages = "330334",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IRE Transactions on Electronic Computers",
} 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 = acknhfb,
fjournal = "The Computer Journal",
journalURL = "http://comjnl.oxfordjournals.org/",
}š
aûaY #3'57Eƒ;Qo'ŽSarticlefparith.bibBockstaele:1960:NFAP. BockstaeleNotes on the First Arithmetics Printed in Dutch and EnglishjISIS513315321sep91960ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:28:03 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302265; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1960.bib2013.07.30 21:28:03 MDThttp://www.jstor.org/stable/226510Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlP. BockstaeleNotes on the First Arithmetics Printed in {Dutch} and {English}
@Article{Bockstaele:1960:NFA,
author = "P. Bockstaele",
title = "Notes on the First Arithmetics Printed in {Dutch} and
{English}",
journal = jISIS,
volume = "51",
number = "3",
pages = "315321",
month = sep,
year = "1960",
CODEN = "ISISA4",
ISSN = "00211753 (print), 15456994 (electronic)",
ISSNL = "00211753",
bibdate = "Tue Jul 30 21:28:03 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302265;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1960.bib",
URL = "http://www.jstor.org/stable/226510",
acknowledgement = acknhfb,
fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}ˆW '#)/E3=Em;/ˆ!mastersthesisfparith.bibYoung:1959:SSMJohn Mackay YoungA study of some methods of numerical integration using floating point arithmeticThesis (M.S. in Mathematics)Texas A.&M. CollegeCollege Station, TX, USA501959Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTacknhfbJohn Mackay YoungA study of some methods of numerical integration using floating point arithmetic
@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 = acknhfb,
}.;
j;w „î\…K‹
@Article{Egbert:1978:PCA,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {IV}: Logarithmic
Functions",
journal = jHEWLETTPACKARDJ,
volume = "29",
numbe ‡#ŽG
@Article{Edenfield:1990:PPD,
author = "R. W. Edenfield and M. G. Gallup and W. B. {Ledbetter,
Jr.} and R. C. McGarity and E. E. Quintana and R. A.
Reininger",
title = "The 68040 Processor. {Part} 1, Design and
Implementation",
journal = jIEEEMICRO,
volume = "10",
number = "1",
pages = "6678",
month = feb,
year = "1990",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/40.46770",
ISSN = "02721732 (print), 19374143 (electronic)",
ISSNL = "02721732",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEEE Micro",
journalURL = "http://www.computer.org/csdl/mags/mi/index.html",
} 8@†:Œu
@Article{Ercegovac:1987:FCR,
author = "M. D. Ercegovac and T. Lang",
title = "Onthefly conversion of redundant into conventional
representations",
journal = jIEEETRANSCOMPUT,
volume = "C36",
number = "7",
pages = "895897",
month = jul,
y\ˆ"E
@Article{Efstathiou:2005:EDM,
author = "C. Efstathiou and H. T. Vergos and G. Dimitrakopoulos
and D. Nikolos",
title = "Efficient diminished$1$ modulo $ 2^n + 1 $
multipliers",
journal = jIEEETRANSCOMPUT,
volume = "54",
number = "4",
pages = "491496",
month = apr,
year = "2005",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2005.63",
ISSN = •V‹F—
@Article{Emmart:2010:HPI,
author = "Niall Emmart and Charles Weems",
title = "High Precision Integer Addition, Subtraction and
Multiplication with a Graphics Processing Unit",
journal = jPARALLELPROCESSLETT,
volume = "20",
number = "4",
pages = "293306",
mon—ˆ
@Article{Elsayed:2015:NPE,
author = "Essam Elsayed and Hatem M. ElBoghdadi",
title = "A novel powerefficient multioperand digitmultiplier
using reconfiguration and clock gating",
journal = jJSUPERCOMPUTING,
volume = "71",
number = "7",
pages = "25392564",
month = jul,
year = "2015",
CODEN = "JOSUED",
DOI = "http://dx.doi.org/10.1007/s1122701514032",
ISSN = É
”z©u
@Article{Eisen:2007:IPA,
author = "L. Eisen and J. W. {Ward III} and H.W. Tast and N.
M{\"a}ding and J. Leenstra and S. M. Mueller and C.
Jacobi and J. Preiss and E. M. Schwarz and S. R.
Carlough",
title = "{IBM POWER6} accelerators: {VMX} and {DFU}",
journal = jIBMJRD,
volume = "51",
number = "6",
pages = "663683",
month = nov,
year = "2007",
CODEN = = …Š!
@Article{Edalat:1999:NIE,
author = "A. Edalat and M. Krznaric",
title = "Numerical Integration with Exact Real Arithmetic",
journal = jLECTNOTESCOMPSCI,
volume = "1644",
pages = "90??",
year = "1999",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Mon Sep 13 16:57:02 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/lncs1999b.bib",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}»
# Þ#‹7W #'%e;a7E‚;]%eŒ{articlefparith.bibCroy:1960:IADJohn E. CroyImproved Arrangement of a Decimal MultiplierjIRETRANSELECCOMPUTEC92263263jun61960IRELAOhttp://dx.doi.org/10.1109/TEC.1960.521983003679950 OR 03679950Thu Jul 14 15:34:11 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:34:11 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830IRE Transactions on Electronic ComputersacknhfbJohn E. CroyImproved Arrangement of a Decimal Multiplier
@Article{Croy:1960:IAD,
author = "John E. Croy",
title = "Improved Arrangement of a Decimal Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC9",
number = "2",
pages = "263263",
month = jun,
year = "1960",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1960.5219830",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}ŒY #));a7E‚;])Uarticlefparith.bibBrown:1960:EDCDavid T. BrownError Detecting and Correcting Binary Codes for Arithmetic OperationsjIRETRANSELECCOMPUTEC93333337sep91960IRELAOhttp://dx.doi.org/10.1109/TEC.1960.521985503679950 OR 03679950Thu Jul 14 15:34:12 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:34:12 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219855IRE Transactions on Electronic ComputersacknhfbDavid T. BrownError Detecting and Correcting Binary Codes for Arithmetic Operations
@Article{Brown:1960:EDC,
author = "David T. Brown",
title = "Error Detecting and Correcting Binary Codes for
Arithmetic Operations",
journal = jIRETRANSELECCOMPUT,
volume = "EC9",
number = "3",
pages = "333337",
month = sep,
year = "1960",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1960.5219855",
ISSN = "03679950",
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 = acknhfb,
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ââ
>ÑÚÀ–¬
@Article{Cmelik:1991:AMS,
author = "Robert F. Cmelik and Shing I. Kong and David R. Ditzel
and Edmund J. Kelly",
title = "An Analysis of {MIPS} and {SPARC} Instruction Set
Utilization on the {SPEC} Benchmarks",
journal = jSIGPLAN,
volume = "26",
number = "4",
pages = "290301 (or 290302??)",
month = apr,
year = "1991",
CODEN = "SINODQ",
ISSN = "03621340 (p"Œu™k
@Article{Cody:1964:DPS,
author = "W. J. {Cody, Jr.}",
title = "DoublePrecision Square Root for the {CDC3600}",
journal = jCACM,
volume = "7",
number = "12",
pages = "715718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/355588.365122",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 1 †Œ1
@Article{Cody:1971:DHC,
author = "W. J. Cody",
title = "Desirable Hardware Characteristics for Scientific
Computation",
journal = jSIGNUM,
volume = "6",
number = "1",
pages = "1631",
month = jan,
year = "1971",
CODEN = "SNEWD6",
DOI = "http://doi.acm.org/10.1145/1052614.1052616",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
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 = acknhfb,
fjournal = "ACM SIGNUM Newsletter",
xxtitle = "Hardware characteristics (pages missing from print)",
}%„b‰E
@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 = "411",
year = "1967",
bibdate = "Fri Aug 20 08:52:04 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/codywilliamj.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}qŽœ
@Article{Codenotti:1990:ATT,
author = "B. Codenotti and G. Lotti and F. Romani",
title = "Areatime tradeoffs for matrixvector
multiplication",
journal = jJPARDISTCOMP,
volume = "8",
number = "1",
pages = "5259",
month = jan,
year = "1990",
CODEN = "JPDCER",
ISSN = "07437315 (print), 10960848 (electronic)",
ISSNL = "07437315",
bibdate = "Sat Apr 12 19N‡Q#
@Article{Cody:1973:SDN,
author = "William J. {Cody, Jr.}",
title = "Static and Dynamic Numerical Characteristics of
FloatingPoint Arithmetic",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "6",
pages = "598601",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009112",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
acknowledgement = acknj,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH2",
}“
È £ÈW W #)!57Eƒ1;?c!articlefparith.bibGurzi:1960:HSMFred GurziA HighSpeed Multiplication Process for Digital ComputersjCACM34241245apr41960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:26 MST 2005http://dblp.unitrier.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.bib2005.11.25 18:19:26 MSTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Fred GurziA HighSpeed Multiplication Process for Digital Computers
@Article{Gurzi:1960:HSM,
author = "Fred Gurzi",
title = "A HighSpeed Multiplication Process for Digital
Computers",
journal = jCACM,
volume = "3",
number = "4",
pages = "241245",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.unitrier.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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Gurzi60",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gurzi60",
}ŒYY #+%57E‚5;??c%Ccarticlefparith.bibErcoli:1960:LEEPaolo ErcoliLetter to the Editor: Errors Due to Overflow in Arithmetic OperationsjCACM312A9A9dec121960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://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.bib2005.11.25 18:19:29 MSTSee cite Ercoli:1957:EDO.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Paolo ErcoliSee \cite{Ercoli:1957:EDO}.Letter to the {Editor}: {Errors} Due to Overflow in Arithmetic Operations
@Article{Ercoli:1960:LEE,
author = "Paolo Ercoli",
title = "Letter to the {Editor}: {Errors} Due to Overflow in
Arithmetic Operations",
journal = jCACM,
volume = "3",
number = "12",
pages = "A9A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}tp://dblp.unitrier.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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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‹x!X !#+%m%1Em;m9%mŒktechreportfparith.bibJensen:1960:CIFB. A. JensenCoding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functionsGroup report30G0009Massachusetts Institute of Technology, Lincoln LaboratoryLexington, MA, USA71960Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTTrigonometrical functions  Computer programs.Cover title. ``Millstone Hill Radar Station.'' ``1 November 1960.'' Air Force ContractacknhfbB. A. JensenCoding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functions
@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 = "30G0009",
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 = acknhfb,
keywords = "Trigonometrical functions  Computer programs.",
remark = "Cover title. ``Millstone Hill Radar Station.'' ``1
November 1960.'' Air Force Contract",
}i Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.unitrier.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 = acknhfb,
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€€š"[ #)+A57Eƒ[;‚7„q?c„q+‚WAœarticlefparith.bibKnuth:1960:INSDonald E. KnuthAn Imaginary Number SystemjCACM34245247apr41960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.9923\#B554C. B. HaselgroveFri Nov 25 18:19:26 MST 2005http://dblp.unitrier.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 database2005.11.25 18:19:26 MSTErrata, sl Communications of the ACM bf 4 (August 1961), 355 cite Knuth:1961:EIN. See cite Nadler:1961:DSR for extension to division and square root.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.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79For 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.Donald E. KnuthErrata, {\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.An Imaginary Number System
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–2g‡G%W #+Y=m;'ˆ'articlefparith.bibPawlak:1960:ODCZ. PawlakThe organization of a digital computer based on the `$  2 $' systemBull. Acad. Pol. Sci., Ser. Tech. Sci.82532581960Thu Nov 06 06:00:08 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 06:00:08 ???negative baseacknhfbZ. PawlakThe organization of a digital computer based on the `$  2 $' system
@Article{Pawlak:1960:ODC,
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title = "The organization of a digital computer based on the `$
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month = "????",
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acknowledgement = acknhfb,
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;A=+9‹Iarticlefparith.bibLowan:1960:PREbArnold N. LowanOn the Propagation of RoundOff Errors in the Numerical Treatment of the Wave EquationjMATHCOMPUT1471223228jul71960MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknhfbhttp://www.ams.org/mcom/Arnold N. LowanOn the Propagation of RoundOff Errors in the Numerical Treatment of the Wave Equation
@Article{Lowan:1960:PREb,
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@Article{Lowan:1960:PREa,
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@Article{Kunz:1981:QZ,
author = "W. Kunz",
title = "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
{Square Roots with the Z80 Microprocessor}
\endtoenglish",
journal = jELECTRONIK,
volume = "7",
pages = "109110",
year = "1981",
CODEN = "EKRKAR",
ISSN = "00135658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Elektronik",
} †kW
@Article{Kundu:1964:TMD,
author = "P. Kundu and S. Banerji",
title = "Transistorized Multiplier and Divider and Its
Applications",
journal = jIEEETRANSELECCOMPUT,
volume = "EC13",
number = "3",
pages = "288295",
month = jun,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263919",
ISSN = "03677508",
bibdate = "Thu Jul 14 06:57:00 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038157",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}¢KÅ
@Article{Kulisch:2011:VFE,
author = "Ulrich Kulisch",
title = "Very fast and exact accumulation of products",
journal = jCOMPUTING,
volume = "91",
number = "4",
pages = "397405",
month = apr,
year = "2011",
CODEN = "CMPTA2",
DOI = "http://dx.doi.org/10.1007/s006070100131y",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
bibdate = "Tue S1šBµ
@Article{Kulisch:2011:EDP,
author = "Ulrich Kulisch and Van Snyder",
title = "The exact dot product as basic tool for long interval
arithmetic",
journal = jCOMPUTING,
volume = "91",
number = "3",
pages = "307313",
month = mar,
year = "2011",
CODEN = "CMPTA2",
DOI = "http://dx.doi.org/10.1007/s0060701001277",
ISSN = "0010485X (print), 14365057 (electronic)",
.ˆ`‘A
@Article{Kumar:2006:ODS,
author = "Sandeep Kumar and T. Wollinger and C. Paar",
title = "Optimum Digit Serial {$ \mathrm {GF}(2^m) $}
Multipliers for CurveBased Cryptography",
journal = jIEEETRANSCOMPUT,
volume = "55",
number = "10",
pages = "13061311",
month = oct,
year = "2006",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2006.165",
ISSN = "0018934¬ŠN•
@Article{Kum:2000:ACO,
author = "KiIl Kum and Jiyang Kang and Wonyong Sung",
title = "{AUTOSCALER} for {C}: an optimizing floatingpoint to
integer {C} program converter for fixedpoint digital
signal processors",
journal = jIEEETRANSCIRCUITSSYST2,
volume = "47",
number = "9",
pages = "840848",
month = sep,
year = "2000",
CODEN = "ICSPE5",
DOI = "http:Š“x§q
@Article{Kulisch:1986:ADC,
author = "Ulrich W. Kulisch and Willard L. Miranker",
title = "The Arithmetic of the Digital Computer: a New
Approach",
journal = jSIAMREVIEW,
volume = "28",
number = "1",
pages = "140",
month = mar,
year = "1986",
CODEN = "SIREAD",
DOI = "http://dx.doi.org/10.1137/1028001",
ISSN = "00361445 (print), 10957200 (electronic)",
ISSNL =¦
$
S¢$³ˆ+
@Article{RodriguezHenriquez:2003:PMB,
author = "F. RodriguezHenriquez and {\c{C}}. K. Ko{\c{c}}",
title = "Parallel multipliers based on special irreducible
pentanomials",
journal = jIEEETRANSCOMPUT,
volume = "52",
number = "12",
pages = "15351542",
month = dec,
year = "2003",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2003.1252850",
ISSN = "001893% =
@Article{Roesler:2002:NOH,
author = "Eric Roesler and Brent Nelson",
title = "Novel Optimizations for Hardware FloatingPoint Units
in a Modern {FPGA} Architecture",
journal = jLECTNOTESCOMPSCI,
volume = "2438",
pages = "637646",
year = "2002",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2438.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/2438/24380637.htm;
http://link.springerny.com/link/service/series/0558/papers/2438/24380637.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}ëˆM‘
@Article{RodriguezHenriquez:2008:LCB,
author = "F. RodriguezHenriquez and G. MoralesLuna and J.
Lopez",
title = "LowComplexity BitParallel Square Root Computation
over {$ \mathrm {GF}(2^m) $} for All Trinomials",
journal = jIEEETRANSCOMPUT,
volume = "57",
number = "4",
pages = "472480",
month = apr,
year = "2008",
CODEN = "ITCOB4",
DOI = "http://dx.dE…/Š_
@Article{Rodrigues:1981:HEM,
author = "M. R. D. Rodrigues and J. H. P. Zurawski and J. B.
Gosling",
title = "Hardware evaluation of mathematical functions",
journal = jIEEPROCE,
volume = "128",
number = "4",
pages = "155164",
month = jul,
year = "1981",
CODEN = "IPETD3",
ISSN = "01437062",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEE proceedings, E: Computers and digital techniques",
}9„8ˆq
@Article{Robison:1983:USF,
author = "A. D. Robison",
title = "Use Squares for Fast Multiplication",
journal = jEDN,
volume = "28",
number = "21",
pages = "263, 267",
month = oct,
year = "1983",
CODEN = "EDNSBH",
ISSN = "00127515, 03646637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "EDN",
}†qc
@Article{Robertson:1979:VPA,
author = "D. A. Robertson",
title = "Variable precision arithmetic on {CDC 6000\slash 7000}
machines",
journal = jSPE,
volume = "9",
number = "3",
pages = "247248",
month = mar,
year = "1979",
CODEN = "SPEXBL",
DOI = "http://dx.doi.org/10.1002/spe.4380090310",
ISSN = "00380644 (print), 1097024X (electronic)",
ISSNL = "00380644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = acknhfb,
fjournal = "Software  Practice and Experience",
journalURL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097024X",
onlinedate = "27 Oct 2006",
}p
e e‰'V #)o57;m;?co‰warticlefparith.bibPerry:1960:CBFC. PerryConversion between floating point representationsjCACM32702741960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782352.68.0022\#8714Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79C. PerryConversion between floating point representations
@Article{Perry:1960:CBF,
author = "C. Perry",
title = "Conversion between floating point representations",
journal = jCACM,
volume = "3",
year = "1960",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "352.68.00",
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bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}x&Y#+I‚;'57Ek;A=I‚QŽGarticlefparith.bibPerlin:1960:HPCI. E. Perlin and J. R. GarrettHigh Precision Calculation of $ operatorname Arcsin x $, $ operatorname Arccos x $, and $ operatorname Arctan x $ (in Technical Notes and Short Papers)jMATHCOMPUT1471270274jul71960MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknjhttp://www.ams.org/mcom/I. E. Perlin and J. R. GarrettHigh Precision Calculation of $ \operatorname {Arcsin} x $, $ \operatorname {Arccos} x $, and $ \operatorname {Arctan} x $ (in {Technical Notes and Short Papers})
@Article{Perlin:1960:HPC,
author = "I. E. Perlin and J. R. Garrett",
title = "High Precision Calculation of $ \operatorname {Arcsin}
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¬
÷Z¬**Y #/)57E‚5;?Mc)articlefparith.bibSarafyan:1960:DCSDiran SarafyanDivisionless computation of square roots through continued squaringjCACM35319321may51960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.0022\#8639Fri Nov 25 18:19:26 MST 2005http://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.bib2005.11.25 18:19:26 MSTCommunications of the ACM$sqrt (x)$; elementary functionsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Diran SarafyanDivisionless computation of square roots through continued squaring
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = jCACM,
volume = "3",
number = "5",
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month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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ZMreviewer = "M. Lotkin",
}…)U %#3//#=m;//…;Nincollectionfparith.bibReitwiesner:1960:BAG. W. ReitwiesnerBinary arithmeticAlt:1960:AC2313081960Sat May 18 14:36:56 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:36:56 ???acknhfbG. W. ReitwiesnerBinary arithmetic
@InCollection{Reitwiesner:1960:BA,
author = "G. W. Reitwiesner",
title = "Binary arithmetic",
crossref = "Alt:1960:AC",
pages = "231308",
year = "1960",
bibdate = "Sat May 18 14:36:56 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}Š(W#'AG57;K;?cAG‹articlefparith.bibPope:1960:MPAD. A. Pope and M. L. SteinMultiple Precision ArithmeticjCACM312652654dec121960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:15:08 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:08 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79D. A. Pope and M. L. SteinMultiple Precision Arithmetic
@Article{Pope:1960:MPA,
author = "D. A. Pope and M. L. Stein",
title = "Multiple Precision Arithmetic",
journal = jCACM,
volume = "3",
number = "12",
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Š ½Š†/,U #/#I#=m;;#I‡articlefparith.bibSklansky:1960:CSAJ. SklanskyConditional Sum Addition LogicjTRANSIREEC92226230jun61960Fri Nov 09 19:17:08 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 19:17:08 ???Transactions of the IREacknhfbJ. SklanskyConditional Sum Addition Logic
@Article{Sklansky:1960:CSA,
author = "J. Sklansky",
title = "Conditional Sum Addition Logic",
journal = jTRANSIRE,
volume = "EC9",
number = "2",
pages = "226230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Transactions of the IRE",
}Œ?+Y #+'57E‚5;?ac'karticlefparith.bibSilver:1960:LERRoland SilverLetter to the Editor: Rounding in FloatingPoint ArithmeticjCACM312A9A9dec121960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://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.bib2005.11.25 18:19:29 MSTCommunications of the ACMfloatingpoint arithmetic; rounding errorsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Roland SilverLetter to the {Editor}: Rounding in FloatingPoint Arithmetic
@Article{Silver:1960:LER,
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title = "Letter to the {Editor}: Rounding in FloatingPoint
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journal = jCACM,
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CODEN = "CACMA2",
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title = "Sources and Development of Mathematical Software",
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address = pubPH:adr,
pages = "xii + 404",
year = "1984",
ISBN = "0138235015",
ISBN13 = "9780138235017",
LCCN = "QA76.95 .S68 1984",
bibdate = "Tue Dec 14 22:44:45 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "PrenticeHall Series in Computational Mathematics,
Cleve Moler, Advisor",
acknowledgement = acknhfb,
}¡…Š
@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 = "GauthierVillars",
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 = acknhfb,
language = "French",
}¬Ø
@Book{Copeland:2005:ATA,
editor = "B. Jack Copeland",
booktitle = "{Alan Turing}'s {Automatic Computing Engine}: the
master codebreaker's struggle to build the modern
computer",
title = "{Alan Turing}'s {Automatic Computing Engine}: the
master codebreaker's struggle to build the modern
computer",
publisher = pubOXFORD,
address = pubOXFORD:adr,
pages = "xx + 553",
yea „/ˆ_
@Book{Cody:1980:SME,
author = "W. J. Cody and W. Waite",
title = "Software Manual for the Elementary Functions",
publisher = pubPH,
address = pubPH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0138220646",
ISBN13 = "9780138220648",
LCCN = "QA331 .C635 1980",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
}ƒg‡O
@Book{Chow:1989:MRM,
editor = "Paul Chow",
title = "The {MIPSX RISC} Microprocessor",
publisher = pubKLUWER,
address = pubKLUWER:adr,
pages = "xxiv + 231",
year = "1989",
ISBN = "0792390458",
ISBN13 = "9780792390459",
LCCN = "QA76.8.M524 M57 1989",
bibdate = "Tue Dec 14 23:27:43 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}‡Œl™Y
@Book{ChaitinChatelin:1996:LFP,
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Frayss{\'e}",
title = "Lectures on Finite Precision Computations",
publisher = pubSIAM,
address = pubSIAM:adr,
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year = "1996",
ISBN = "0898713587",
ISBN13 = "9780898713589",
LCCN = "QA297 .C417 1996",
bibdate = "Wed Nov 16 14:38:30 MST 2005",
bibsource = "htt„u‰k
@Book{Cavanagh:1984:DCA,
author = "Joseph J. F. Cavanagh",
title = "Digital Computer Arithmetic: Design and
Implementation",
publisher = pubWILEY,
address = pubWILEY:adr,
pages = "xi + 468",
year = "1984",
ISBN = "0070102821",
ISBN13 = "9780070102828",
LCCN = "QA76.9.C62 C38 1984",
bibdate = "Sat May 18 14:16:35 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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price = "US\$21.95",
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bibsource = "http://dblp.unitrier.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;
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note = "See \cite{Sarafyan:1959:NMC}.",
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((TY #)#S57Eƒ1;C?c#GW‘karticlefparith.bibTraub:1960:CNMJ. F. TraubComments on a recent paper [``A New Method of Computation of Square Roots Without Using Division'']jCACM328686feb21960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:25 MST 2005http://dblp.unitrier.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.bib2005.11.25 18:19:25 MSTSee cite Sarafyan:1959:NMC.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79J. F. TraubSee \cite{Sarafyan:1959:NMC}.Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]
@Article{Traub:1960:CNM,
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h,h‹@/W #1+e!577=;7U+eŒmarticlefparith.bibWilkinson:1960:EAFJ. H. WilkinsonError Analysis of FloatingPoint ComputationjNUMMATH2319340dec121960NUMMA70029599X (print), 09453245 (electronic) OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599X65.00MR0116477 (22 \#7264)C. B. HaselgroveFri May 14 17:18:08 2010http://www.math.utah.edu/pub/bibnet/authors/w/wilkinsonjameshardy.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.05.14 17:18:08 ???Numerische Mathematikacknhfbhttp://link.springer.com/journal/211J. H. WilkinsonError Analysis of FloatingPoint Computation
@Article{Wilkinson:1960:EAF,
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title = "Error Analysis of FloatingPoint Computation",
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pages = "319340",
month = dec,
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CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
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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/wilkinsonjameshardy.bib;
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acknowledgement = acknhfb,
fjournal = "Numerische Mathematik",
journalURL = "http://link.springer.com/journal/211",
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articlefparith.bibWadey:1960:FAW. G. WadeyFloatingPoint ArithmeticsjJACM72129139apr41960JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541165.00 (68.00)22\#6090Fri Dec 08 14:44:46 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 14:44:46 ???Three types of floatingpoint arithmetics with error control are discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.Journal of the ACMCited in cite Sterbenz:1974:FPC.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401C. B. HaselgroveThree types of floatingpoint arithmetics with error control are discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.W. G. WadeyFloatingPoint Arithmetics
@Article{Wadey:1960:FA,
author = "W. G. Wadey",
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volume = "7",
number = "2",
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ISSN = "00045411 (print), 1557735X (electronic)",
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bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Three types of floatingpoint arithmetics with error
control are discussed and compared with conventional
floatingpoint arithmetic. General multiplication and
division shift criteria are derived (for any base) for
Metropolisstyle arithmetics. The limitations and most
suitable range of application for each arithmetic are
discussed.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
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note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220",
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z+z‡1U !#1==E[=m;M=ˆ techreportfparith.bibAnonymous:1961:MCMAnonymousModern Computing MethodsNotes on Applied Science16National Physical LaboratoryHer Majesty's Stationery Office, London2202221961Fri Aug 20 10:05:25 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 10:05:25 ???Cited in cite Sterbenz:1974:FPC.acknhfbAnonymousModern Computing Methods
@TechReport{Anonymous:1961:MCM,
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bibdate = "Fri Aug 20 10:05:25 2010",
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acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}‘Q0Z#)C#I)U57C‚;cKqYCg’{articlefparith.bibAmble:1961:AFPO. Amble and Jan V. GarwickOn the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp. 8788]jNORDISKTIDSKRINFORMBEHAND13220222sep91961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0193343400063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=3; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee cite Garwick:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543O. Amble and Jan V. GarwickSee \cite{Garwick:1961:AFP,Garwick:1961:RAF}.On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 8788]}
@Article{Amble:1961:AFP,
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title = "On the Accuracy of Floating Point Computers {[BIT {\bf
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pages = "220222",
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year = "1961",
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DOI = "http://dx.doi.org/10.1007/BF01933434",
ISSN = "00063835 (print), 15729125 (electronic)",
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bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=3;
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note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220",
acknowledgement = acknhfb,
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‘þ
î— €‘‘~£}
@Article{Croot:2004:ACC,
author = "Ernie Croot and RenCang Li and H. J. Hui June Zhu",
title = "The {\em abc\/} conjecture and correctly rounded
reciprocal square roots",
journal = jTHEORCOMPSCI,
volume = "315",
number = "23",
pages = "405417",
day = "6",
month = may,
year = "2004",
CODEN = "TCSCDI",
ISSN = "03043975 (print), 18792294 (electronic)",
ISSN„‰{
@Article{Crockett:1955:GMM,
author = "J. B. Crockett and H. Chernoff",
title = "Gradient Methods of Maximization",
journal = jPACJMATH,
volume = "5",
number = "??",
pages = "3350",
year = "1955",
CODEN = "PJMAAI",
ISSN = "00308730 (print), 19455844 (electronic)",
ISSNL = "00308730",
bibdate = "Fri Aug 20 08:54:24 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Pacific Journal of Mathematics",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}V„
ˆ
@Article{Crenshaw:1995:PTFa,
author = "Jack W. Crenshaw",
title = "Programmer's Toolbox: FloatingPoint Math",
journal = jEMBEDSYSPROG,
volume = "8",
number = "11",
pages = "25??",
year = "1995",
CODEN = "EYPRE4",
ISSN = "10403272",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Embedded Systems Programming",
}Š„ˆ%
@Article{Crenshaw:1995:PTFb,
author = "Jack W. Crenshaw",
title = "Programmer's Toolbox: FloatingPoint Math, Part 2",
journal = jEMBEDSYSPROG,
volume = "8",
number = "12",
pages = "29??",
year = "1995",
CODEN = "EYPRE4",
ISSN = "10403272",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Embedded Systems Programming",
}‹„w‰o
@Article{CrisansanZverca:1967:PED,
author = "Mariana Cri{\c{s}}anZverca",
title = "Pseudooperations of an electronic digital machine
with floating point. ({Romanian})",
journal = jSTUDCERCETMAT,
volume = "19",
pages = "14131424",
year = "1967",
ISSN = "00394068, 05676401",
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 = acknhfb,
fjournal = "Studii {\c{s}}i cercet{\u{a}}ri Matematice",
}s„U‰+
@Article{Crenshaw:1998:ISR,
author = "Jack W. Crenshaw",
title = "Integer Square Roots",
journal = jEMBEDSYSPROG,
volume = "11",
number = "2",
pages = "1532",
month = feb,
year = "1998",
CODEN = "EYPRE4",
ISSN = "10403272",
bibdate = "Fri Nov 28 16:31:58 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.embedded.com/98/9802fe2.htm",
acknowledgement = ackmfc # " and " # acknhfb,
fjournal = "Embedded Systems Programming",
}4„ˆ!
@Article{Crenshaw:1996:PTF,
author = "Jack W. Crenshaw",
title = "Programmer's Toolbox: FloatingPoint Math, Part 3",
journal = jEMBEDSYSPROG,
volume = "9",
number = "1",
pages = "19??",
year = "1996",
CODEN = "EYPRE4",
ISSN = "10403272",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Embedded Systems Programming",
}
"VûêŒV
÷"³ ³†0Œa
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "2",
pages = "140147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5219515",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Œ&>š}
@Article{Ganesan:1996:CSM,
author = "Ravikanth Ganesan and Kannan Govindarajan and MinYou
Wu",
title = "Comparing {SIMD} and {MIMD} Programming Modes",
journal = jJPARDISTCOMP,
volume = "35",
number = "1",
pages = "9196",
day = "25",
month = may,
year = "1996",
CODEN = "JPDCER",
DOI = "http://dx.doi.org/10.1006/jpdc.1996.0071",
ISSN = "07437315 (pr¬£†_?
@Article{Gavrilova:2009:ESC,
author = "Marina L. Gavrilova",
title = "An Explicit Solution for Computing the Vertices of the
{Euclidean} $d$Dimensional {Voronoi} Diagram of
Spheres in a FloatingPoint Arithmetic",
journal = jINTJCOMPUTGEOMAPPL,
volume = "19",
number = "5",
pages = "415424",
month = oct,
year = "2009",
CODEN = "IJCAEV",
DOI = "http://dx.doi.org/10.1142/S0218195909003040",
ISSN = "02181959",
bibdate = "Mon Aug 30 10:25:06 MDT 2010",
bibsource = "http://ejournals.wspc.com.sg/ijcga/;
…O‹
@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 = "133139",
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 = acknhfb,
reviewer = "R. N. Goss",
}íUˆ}‘{
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "2",
pages = "8788",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01939221",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate º,†Œ!
@Article{Gallant:1990:MCI,
author = "John Gallant and Bill Travis",
title = "Math coprocessor {ICs}: Floatingpoint chips boost
{muP} performance",
journal = jEDN,
volume = "35",
number = "12",
pages = "63??",
month = jun,
year = "1990",
CODEN = "EDNSBH",
ISSN = "00127515, 03646637",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floatingpoint arithmetic exacts huge penalties in CPU
computation time. Dedicated coprocessor ICs execute
this onerous task automatically and efficiently.",
acknowledgement = acknhfb,
fjournal = "EDN",
} =¾
ÚAæ¾…K‹
@Article{Barany:1988:FEI,
author = "T. E. Barany",
title = "Fast evaluation of integer roots in micG„M‰
@Article{Anonymous:1993:FPe,
author = "Anonymous",
title = "Floating Point",
journal = jCOMPUTAIDEDENG,
volume = "12",
number = "11",
pages = "42??",
month = nov,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "07333536",
ISSNL = "07333536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Cost Benefits CAD/CAM.",
acknowledgement = acknhfb,
fjournal = "Computeraided engineering: CAE",
})ˆp‘a
@Article{Aridgides:1985:EIQ,
author = "A. Aridgides and D. Morgan",
title = "Effects of input quantization in floatingpoint
digital pulse compression",
journal = jIEEETRANSACOUSTSPEECH,
volume = "33",
number = "2",
pages = "434435",
month = apr,
year = "1985",
CODEN = "IETABA",
ISSN = "00963518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://“m‡Ž
@Article{Anonymous:2007:CPSb,
author = "Anonymous",
title = "Call for Papers for Special Section on Computer
Arithmetic",
journal = jIEEETRANSCOMPUT,
volume = "56",
number = "2",
pages = "287287",
month = feb,
year = "2007",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2007.22",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Mon Jul 4 15:03:37 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/ieeetranscomput2000.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}.W‡Ž/
@Article{Anonymous:1893:IDb,
author = "Anonymous",
title = †U+
@Article{Ambikairajah:1980:TPM,
author = "E. Ambikairajah and M. J. Carey",
title = "Technique for Performing Multiplication on a 16bit
Microprocessor Using an Extension of {Booth}'s
Algorithm",
journal = jELECTLETTERS,
volume = "16",
number = "2",
pages = "5354",
month = jan,
year = "1980",
CODEN = "ELLEAK",
ISSN = "00135194 (print), 1350911X (electronic)",
ISSNL = "00135194",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Electronics Letters",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}€‡9Žs
@Article{Akbarpour:2002:FCS,
author = "Behzad Akbarpour and Abdelkader Dekdouk and
Sofi{\`e}ne Tahar",
title = "Formalization of Cadence {SPW} FixedPoint Arithmetic
in {HOL}",
journal = jLECTNOTESCOMPSCI,
volume = "2335",
pages = "185??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Tue Sep 10 19:09:38 MDT 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2335.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/2335/23350185.htm;
http://link.springerny.com/link/service/series/0558/papers/2335/23350185.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
}{
ù×<FÛ
ù7‡Ž
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division of Scales before the Metric System",
journal = jISIS,
volume = "25",
number = "2",
pages = "433436",
month = sep,
year = "1936",
CODEN = "ISISA4",
ISSN = "00211753 (print), 15456994 (electroô…\‹9
@Article{Brent:1982:RLP,
author = "R. P. Brent and H. T. Kung",
title = "A regular layout for parallel adders",
journal = jIEEETRANSCOMPUT,
volume = "C31",
number = "??",
pages = "260264",
year = "1982",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1982.1675982",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Mon Sep 16 16:06:24 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}^`„e‰K
@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/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
}B…S‹'
@Article{Barsi:1991:MAB,
author = "Ferruccio Barsi",
title = "Mod $m$ arithmetic in binary systems",
journal = jINFOPROCLETT,
volume = "40",
number = "6",
pages = "303309",
year = "1991",
CODEN = "IFPLAT",
ISSN = "00200190 (print), 18726119 (electronic)",
ISSNL = "00200190",
MRclass = "68M07 (68Q35)",
MRnumber = "MR1156823 (92m:68009)",
bibdate = "Thu Nov 8 14:50:34 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Information Processing Letters",
journalURL = "http://www.sciencedirect.com/science/journal/00200190",
} ‡hQ
@Article{Brosnan:1988:MED,
author = "T. J. Brosnan and N. R. {Strader II}",
title = "Modular error detection for bitserial
multiplication",
journal = jIEEETRANSCOMPUT,
volume = "37",
number = "9",
pages = …K‹
@Article{Barany:1988:FEI,
author = "T. E. Barany",
title = "Fast evaluation of integer roots in microcontroller
systems",
journal = jMICROPROCMICROSYS,
volume = "12",
number = "6",
pages = "341344",
month = jul # "" # aug,
year = "1988",
CODEN = "MIMID5",
ISSN = "01419331 (print), 18729436 (electronic)",
ISSNL = "01419331",
bibdate = "Fri Dec 08 13:06:02 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Microprocessors and Microsystems",
}ï
G;žw
@Article{Boisvert:1987:AAH,
author = "Ronald F. Boisvert",
title = "{Algorithm 651}: Algorithm {HFFT}\emdash HighOrder
FastDirect Solution of the {Helmholtz} Equation",
journal = jTOMS,
volume = "13",
number = "3",
pages = "235249",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/29380.214342",
ISSN = "00983500 (print), 15577295á
Ë ËŒ12Y #11
;a7E‚;]=
iarticlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSignedDigit Number Representations for Fast Parallel ArithmeticjIRETRANSELECCOMPUTEC103389400sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521922703679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227IRE Transactions on Electronic ComputersacknhfbAlgirdas Avi{\v{z}}ienisSignedDigit Number Representations for Fast Parallel Arithmetic
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
title = "SignedDigit Number Representations for Fast Parallel
Arithmetic",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "3",
pages = "389400",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219227",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}T 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, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}³
MM/3Y #+5{;a7E‚;Š=]Š=5{›7articlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number SystemjIRETRANSELECCOMPUTEC1016370mar31961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521915403679950 OR 03679950Thu Jul 14 14:45:02 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:02 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154A system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog 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.IRE Transactions on Electronic ComputersacknhfbA system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog 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.Philip Warren CheneyA Digital Correlator Based on the Residue Number System
@Article{Cheney:1961:DCB,
author = "Philip Warren Cheney",
title = "A Digital Correlator Based on the Residue Number
System",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "1",
pages = "6370",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219154",
ISSN = "03679950",
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, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
[[‰!4V #/)c57=m;?c)cŠarticlefparith.bibClarkson:1961:DMIW. K. ClarksonA Divisionless Method of Integer ConversionjCACM47315316jul71961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 08:14:59 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:59 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79W. K. ClarksonA Divisionless Method of Integer Conversion
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Method of Integer Conversion",
journal = jCACM,
volume = "4",
number = "7",
pages = "315316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/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 = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision additionsubtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}µ
''U5Y #%I[]57=ƒ;Š?cŠI[›Warticlefparith.bibCox:1961:NMPAlbert G. Cox and H. A. LutherA Note on Multiple Precision ArithmeticjCACM48353353aug81961CACMA2http://doi.acm.org/10.1145/366678.36669300010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Sat Dec 03 14:07:44 2005ftp://garbo.uwasa.fi/pc/docsoft/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.bib2005.12.03 14:07:44 ???Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision additionsubtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a pm b = (a_0 pm b_0) + (a_1 pm b_1)t + cdots + (a_n pm b_n)t^n$. Here $ a_i pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision additionsubtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a \pm b = (a_0 \pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$. Here $ a_i \pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.Albert G. Cox and H. A. LutherA Note on Multiple Precision Arithmetic
@Article{Cox:1961:NMP,
author = "Albert G. Cox and H. A. Luther",
title = "A Note on Multiple Precision Arithmetic",
journal = jCACM,
volume = "4",
number = "8",
pages = "353353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/366678.366693",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/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 = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision additionsubtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
{ˆ[7W #'!=m;+'‹
articlefparith.bibFreiman:1961:SACC. V. FreimanStatistical analysis of certain binary division algorithmsjIREPROC49191103jan11961Mon Sep 16 16:12:21 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.09.16 16:12:21 ???IRE ProceedingsacksfoC. V. FreimanStatistical analysis of certain binary division algorithms
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = jIREPROC,
volume = "49",
number = "1",
pages = "91103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
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.",
}6Y #'%];a7E‚;]%]Žarticlefparith.bibCroy:1961:RTMJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix ArithmeticjIRETRANSELECCOMPUTEC104777777dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521928603679950 OR 03679950Thu Jul 14 14:45:05 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:05 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286IRE Transactions on Electronic ComputersacknhfbJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix Arithmetic
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine BinarytoDecimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "777777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219286",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
Ù
€
0êû‡ti
@Article{Ferro:1986:DTF,
author = "F. Ferro",
title = "{DSP} tackles floatingpoint arithmetic",
journal = jCOMPDESIGN,
volume = "25",
number = "15",
pages = "5356",
day = "15",
month = aug,
year = "1986",
CODEN = "CMPDAM",
ISSN = "00104566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CDROM database (1991);
http://wwˆ)
@Article{Ferrari:1969:CDM,
author = "D. Ferrari",
title = "Correction to {``A Division Method Using a Parallel
Multiplier''}",
journal = jIEEETRANSCOMPUT,
volume = "C18",
number = "10",
pages = "960960",
month = oct,
year = "1969",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1969.222555",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL =ÄŽ7œo
@Article{Ferrari:1967:DMU,
author = "Domenico Ferrari",
title = "A Division Method Using a Parallel Multiplier",
journal = jIEEETRANSELECCOMPUT,
volume = "EC16",
number = "2",
pages = "224226",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1967.264580",
ISSN = "03677508",
bibdate = "Wed Jul 13 21:15:02 MDT 2011",
bibsource = "v”K©
@Article{Fernandez:2003:FPA,
author = "Jos{\'e}Jes{\'u}s Fern{\'a}ndez and Inmaculada
Garc{\'\i}a and Ester M. Garz{\'o}n",
title = "Floating point arithmetic teaching for computational
science",
journal = jFUTGENCOMPSYS,
volume = "19",
number = "8",
pages = "13211334",
month = nov,
year = "2003",
CODEN = "FGSEVI",
ISSN = "0167739X (print), 18727115 (eÅ„U‰+
@Article{Fenwick:1972:BRD,
author = "Peter M. Fenwick",
title = "A Binary Representation for Decimal Numbers",
journal = jAUSTRALIANCOMPJ,
volume = "4",
number = "4",
pages = "146149",
month = nov,
year = "1972",
CODEN = "ACMJB2",
ISSN = "00048917",
bibdate = "Fri Nov 28 11:31:38 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Australian Computer Journal",
keywords = "decimal floatingpoint arithmetic",
}[†N
@Article{Ferguson:1991:SMC,
author = "Warren E. {Ferguson, Jr.}",
title = "Selecting math coprocessors",
journal = jIEEESPECTRUM,
volume = "28",
number = "7",
pages = "3841",
month = jul,
year = "1991",
CODEN = "IEESAM",
DOI = "http://dx.doi.org/10.1109/6.83469",
ISSN = "00189235 (print), 19399340 (electronic)",
ISSNL = "00189235",
bibdate = "Thu Sep 01 16:17:34 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Spectrum",
keywords = "floatingpoint arithmetic",
remark = "Contains performancecomparison tables for Cyrix,
Intel, Motorola, and Weitek floatingpoint coprocessor
chips.",
} Ý„~‰}
@Article{Ferguson:1984:SFP,
author = "Kenneth M. Ferguson",
title = "{Savage} floatingpoint benchmark deficiencies of in
{16BST}",
journal = jDDJ,
volume = "9",
number = "8",
pages = "107??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}@ibdate = "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 = acknhfb,
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..",
}¸His work was supported by this contract, and led to the Ph.D..acknhfbThe 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.H. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computers
@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 = "61483",
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 = acknhfb,
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..",
}
°g8\!#+[U51=m;#Žy‹Žy[Uw
techreportfparith.bibGarner:1961:RNSH. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computersASD Technical Report61483Electronic Technology Laboratory, The University of MichiganAnn Arbor, MI, USA91103oct101961Thu Nov 18 09:27:06 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:27:06 ???http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txtThe 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.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. ¸= "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&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=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}¹
¨:Y #'AI)57=I;_qY'cK[articlefparith.bibGarwick:1961:RAFJ. V. GarwickReply to ``On the Accuracy of Floating Point Computers'' [BIT bf 1(3), 1961, pp. 220221]jNORDISKTIDSKRINFORMBEHAND132222221961BITTEL, NBITAB00063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Mon Nov 16 14:36:22 1998http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.11.16 14:36:22 ???See cite Garwick:1961:AFP,Amble:1961:AFP.floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543J. V. GarwickSee \cite{Garwick:1961:AFP,Amble:1961:AFP}.Reply to {``On the Accuracy of Floating Point Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "3",
pages = "222222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
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 = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}T9Z #)]I)U57C‚;
IqY)]‘{articlefparith.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point ComputersjNORDISKTIDSKRINFORMBEHAND128788jun61961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0193922100063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee also comment and reply cite Amble:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543Jan V. GarwickSee also comment and reply \cite{Amble:1961:AFP,Garwick:1961:RAF}.The Accuracy of Floating Point Computers
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "2",
pages = "8788",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01939221",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&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=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}.bib",
abstract = "Error checking codes based on residues have the
advantage over paritybased codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect bursttype errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
singledigit error in a decimal operation.",
acknowledgement = acknhfb,
keywords = "decimal arithmetic",
}»
Q5Q‹`W#EO;a7E‚;]ESarticlefparith.bibKovatch:1961:HEAG. Kovatch and W. E. MeserveThe HallEffect Analog MultiplierjIRETRANSELECCOMPUTEC103512515sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521924003679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240IRE Transactions on Electronic ComputersacknhfbG. Kovatch and W. E. MeserveThe {HallEffect} Analog Multiplier
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {HallEffect} Analog Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "3",
pages = "512515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219240",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Šo=W #)+Y57=S;=?c+A]‹warticlefparith.bibKnuth:1961:EINDonald E. KnuthErrata: ``An imaginary number system''jCACM48355355aug81961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Tue Jan 09 07:10:22 1996http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.01.09 07:10:22 ???See cite Knuth:1960:INS.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Donald E. KnuthSee \cite{Knuth:1960:INS}.Errata: {``An imaginary number system''}
@Article{Knuth:1961:EIN,
author = "Donald E. Knuth",
title = "Errata: {``An imaginary number system''}",
journal = jCACM,
volume = "4",
number = "8",
pages = "355355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
Õ ®Õ‡U@U #1+_!=m;]++a_ˆarticlefparith.bibMacSorley:1961:HSAO. L. MacSorleyHighspeed arithmetic in binary computersjIREPROC496791jan11961Sat May 18 14:34:55 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:34:55 ???Reprinted in cite Swartzlander:1976:CDD.IRE ProceedingsacknhfbO. L. MacSorleyReprinted in \cite{Swartzlander:1976:CDD}.Highspeed arithmetic in binary computers
@Article{MacSorley:1961:HSA,
author = "O. L. MacSorley",
title = "Highspeed arithmetic in binary computers",
journal = jIREPROC,
volume = "49",
number = "??",
pages = "6791",
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 = acknhfb,
fjournal = "IRE Proceedings",
}ŒN?Y#+9#;a7E‚;]9#uarticlefparith.bibLehman:1961:STHM. Lehman and N. BurlaSkip Techniques for HighSpeed CarryPropagation in Binary Arithmetic UnitsjIRETRANSELECCOMPUTEC104691698dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521927403679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274IRE Transactions on Electronic ComputersacknhfbM. Lehman and N. BurlaSkip Techniques for HighSpeed CarryPropagation in Binary Arithmetic Units
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for HighSpeed CarryPropagation in
Binary Arithmetic Units",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "691698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219274",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}date = "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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}Á
AY #+' 57E‚5;=?Mc'A qarticlefparith.bibNadler:1961:DSRMorton NadlerDivision and square root in the quaterimaginary number systemjCACM44192193apr41961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.9923\#B555Fri Nov 25 18:19:32 MST 2005http://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.bib2005.11.25 18:19:32 MSTSee cite Knuth:1960:INS.Communications of the ACM$sqrt (x)$; elementary functionsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Morton NadlerSee \cite{Knuth:1960:INS}.Division and square root in the quaterimaginary number system
@Article{Nadler:1961:DSR,
author = "Morton Nadler",
title = "Division and square root in the quaterimaginary
number system",
journal = jCACM,
volume = "4",
number = "4",
pages = "192193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}/links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2T",
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 = acknhfb,
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 nontrivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of roundoff 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}.",
}Âstants 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.Roger S. PinkhamOn the Distribution of First Significant Digits
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = jANNMATHSTAT,
volume = "32",
number = "4",
pages = "12231230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "00034851",
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=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2T",
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 = acknhfb,
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 nontrivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of roundoff 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}.",
}
f×fˆmCV #3'C57=m;?c'C‰uarticlefparith.bibRabinowitz:1961:MPDP. RabinowitzMultiplePrecision DivisionjCACM429898feb21961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 00:29:25 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 00:29:25 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79P. RabinowitzMultiplePrecision Division
@Article{Rabinowitz:1961:MPD,
author = "P. Rabinowitz",
title = "MultiplePrecision Division",
journal = jCACM,
volume = "4",
number = "2",
pages = "9898",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}´BY #k+!7=m;CŽmOsŽ7Žuk³5articlefparith.bibPinkham:1961:DFSRoger S. PinkhamOn the Distribution of First Significant DigitsjANNMATHSTAT32412231230dec121961AASTAD00034851 OR 00034851Thu Feb 15 15:07:57 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 15:07:57 ???http://links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2TIt 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.Annals of Mathematical StatisticsBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom 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 nontrivial mathematical result, for the variable $n$ is discrete.''.par From p. 1230: ``The foregoing results bear on questions of roundoff in computing machines. Since $ d(u v) = u d v + v d u $, the error resulting from multiplying two rounded numbers will be governed primarily by the first significant digits of the two numbers being multiplied. Now the distribution of first significant digits, favoring as it does low order digits, tends to produce less error than would be the case if first significant digits were uniform as has sometimes been assumed.''par Cited in cite Sterbenz:1974:FPC.acknhfbIt has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are more physical conÄ
—q ©Îq—†$ŒI
@Article{Ruess:1999:MVS,
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@Article{Rudra:2001:ERE,
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Composite Field Arithmetic",
journal = jLECTNOTESCOMPSCI,
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@Article{Rudeanu:1976:SRF,
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GX #'!O%1%=m;†M!†MSEbookfparith.bibTaub:1961:JNCA. H. TaubJohn von Neumann: Collected WorkspubPERGAMONpubPERGAMON:adr??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol. 4), ??? (vol. 5), ??? (vol. 6)1961  1963Wed Jun 01 16:58:29 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 16:58:29 ???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).acknhfbA. H. TaubSix 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).{John von Neumann}: Collected Works
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}‹\FY #1%[57=K;1e%[ŒGarticlefparith.bibSpielberg:1961:RPSK. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued FractionsjJACM84613627oct101961JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Sat Dec 09 14:01:44 1995ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.09 14:01:44 ???Journal of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J401K. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractions
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;A=;5‹Warticlefparith.bibThacher:1961:ISRHenry C. Thacher, Jr.Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic CosinejMATHCOMPUT1576399403oct101961MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknhfbhttp://www.ams.org/mcom/Henry C. {Thacher, Jr.}Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
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hundred twentytwo 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
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bibliography, and a complete glossary of computer
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acknowledgement = ackmfc # " and " # acknhfb,
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H·‰!MV %#/)+c=+3%=%;M)g+=Šincollectionfparith.bibCampbell:1962:FPOS. G. CampbellWerner BuchholzPlanning a Computer System: Project StretchFloatingPoint OperationpubMCGRAWHILLpubMCGRAWHILL:adr921211962QA76.8.I2 I5Wed Feb 14 17:24:27 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2007.02.14 17:24:27 ???IBM 7030 (Computer); IBM Stretchacknhfb322S. G. CampbellPlanning a Computer System: {Project Stretch}Werner BuchholzFloatingPoint Operation
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acknowledgement = acknhfb,
}‹aJW#+GY;a7E‚;]GY articlefparith.bibWilson:1961:ARBJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary DivisionjIRETRANSELECCOMPUTEC104662670dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521927103679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271IRE Transactions on Electronic ComputersacknhfbJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary Division
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "662670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219271",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Ð
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://edthelen.org/comphist/IBM7030PlanningMcJones.pdf",
acknowledgement = acknhfb,
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 floatingpoint 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 ndigit 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). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisymode 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 builtin 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 noisymode 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 fixedpoint arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
Ñ fixedpoint 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 fixedpoint arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixedpoint
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 fixedpoint operands do
give correct significance indications, the use of other
operations and of builtin scaling loops frequently
destroys entirely the leadingzeros 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. Highspeed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Indexarithmetic Unit 21 \\
3.10. Instruction Lookahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radixconversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Indexarithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. InputOutput 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 \Ò\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Taperecording Convention 71 \\
6.15. Cardpunching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variablefieldlength Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variablefieldlength 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. Radixconversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floatingpoint Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixedpoint Arithmetic 92 \\
8.2. Floatingpoint Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floatingpoint Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Roundoff Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floatingpoint Arithmetic 103 \\
8.9. Structure of Floatingpoint Data 104 \\
Floatingpoint Features of the 7030 \\
8.10. Floatingpoint Instruction Format 106 \\
8.11. Floatingpoint Data Formats 106 \\
8.12. Singular Floatingpoint Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floatingpointarithmetic Operations 114 \\
8.17. Fixedpoint Arithmetic Using Unnormalized \\
Floatingpoint Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multipleprecision 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 Singleaddress 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. Programinterrupt System 136 \\
10.6. Components of the Programinterrupt System 137
\\
10.7. Examples of Programinterrupt 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 \\
Ó 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. Recordhandling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. InputOutput Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
InputOutput and External Storage 179 \\
12.2. InputOutput 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 InputOutput 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 Lookahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timingsimulation Program 230 \\
15.3. Description of the Lookahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Lookback at the Lookahead 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 Setup Mode 258 \\
17.3. Bytesequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTEBYBYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Lookup Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Storedprogram 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. Cuberoot Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floatingpoint Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}ÌÕects.http://edthelen.org/comphist/IBM7030PlanningMcJones.pdfThe 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 floatingpoint 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 ndigit 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). So all numbers tend to be too large in absolute value. The true value, if there had been no significance loss, should lie between these two extremes. Hence, two runs, one made without and one made with the noisy mode, should show differences in result that indicate which digits may have been affected by significance loss. The principal weakness of the noisymode 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 builtin 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 noisymode 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 fixedpoint arithmetic. In other words, the contention is not that normalized FLP arithmetic is more prone to significance loss than equivalent fixedpoint 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 fixedpoint arithmetic; multiplication and division do not handle it at all correctly by means of leading zeros. (In particular, fixedpoint 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 fixedpoint operands do give correct significance indications, the use of other operations and of builtin scaling loops frequently destroys entirely the leadingzeros method of counting significance.)''Computer architectureForeword 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. Highspeed Disk Units 20 3.7. Central Processing Unit 20 3.8. Instruction Controls 21 3.9. Indexarithmetic Unit 21 3.10. InstrÖuction Lookahead 21 3.11. Arithmetic Unit 22 3.12. Instruction Set 24 3.13. Data Arithmetic 24 3.14. Radixconversion Operations 27 3.15. Connective Operations 27 3.16. Indexarithmetic Operations 27 3.17. Branching Operations 28 3.18. Transmission Operations 28 3.19. InputOutput 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. Taperecording Convention 71 6.15. Cardpunching Convention 71 6.16. List of 7030 Character Set 72 7. Variablefieldlength Operation 75 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 7.1. Introduction 75 7.2. Addressing of Variablefieldlength 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. Radixconversion Operation 87 7.13. Logical Connectives of Two Variables 87 7.14. Connective Operations 89 8. Floatingpoint Operation 92 [by S. G. Campbell] General Discussion 8.1. Problems of Fixedpoint Arithmetic 92 8.2. Floatingpoint Arithmetic 94 8.3. Normalization 97 8.4. Floatingpoint Singularities 98 8.5. Range and Precision 99 8.6. Roundoff Error 100 8.7. Significance Checks 101 8.8. Forms of Floatingpoint Arithmetic 103 8.9. Structure of Floatingpoint Data 104 Floatingpoint Features of the 7030 8.10. Floatingpoint Instruction Format 106 8.11. Floatingpoint Data Formats 106 8.12. Singular Floatingpoint Numbers 108 8.13. Indicators 112 8.14. Universal Accumulator 113 8.15. Fraction Arithmetic 114 8.16. Floatingpointarithmetic Operations 114 8.17. Fixedpoint Arithmetic Using Unnormalized Floatingpoint Operations 118 8.18. Special Functions and Forms of Arithmetic 119 8.19. Multipleprecision 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 Singleaddress 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. Programinterrupt System 136 10.6. Components of the Programinterrupt System 137 10.7. Examples of Programinterrupt 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. Recordhandling Applications 172 11.14. File Maintenance 175 11.15. Subroutine Control 177 11.16. Conclusion 178 12. InputOutput Control 179 [by W. Buchholz] 12.1. A Generalized Approach to Connecting InputOutput and External Storage 179 12.2. InputOutput ×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 InputOutput 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 Lookahead Unit 228 [by R. S. Balance, J. Cocke, and H. G. Kolsky] 15.1. General Description 228 15.2. Timingsimulation Program 230 15.3. Description of the Lookahead Unit 238 15.4. Forwarding 240 15.5. Counter Sequences 241 15.6. Recovery after Interrupt 246 15.7. A Lookback at the Lookahead 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 Setup Mode 258 17.3. Bytesequence Formation 259 17.4. Pattern Selection 260 17.5. Transformation Facilities 261 17.6. Statistical Aids 263 17.7. The BYTEBYBYTE Instruction 263 17.8. Monitoring for Special Conditions 264 17.9. Instruction Set 265 17.10. Collating Operations 266 17.11. Table Lookup Operations 267 17.12. Example 267 Appendix A. Summary Data 273 A.1. List of the Larger IBM Storedprogram 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. Cuberoot Extraction 296 B.3. Matrix Multiplication 298 B.4. Conversion of Decimal Numbers to a Floatingpoint Normalized Vector 299 B.5. Editing a Typed Message 301 B.6. Transposition of a Large Bit Matrix 303 Index 305acknhfbWerner BuchholzThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.Planning a computer system: {Project Stretch}
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a computer system: {Project Stretch}",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL: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/tukeyjohnw.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://edthelen.org/comphist/IBM7030PlanningMcJones.pdf",
acknowledgement = acknhfb,
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 floatingpoint arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detailØ 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 ndigit 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). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisymode 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 builtin 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 noisymode 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 fixedpoint arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixedpoint 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 fixedpoint arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixedpoint
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 fixedpoint operands do
give correct significance indications, the use of other
operations and of builtin scaling loops frequently
destÙroys entirely the leadingzeros 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. Highspeed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Indexarithmetic Unit 21 \\
3.10. Instruction Lookahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radixconversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Indexarithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. InputOutput 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. Taperecording Convention 71 \\
6.15. Cardpunching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variablefieldlength Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variablefieldlength 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 SiÚgns 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radixconversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floatingpoint Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixedpoint Arithmetic 92 \\
8.2. Floatingpoint Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floatingpoint Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Roundoff Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floatingpoint Arithmetic 103 \\
8.9. Structure of Floatingpoint Data 104 \\
Floatingpoint Features of the 7030 \\
8.10. Floatingpoint Instruction Format 106 \\
8.11. Floatingpoint Data Formats 106 \\
8.12. Singular Floatingpoint Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floatingpointarithmetic Operations 114 \\
8.17. Fixedpoint Arithmetic Using Unnormalized \\
Floatingpoint Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multipleprecision 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 Singleaddress 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. Programinterrupt System 136 \\
10.6. Components of the Programinterrupt System 137
\\
10.7. Examples of Programinterrupt 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. Recordhandling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. InputOutput Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
InputOutput and External Storage 179 \\
12.2. InputOutput 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 InputOutput 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 Lookahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timingsimulation Program 230 \\
15.3. Description of the Lookahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Lookback at the Lookahead 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 Setup Mode 258 \\
17.3. Bytesequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTEBYBYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Lookup Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Storedprogram 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. Cuberoot Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floatingpoint Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
æßæuOZ !#/#1+Em;‚Yy/#1#techreportfparith.bibDescloux:1962:REFJ. DesclouxRemarks on errors in first order iterative processes with floatingpoint computersUniversity of Illinois Graduate College, Digital Computer LaboratoryUrbana, IL, USA71962Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTReport / University of Illinois, Digital Computer Laboratory; no. 113 Report (University of Illinois (UrbanaChampaign campus). Digital Computer Laboratory); no. 113.Electronic digital computers.; Numerical calculations.Supported by: National Science Foundation under grant G16489. ``March 22, 1962.''acknhfbJ. DesclouxRemarks on errors in first order iterative processes with floatingpoint computers
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articlefparith.bibCantor:1962:LEFD. Cantor and G. Estrin and R. TurnLogarithmic and Exponential Function Evaluation in a Variable Structure Digital ComputerjIRETRANSELECCOMPUTEC112155164apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521934803679950 OR 03679950Thu Jul 14 09:11:49 MDT 2011ftp://garbo.uwasa.fi/pc/docsoft/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.bib2011.07.14 09:11:49 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348IRE Transactions on Electronic ComputersacknjD. Cantor and G. Estrin and R. TurnLogarithmic and Exponential Function Evaluation in a Variable Structure Digital Computer
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@InProceedings{Soderstrand:1984:AQL,
author = "M. Soderstrand and G. Poe",
booktitle = "IEEE International Conference on Acoustics, Speech,
and Signal Processing, ICASSP '84",
title = "Application of quadraticlike complex residue number
system arithmetic to ultrasonics",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "484487",
year = "1984",
CODEN = "ITCOB4",
ISSN = }…I‹
@InProceedings{Soderquist:1995:APC,
author = "Peter Soderquist and Miriam Leeser",
title = "An Area\slash Performance Comparison of Subtractive
and Multiplicative Divide\slash Square Root
Implementations",
crossref = "Knowles:1995:PSC",
pages = "132139",
month = jul,
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
URL = "http://www.acsellab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
acknowledgement = acksfo # " and " # acknhfb,
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}ë‰s“g
@InProceedings{Smith:1987:SAE,
author = "S. G. Smith and P. B. Denyer",
title = "Synthesis of AreaEfficient {VLSI} Architectures for
Vector and Matrix Multiplication",
crossref = "Irwin:1987:PSC",
pages = "1320",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith8/papers/ARITH8_Smith hŽ6œm
@InProceedings{Smith:1985:DFI,
author = "S. P. Smith and H. C. Torng",
title = "Design of a Faster Inner Product Processor",
crossref = "Hwang:1985:PSC",
pages = "3843",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith7/papers/ARITH7_Smith_Torng.pdf",
abstract = "This paper presents the design@ˆy‘s
@InProceedings{Slekys:1978:MBI,
author = "Arunas G. Slekys and Algirdas Avi{\v{z}}ienis",
title = "A Modified BiImaginary Number Systems",
crossref = "IEEE:1978:PSC",
pages = "4855",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith4/papers/ARITH4_Slekys.pdf",
abstract = "In this paper the proÐ‡y
@InProceedings{Skelton:1990:GSE,
author = "R. E. Skelton and D. Williamson",
booktitle = "Proceedings of the 29th IEEE Conference on Decision
and Control, 1990",
title = "Guaranteed state estimation accuracies with roundoff
error",
volume = "1",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "297298",
year = "1990",
CODEN = "????",
ISSN = "????",
bibdate = Àˆg‘O
@InProceedings{Skavantzos:1999:NER,
author = "A. Skavantzos and Y. Wang",
booktitle = "Conference Record of the ThirtyThird Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "New efficient {RNS}toweighted decoders for
conjugatepairmoduli residue number systems",
volume = "2",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "13451350",
year = "1999",
Cÿ
‹sPW#/Ee;a7E‚;]Ee%articlefparith.bibFischler:1962:TRAM. A. Fischler and E. A. PoeThreshold Realization of Arithmetic CircuitsjIRETRANSELECCOMPUTEC112287288apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521936603679950 OR 03679950Thu Jul 14 09:11:50 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:50 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366IRE Transactions on Electronic ComputersacknhfbM. A. Fischler and E. A. PoeThreshold Realization of Arithmetic Circuits
@Article{Fischler:1962:TRA,
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¤¤žXQZ #'!%57;m;‹c?c‹w!%œarticlefparith.bibGrau:1962:FNRA. A. GrauOn a floatingpoint number representation for use with algorithmic languagesjCACM53160161mar31962CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078268.0026\#4506Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???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 floatingpoint and fixedpoint 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 fixedpoint numbers is not a proper subset of the set of floatingpoint 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, fixedpoint addition or floatingpoint addition.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79R. L. AshenhurstAlgorithmic languages, such as ALGOL, make provision for two types of numbers, real and integer, which are usually implemented on the computer by means of floatingpoint and fixedpoint 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 fixedpoint numbers is not a proper subset of the set of floatingpoint 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, fixedpoint addition or floatingpoint addition.A. A. GrauOn a floatingpoint number representation for use with algorithmic languages
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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
fixedpoint numbers is not a proper subset of the set
of floatingpoint numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
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ª §ª‰ySV #Ii+3!E%;uMmIiŠibookfparith.bibHamming:1962:NMSR. W. (Richard Wesley) HammingNumerical methods for scientists and engineerspubMCGRAWHILLpubMCGRAWHILL:adr4111962QA297 .H28Fri Aug 20 09:12:08 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 09:12:08 MDTInternational series in pure and applied mathematicsCited in cite Sterbenz:1974:FPC.Numerical analysis; Electronic digital computersacknhfbR. W. (Richard Wesley) HammingNumerical methods for scientists and engineers
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articlefparith.bibGuffin:1962:CSLRonald M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number SystemjIRETRANSELECCOMPUTEC112164173apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521934903679950 OR 03679950Thu Jul 14 09:11:49 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:49 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349IRE Transactions on Electronic ComputersacknhfbRonald M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number System
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¡ª‡sUU#1?m7=m;A?mˆcarticlefparith.bibKaratsuba:1962:MMNA. Karatsuba and Y. OfmanMultiplication of multidigit numbers on automatajDOKLAKADNAUK1452932941962DANKAS00023264 OR 00023264Tue Jul 05 10:35:11 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.07.05 10:35:11 ???Doklady Akademii nauk SSSRacknhfbA. Karatsuba and Y. OfmanMultiplication of multidigit numbers on automata
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number = "??",
pages = "293294",
month = "????",
year = "1962",
CODEN = "DANKAS",
ISSN = "00023264",
bibdate = "Tue Jul 05 10:35:11 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Doklady Akademii nauk SSSR",
}Š[TV#)Ec7=m;OO‚Eg‹{articlefparith.bibJones:1962:FPFF. B. Jones and A. W. WymoreFloating Point Feature on the IBM Type 1620jIBMTDB05624346may51962IBMTAA00188689 OR 00188689Fri Nov 28 11:26:02 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 11:26:02 ???IBM Technical Disclosure Bulletindecimal floatingpoint arithmeticThe IBM 1620 normalized variableprecision arithmetic provides up to 100 decimal digits with an exponent range of $ pm 99 $.acknhfbF. B. Jones and A. W. WymoreFloating Point Feature on the {IBM Type 1620}
@Article{Jones:1962:FPF,
author = "F. B. Jones and A. W. Wymore",
title = "Floating Point Feature on the {IBM Type 1620}",
journal = jIBMTDB,
volume = "0562",
pages = "4346",
month = may,
year = "1962",
CODEN = "IBMTAA",
ISSN = "00188689",
bibdate = "Fri Nov 28 11:26:02 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floatingpoint arithmetic",
remark = "The IBM 1620 normalized variableprecision arithmetic
provides up to 100 decimal digits with an exponent
range of $ \pm 99 $.",
}
ééw
ˆ¶ÇØC‡#ŽG
@Article{Kwon:2002:EBS,
author = "Soonhak Kwon and Heuisu Ryu",
title = "Efficient Bit Serial Multiplication Using Optimal
Normal Bases of Type {II} in {{\em GF\/}}$ (2^m) $",
journal = jLECTNOTESCOMPSCI,
volume = "2433",
pages = "300??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = ‹l—Y
@Article{Kupriianova:2013:RCI,
author = "O. Kupriianova and Ch. Lauter and J.M. Muller",
title = "Radix Conversion for {IEEE7542008} Mixed Radix
FloatingPoint Arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "????",
day = "2",
month = dec,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSNL = "????",
bibdate = "Wed Sep 30)ˆ3g
@Article{Kwan:1985:MOW,
author = "Hon Kwan",
title = "A multioutput wave  digital biquad using magnitude
truncation instead of controlled rounding",
journal = jIEEETRANSCIRCUITSSYST,
volume = "32",
number = "11",
pages = "11851187",
month = nov,
year = "1985",
CODEN = "ICSYBT",
ISSN = "00984094 (print), 15581276 (electronic)",
ISSNL = "00984094",
bibdateûˆz‘u
@Article{Kusterer:1979:SEP,
author = "Roland Kusterer and Manfred Reimer",
title = "Stable Evaluation of Polynomials in Time $ \log n $",
journal = jMATHCOMPUT,
volume = "33",
number = "147",
pages = "10191031",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
MRclass = "65G05 (68C25)",
MRnumber = "8…P‹!
@Article{Kushner:2006:I,
author = "David Kushner",
title = "The Insomniacs",
journal = jIEEESPECTRUM,
volume = "43",
number = "12",
pages = "2429",
month = dec,
year = "2006",
CODEN = "IEESAM",
DOI = "http://dx.doi.org/10.1109/MSPEC.2006.253405",
ISSN = "00189235 (print), 19399340 (electronic)",
ISSNL = "00189235",
bibdate = "Thu Sep 01 16:23:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Spectrum",
keywords = "floatingpoint arithmetic; IBM Cell processor; Sony
Playstation 3",
}ñŒ,˜Y
@Article{Kurokawa:1991:CGU,
author = "T. Kurokawa and T. Mizukoshi",
title = "Computer graphics using logarithmic number systems",
journal = "IEICE Transactions",
volume = "E74",
number = "2",
pages = "447451",
month = feb,
year = "1991",
ISSN = "09171673",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Logarithml‡Ž
@Article{Kurka:2012:FAA,
author = "Petr K{\r{u}}rka",
title = "Fast Arithmetical Algorithms in {M{\"o}bius} Number
Systems",
journal = jIEEETRANSCOMPUT,
volume = "61",
number = "8",
pages = "10971109",
month = aug,
year = "2012",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2012.87",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Fri Jul 27 08:30:49 2012",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}5
_VW#'g;a75%E‚;]gCarticlefparith.bibKeir:1962:DODY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow detection in residue number systemsjIRETRANSELECCOMPUTEC114501507aug81962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521938903679950 OR 0367995068.00MR0150990 (27 \#976)N. H. ChoksyThu Jul 14 09:11:51 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:51 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389IRE Transactions on Electronic ComputersacknhfbY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow detection in residue number systems
@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 = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "4",
pages = "501507",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219389",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}umber = "27 #970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "The author that Motzkin (1962) showed that Horner's
rule for polynomial evaluation may not be optimal, and
develops the idea further for arbitrary polynomials,
but also observes that the coefficients of the revised
polynomials may be difficult to find. He also asks
about, but does not answer, the question of error
analysis of the various methods.",
}×
ÔÔ–(WX #)+W]57'=„K;K?…Ec+OW™%articlefparith.bibKnuth:1962:EPCDonald E. KnuthEvaluation of polynomials by computerjCACM512595599dec121962CACMA2http://doi.acm.org/10.1145/355580.36907400010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078268.00 (12.00)27 #970Thu Dec 08 11:11:03 2005http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database2005.12.08 11:11:03 ???See letter cite Knuth:1963:LEE.Communications of the ACMThe author that Motzkin (1962) showed that Horner's rule for polynomial evaluation may not be optimal, and develops the idea further for arbitrary polynomials, but also observes that the coefficients of the revised polynomials may be difficult to find. He also asks about, but does not answer, the question of error analysis of the various methods.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Donald E. KnuthSee letter \cite{Knuth:1963:LEE}.Evaluation of polynomials by computer
@Article{Knuth:1962:EPC,
author = "Donald E. Knuth",
title = "Evaluation of polynomials by computer",
journal = jCACM,
volume = "5",
number = "12",
pages = "595599",
month = dec,
year = "1962",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/355580.369074",
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MRclass = "68.00 (12.00)",
MRnumber = "27 #970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "The author that Motzkin (1962) showed that Horner's
rule for polynomial evaluation may not be optimal, and
develops the idea further for arbitrary polynomials,
but also observes that the coefficients of the revised
polynomials may be difficult to find. He also asks
about, but does not answer, the question of error
analysis of the various methods.",
}
`
š…`Š!ZX #1+A;7=a;]+I‹ articlefparith.bibMacSorley:1962:RBAO. L. MacSorleyReview: booktitle An Algorithm for Rapid Binary Division, by J. B. Wilson and R. S. LedleyjIRETRANSELECCOMPUTEC113420420jun61962IRELAO03679950 OR 03679950Sat Jul 16 20:52:08 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.16 20:52:08 ???IRE Transactions on Electronic ComputersacknhfbO. L. MacSorleyReview: \booktitle{An Algorithm for Rapid Binary Division}, by {J. B. Wilson and R. S. Ledley}
@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 = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "3",
pages = "420420",
month = jun,
year = "1962",
CODEN = "IRELAO",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}ŠYV #)#o57=m;?Oc#o‹/articlefparith.bibLynch:1962:WBDW. C. LynchOn a WiredIn BinarytoDecimal Conversion SchemejCACM53159159mar31962CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 28 18:21:41 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:21:41 ???Communications of the ACMdecimal floatingpoint arithmeticackmfchttp://portal.acm.org/browse_dl.cfm?idx=J79W. C. LynchOn a WiredIn BinarytoDecimal Conversion Scheme
@Article{Lynch:1962:WBD,
author = "W. C. Lynch",
title = "On a WiredIn BinarytoDecimal Conversion Scheme",
journal = jCACM,
volume = "5",
number = "3",
pages = "159159",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Fri Nov 28 18:21:41 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
}ŠbXX #'!57=m;?Oc!‹yarticlefparith.bibLake:1962:LEHG. T. LakeLetter to the Editor: Hardware Conversion of Decimal and Binary NumbersjCACM59468469sep91962CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 28 18:16:30 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:16:30 ???Communications of the ACMdecimal floatingpoint arithmeticackmfchttp://portal.acm.org/browse_dl.cfm?idx=J79G. T. LakeLetter to the Editor: Hardware Conversion of Decimal and Binary Numbers
@Article{Lake:1962:LEH,
author = "G. T. Lake",
title = "Letter to the Editor: Hardware Conversion of Decimal
and Binary Numbers",
journal = jCACM,
volume = "5",
number = "9",
pages = "468469",
month = sep,
year = "1962",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Fri Nov 28 18:16:30 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
}
0Ò nÐAÒ0†m[
@Article{Ley:1996:PDU,
author = "Eduardo Ley",
title = "On the Peculiar Distribution of the {U.S.} Stock
Indexes' Digits",
journal = jAMERSTAT,
volume = "50",
number = "4",
pages = "311313",
month = nov,
year = "1996",
CODEN = "ASTAAJ",
ISSN = "00031305 (print), 15372731 (electronic)",
ISSNL = "00031305",
bibdate = "Mon Nov 14 15:09:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfordslaw.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2684926",
acknowledgement = acknhfb,
fjournal = "The American Statistician",
journalURL = "http://www.tandfonline.com/loi/utas20",
}
XŸC¿
@Article{Lewis:1994:IMF,
author = "D. M. Lewis",
title = "Interleaved Memory Function Interpolators with
Application to an Accurate {LNS} Arithmetic Unit",
journal = jIEEETRANSCOMPUT,
volume = "43",
number = "8",
pages = "974982",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.295859",
ISSN = "00189340 (print), 15579956 (elecL>k
@Article{Li:1992:CSC,
author = "Zhenyu Li and Victor Milenkovic",
title = "Constructing Strongly Convex Hulls Using Exact or
Rounded Arithmetic",
journal = jALGORITHMICA,
volume = "8",
number = "56",
pages = "345364",
year = "1992",
CODEN = "ALGOEJ",
ISSN = "01784617 (print), 14320541 (electronic)",
ISSNL = "01784617",
MRclass = "68U05 (52B55)",
MRnumber =
]‡/Ž_
@Article{Li:1985:FCD,
author = "S.Y. R. Li",
title = "†`A
@Article{Leuprecht:1982:PAR,
author = "H. Leuprecht and W. Oberaigner",
title = "Parallel Algorithms for the RoundingExact Summation
of FloatingPoint Numbers",
journal = jCOMPUTING,
volume = "28",
number = "2",
pages = "89104",
month = "????",
year = "1982",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
MRclass = "68A05 (65G05)",
MRnumber = "83c:68009",
bibdate = "Fri Dec 08 11:53:42 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journalURL = "http://link.springer.com/journal/607",
keywords = "accurate floatingpoint summation",
}~†.Œ]
@Article{Lewis:1967:CFP,
author = "H. R. {Lewis, Jr.} and E. J. {Stovall, Jr.}",
title = "Comments on a FloatingPoint Version of {Nordsieck}'s
Scheme for the Numerical Integration of Differential
Equations",
journal = jMATHCOMPUT,
volume = "21",
number = "98",
pages = "157161",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}„
uŠm\X #'s57;K;['s‹karticlefparith.bibMeggitt:1962:PDPJ. E. MeggittPseudo Division and Pseudo Multiplication ProcessesjIBMJRD62210226apr41962IBMJAE00188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Thu Sep 1 10:15:31 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:31 ???IBM Journal of Research and Developmentacknjhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520J. E. MeggittPseudo Division and Pseudo Multiplication Processes
@Article{Meggitt:1962:PDP,
author = "J. E. Meggitt",
title = "Pseudo Division and Pseudo Multiplication Processes",
journal = jIBMJRD,
volume = "6",
number = "2",
pages = "210226",
month = apr,
year = "1962",
CODEN = "IBMJAE",
ISSN = "00188646 (print), 21518556 (electronic)",
ISSNL = "00188646",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IBM Journal of Research and Development",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}‹[W #'#;'O57E‚#;#C#;Œgarticlefparith.bibMcGee:1962:BMW. C. McGeeA Binary MultiplicationjSIAMREVIEW432562561962SIREADhttp://dx.doi.org/10.1137/100406600361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 00361445Thu Mar 27 09:04:54 MDT 2014http://epubs.siam.org/toc/siread/4/3; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:04:54 MDTSIAM Reviewacknhfbhttp://epubs.siam.org/sirevJuly 1962W. C. McGeeA Binary Multiplication
@Article{McGee:1962:BM,
author = "W. C. McGee",
title = "A Binary Multiplication",
journal = jSIAMREVIEW,
volume = "4",
number = "3",
pages = "256256",
month = "????",
year = "1962",
CODEN = "SIREAD",
DOI = "http://dx.doi.org/10.1137/1004066",
ISSN = "00361445 (print), 10957200 (electronic)",
ISSNL = "00361445",
bibdate = "Thu Mar 27 09:04:54 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/4/3;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = acknhfb,
fjournal = "SIAM Review",
journalURL = "http://epubs.siam.org/sirev",
onlinedate = "July 1962",
}
Ï äÏŒ^Y #/;a7E‚;]Oarticlefparith.bibMitchell:1962:CMDJohn N. MitchellComputer Multiplication and Division Using Binary LogarithmsjIRETRANSELECCOMPUTEC114512517aug81962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521939103679950 OR 03679950Thu Jul 14 09:11:51 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:51 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219391IRE Transactions on Electronic ComputersacknhfbJohn N. MitchellComputer Multiplication and Division Using Binary Logarithms
@Article{Mitchell:1962:CMD,
author = "John N. Mitchell",
title = "Computer Multiplication and Division Using Binary
Logarithms",
journal = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "4",
pages = "512517",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219391",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Œ]Y #)%;a7E‚;]%Qarticlefparith.bibMetze:1962:CBDGernot MetzeA Class of Binary Divisions Yielding Minimally Represented QuotientsjIRETRANSELECCOMPUTEC116761764dec121962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521946003679950 OR 03679950Thu Jul 14 09:11:53 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:53 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460IRE Transactions on Electronic ComputersacknhfbGernot MetzeA Class of Binary Divisions Yielding Minimally Represented Quotients
@Article{Metze:1962:CBD,
author = "Gernot Metze",
title = "A Class of Binary Divisions Yielding Minimally
Represented Quotients",
journal = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "6",
pages = "761764",
month = dec,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219460",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
:):+ö>ž}
@Article{Seidel:2011:FVI,
author = "PeterMichael Seidel",
title = "Formal Verification of an Iterative LowPower x86
FloatingPoint Multiplier with Redundant Feedback",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "????",
day = "21",
month = oct,
year = "2011",
CODEN = "????",
ISSN = "????",
ISSNL = "????",
bibdate = "Wed Sep 30 12:Nˆ)
@Article{Scott:2007:NHC,
author = "N. S. Scott and F. J{\'e}z{\'e}quel and C. Denis and
J.M. Chesneaux",
title = "Numerical `health check' for scientific codes: the
{CADNA} approach",
journal = jCOMPPHYSCOMM,
volume = "176",
number = "8",
pages = "507521",
day = "15",
month = apr,
year = "2007",
CODEN = "CPHCBZ",
DOI = "http://dx.doi.org/10.10·‡xq
@Article{Seidel:2005:SRR,
author = "P.M. Seidel and L. D. McFearin and D. W. Matula",
title = "Secondary radix recodings for higher radix
multipliers",
journal = jIEEETRANSCOMPUT,
volume = "54",
number = "2",
pages = "111123",
month = feb,
year = "2005",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2005.32",
ISSN = "00189340 (print), 15579956 (electr'=š{
@Article{Seidel:1999:HSR,
author = "PeterMichael Seidel",
title = "HighSpeed Redundant Reciprocal Approximation",
journal = jINTEGRATIONVLSIJ,
volume = "28",
number = "1",
pages = "112",
month = sep,
year = "1999",
CODEN = "IVJODL",
DOI = "http://dx.doi.org/10.1016/S01679260(99)000085",
ISSN = "01679260",
ISSNL = "01679260",
bibdate = "Fri Jun 24 20:25:43 2ø†3Œg
@Article{Sentance:1973:FAB,
author = "W. A. Sentance",
title = "A Further Analysis of {Benford's Law}",
journal = jFIBQUART,
volume = "11",
number = "5",
pages = "490494",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "00150517",
ISSNL = "00150517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/115.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/115/sentance.pdf",
acknowledgement = acknhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journalURL = "http://www.fq.math.ca/",
}Äƒd‡I
@Article{Semba:1986:ADL,
author = "I. Semba",
title = "An Algorithm for Division of Large Integers",
journal = jINFOPROC,
volume = "9",
number = "3",
pages = "145147",
month = "????",
year = "1986",
bibdate = "Thu Sep 1 10:15:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
}RJ›
@Article{Seidel:2004:DOI,
author = "P.M. Seidel and G. Even",
title = "Delayoptimized implementation of {IEEE}
floatingpoint addition",
journal = jIEEETRANSCOMPUT,
volume = "53",
number = "2",
pages = "97113",
month = feb,
year = "2004",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2004.1261822",
ISSN = "00189340 (print), 15579956 (electronic)",
é öéŠ `W#)W_'57E
;A=[aŠyarticlefparith.bibShanks:1962:CDDaniel Shanks and John W. Wrench, Jr.Calculation of $ pi $ to 100,000 DecimalsjMATHCOMPUT16777699jan11962MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknhfbhttp://www.ams.org/mcom/Daniel Shanks and John W. {Wrench, Jr.}Calculation of $ \pi $ to 100,000 Decimals
@Article{Shanks:1962:CD,
author = "Daniel Shanks and John W. {Wrench, Jr.}",
title = "Calculation of $ \pi $ to 100,000 Decimals",
journal = jMATHCOMPUT,
volume = "16",
number = "77",
pages = "7699",
month = jan,
year = "1962",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}Œ_W #+/;a7E‚;]/Garticlefparith.bibRozier:1962:DBCCharles P. RozierDecimaltoBinary Conversion Using Octal Radix ArithmeticjIRETRANSELECCOMPUTEC115708709oct101962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521943603679950 OR 03679950Thu Jul 14 09:11:52 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:52 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219436IRE Transactions on Electronic ComputersacknhfbCharles P. RozierDecimaltoBinary Conversion Using Octal Radix Arithmetic
@Article{Rozier:1962:DBC,
author = "Charles P. Rozier",
title = "DecimaltoBinary Conversion Using Octal Radix
Arithmetic",
journal = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "5",
pages = "708709",
month = oct,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219436",
ISSN = "03679950",
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 = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
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articlefparith.bibSpielberg:1962:PCFKurt SpielbergPolynomial and ContinuedFraction Approximations for Logarithmic FunctionsjMATHCOMPUT1678205217apr41962MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknjhttp://www.ams.org/mcom/Kurt SpielbergPolynomial and ContinuedFraction Approximations for Logarithmic Functions
@Article{Spielberg:1962:PCF,
author = "Kurt Spielberg",
title = "Polynomial and ContinuedFraction Approximations for
Logarithmic Functions",
journal = jMATHCOMPUT,
volume = "16",
number = "78",
pages = "205217",
month = apr,
year = "1962",
CODEN = "MCMPAF",
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bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = acknj # " and " # acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}‹]aW #++K[57E‚5;?c+Sarticlefparith.bibSmith:1962:ACDaRobert L. SmithAlgorithm 116: Complex DivisionjCACM58435435aug81962CACMA2http://dx.doi.org/10.1145/368637.36866100010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:40 MST 2005http://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.bib2005.11.25 18:19:40 MSTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Robert L. Smith{Algorithm 116}: {Complex} Division
@Article{Smith:1962:ACDa,
author = "Robert L. Smith",
title = "{Algorithm 116}: {Complex} Division",
journal = jCACM,
volume = "5",
number = "8",
pages = "435435",
month = aug,
year = "1962",
CODEN = "CACMA2",
DOI = "http://dx.doi.org/10.1145/368637.368661",
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http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
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} "00063835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&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=00063835&volume=2&issue=4&spage=232",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}ã
»Ž»OdY %#'!E‚s3A=m;)I!1ƒincollectionfparith.bibZuse:1962:EREK. ZuseW. HoffmanDigitale InformationswandlerEntwicklungslinien einer RechengerateEntwicklung von der Mechanik zur Elektronik. (German) [Lines of development of computing equipment development from mechanics to electronics]Vieweg & Sohn, GmbHBraunschweig, West Germany5085321962Wed Oct 13 11:23:04 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:23:04 ???Reprinted in cite [ 4.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. Jones.GermanacknhfbK. Zuse{Digitale Informationswandler}W. HoffmanReprinted in \cite[\S 4.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones.{Entwicklungslinien einer Rechenger{\"a}teEntwicklung von der Mechanik zur Elektronik}. ({German}) [Lines of development of computing equipment development from mechanics to electronics]
@InCollection{Zuse:1962:ERE,
author = "K. Zuse",
editor = "W. Hoffman",
booktitle = "{Digitale Informationswandler}",
title = "{Entwicklungslinien einer Rechenger{\"a}teEntwicklung
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publisher = "Vieweg \& Sohn, GmbH",
address = "Braunschweig, West Germany",
pages = "508532",
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 = acknhfb,
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}ŽncX #'wI)U57C‚;KMY{=articlefparith.bibWynn:1962:AAPP. WynnAn Arsenal of ALGOL Procedures for Complex ArithmeticjNORDISKTIDSKRINFORMBEHAND24232255dec121962BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0194017100063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=2&issue=4; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSThttp://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=2&issue=4&spage=232Cited in cite Sterbenz:1974:FPC.acknhfbhttp://link.springer.com/journal/10543P. WynnAn Arsenal of {ALGOL} Procedures for Complex Arithmetic
@Article{Wynn:1962:AAP,
author = "P. Wynn",
title = "An Arsenal of {ALGOL} Procedures for Complex
Arithmetic",
journal = jNORDISKTIDSKRINFORMBEHAND,
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bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&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=00063835&volume=2&issue=4&spage=232",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
i ¿iŠRfW#/iQ!57=K;7UiU‹Oarticlefparith.bibClenshaw:1963:ASFC. W. Clenshaw and G. F. Miller and M. WoodgerAlgorithms for Special Functions IjNUMMATH44034191963NUMMA70029599X (print), 09453245 (electronic) OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599XFri Sep 16 10:21:31 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.16 10:21:31 ???Numerische Mathematikacknjhttp://link.springer.com/journal/211C. W. Clenshaw and G. F. Miller and M. WoodgerAlgorithms for Special Functions {I}
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
title = "Algorithms for Special Functions {I}",
journal = jNUMMATH,
volume = "4",
pages = "403419",
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
ISSNL = "0029599X",
bibdate = "Fri Sep 16 10:21:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Numerische Mathematik",
journalURL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}Œ=eY #)#57E‚5;?cc#iarticlefparith.bibBemer:1963:NRTR. W. BemerA Note on Range Transformations for Square Root and LogarithmjCACM66306307jun61963CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:47 MST 2005http://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.bib2005.11.25 18:19:47 MSTCommunications of the ACM$log (x)$; $sqrt (x)$; elementary functionsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79R. W. BemerA Note on Range Transformations for Square Root and Logarithm
@Article{Bemer:1963:NRT,
author = "R. W. Bemer",
title = "A Note on Range Transformations for Square Root and
Logarithm",
journal = jCACM,
volume = "6",
number = "6",
pages = "306307",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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 = acknhfb,
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journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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‰XhW #/#s'57E
;A=#sŠY
articlefparith.bibDescloux:1963:NREJ. DesclouxNote on the RoundOff Errors in Iterative ProcessesjMATHCOMPUT17811827jan11963MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknhfbhttp://www.ams.org/mcom/J. DesclouxNote on the RoundOff Errors in Iterative Processes
@Article{Descloux:1963:NRE,
author = "J. Descloux",
title = "Note on the RoundOff Errors in Iterative Processes",
journal = jMATHCOMPUT,
volume = "17",
number = "81",
pages = "1827",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}‹sgW#'?m=a7E‚;_?m# articlefparith.bibDaly:1963:HSAW. G. Daly and J. F. KruyA HighSpeed Arithmetic Unit Using Tunnel DiodesjIEEETRANSELECCOMPUTEC125503511oct101963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26364403677508 OR 03677508Thu Jul 14 08:10:42 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:42 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037964IEEE Transactions on Electronic ComputersacknhfbW. G. Daly and J. F. KruyA HighSpeed Arithmetic Unit Using Tunnel Diodes
@Article{Daly:1963:HSA,
author = "W. G. Daly and J. F. Kruy",
title = "A HighSpeed Arithmetic Unit Using Tunnel Diodes",
journal = jIEEETRANSELECCOMPUT,
volume = "EC12",
number = "5",
pages = "503511",
month = oct,
year = "1963",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1963.263644",
ISSN = "03677508",
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 = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
%"%
3a—®
@Article{Fortune:1996:SAY,
author = "Steven Fortune and Christopher J. {Van Wyk}",
title = "Static analysis yields efficient exact integer
arithmetic for computational geometry",
journal = jTOG,
volume = "15",
number = "3",
pages = "223248",
month = jul,
year = "1996",
CODEN = "ATGRDF",
ISSN = "07300301 (print), 15577368 (electronic)",
ISSNL = "07300301",
bibda©š?
@Article{Fousse:2007:MMP,
author = "Laurent Fousse and Guillaume Hanrot and Vincent
Lef{\`e}vre and Patrick P{\'e}lissier and Paul
Zimmermann",
title = "{MPFR}: a multipleprecision binary floatingpoint
library with correct rounding",
journal = jTOMS,
volume = "33",
number = "2",
pages = "115",
month = jun,
year = "2007",
CODEN = "ACMSCU",
DOI = N^
@Article{Fox:1978:AFP,
author = "P. A. Fox and A. D. Hall and N. L. Schryer",
title = "{Algorithm 528}: Framework for a Portable Library
[{Z}]",
journal = jTOMS,
volume = "4",
number = "2",
pages = "177188",
month = jun,
year = "1978",
CODEN = "A‡P!
@Article{Fout:2012:APB,
author = "Nathaniel Fout and KwanLiu Ma",
title = "An Adaptive PredictionBased Approach to Lossless
Compression of FloatingPoint Volume Data",
journal = jIEEETRANSVISCOMPUTGRAPH,
volume = "18",
number = "12",
pages = "22952304",
month = dec,
year = "2012",
CODEN = "ITVGEA",
DOI = "http://dx.doi.org/10.1109/TVCG.2012.194",
ISSN = "10772626 (print), 19410506 (electronic), 21609306",
ISSNL = "10772626",
bibdate = "Mon Oct 22 07:55:05 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Visualization and Computer
Graphics",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}'P¡!
@Article{Fossmeier:1991:ALS,
author = "R. Fossmeier",
title = "On the axiomatization of logarithmic and
semilogarithmic number systems",
journal = jCOMPUTING,
volume = "46",
number = "2",
pages = "175182",
month = "????",
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
bibdate = "Tue Dec 12 09:20:21 M?‰T“)
@Article{Forsythe:1970:PCW,
author = "George E. Forsythe",
title = "Pitfalls in Computation, or Why a Math Book Isn't
Enough",
journal = jAMERMATHMONTHLY,
volume = "77",
number = "9",
pages = "931956",
month = nov,
year = "1970",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
MRclass = "Contributed Item",
MRnumbó‰`“A
@Article{Forsythe:1959:RNR,
author = "George E. Forsythe",
title = "Reprint of a Note on RoundingOff Errors",
journal = jSIAMREVIEW,
volume = "1",
number = "1",
pages = "6667",
month = "????",
year = "1959",
CODEN = "SIREAD",
DOI = "http://dx.doi.org/10.1137/1001011",
ISSN = "00361445 (print), 10957200 (electronic)",
ISSNL = "00361445",
MRclass = "65.00",
MR‡
º Ÿº‰ajW #+%K57;K;?c%KŠuarticlefparith.bibEisman:1963:PERS. H. EismanPolynomial Evaluation RevisitedjCACM67384385jul71963CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:15:41 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:41 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79S. H. EismanPolynomial Evaluation Revisited
@Article{Eisman:1963:PER,
author = "S. H. Eisman",
title = "Polynomial Evaluation Revisited",
journal = jCACM,
volume = "6",
number = "7",
pages = "384385",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}Œ]iW #13}=a7E‚;_G3}Ž3articlefparith.bibDietmeyer:1963:CPNDonald L. DietmeyerConversion from Positive to Negative and Imaginary RadixjIEEETRANSELECCOMPUTEC1212022feb21963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26339103677508 OR 03677508Thu Jul 14 08:10:36 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:36 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037765IEEE Transactions on Electronic Computersimaginary base; negative baseacknhfbDonald L. DietmeyerConversion from Positive to Negative and Imaginary Radix
@Article{Dietmeyer:1963:CPN,
author = "Donald L. Dietmeyer",
title = "Conversion from Positive to Negative and Imaginary
Radix",
journal = jIEEETRANSELECCOMPUT,
volume = "EC12",
number = "1",
pages = "2022",
month = feb,
year = "1963",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1963.263391",
ISSN = "03677508",
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 = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "imaginary base; negative base",
}
Ö
ÄwÖ‹mW#)7ƒ[=m;!7ƒ‹articlefparith.bibGeier:1963:ACDA. Geier and I. SturzThe 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)An. Univ. Timisoara Ser. Sti. Mat.Fiz.1133139196368.0030\#3588Fri Dec 08 13:52:47 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:52:47 ???acknhfbR. N. GossA. Geier and I. SturzThe approximate calculation of a definite integral with automatic choice of integration steps (intervals). The program for the computer {$ {\rm MECIPTI} $} in a floating point regime. (Romanian)
@Article{Geier:1963:ACD,
author = "A. Geier and I. Sturz",
title = "The approximate calculation of a definite integral
with automatic choice of integration steps (intervals).
The program for the computer {$ {\rm MECIPTI} $} in a
floating point regime. (Romanian)",
journal = "An. Univ. Timi{\c{s}}oara Ser. {\c{S}}ti. Mat.Fiz.",
volume = "1",
pages = "133139",
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 = acknhfb,
reviewer = "R. N. Goss",
}†IlV #+M!#;K;M‡ùbookfparith.bibFlores:1963:LCAI. FloresThe Logic of Computer ArithmeticpubPHpubPH:adrxii + 4931963QA76.5 .F46Thu Sep 1 10:12:51 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:12:51 ???acknjI. FloresThe Logic of Computer Arithmetic
@Book{Flores:1963:LCA,
author = "I. Flores",
title = "The Logic of Computer Arithmetic",
publisher = pubPH,
address = pubPH:adr,
pages = "xii + 493",
year = "1963",
LCCN = "QA76.5 .F46",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
}Š8kY #%57=K;5O‹Karticlefparith.bibEve:1963:SAIJ. EveStarting approximation for the iterative calculation of square rootsjCOMPJ62742761963CMPJA600104620 (print), 14602067 (electronic) OR 00104620 (print), 14602067 (electronic)00104620 OR 00104620Thu Sep 15 18:37:30 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:37:30 ???The Computer Journalacknjhttp://comjnl.oxfordjournals.org/J. EveStarting approximation for the iterative calculation of square roots
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting approximation for the iterative calculation
of square roots",
journal = jCOMPJ,
volume = "6",
pages = "274276",
year = "1963",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Thu Sep 15 18:37:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "The Computer Journal",
journalURL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}: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 floatingpoint arithmetic operations.
The manner in which floatingpoint 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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}î
&1 ¥¶ÇØ&‡0Ža
@Article{Joldes:2016:AAE,
author = "M. Joldes and O. Marty and J. M. Muller and V.
Popescu",
title = "Arithmetic Algorithms for Extended Precision Using
FloatingPoint Expansions",
journal = jIEEETRANSCOMPUT,
volume = "65",
number = "4",
pages = "11971210",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2015.2441714",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Sat Mar 19 07:47:06 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers ",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}5’F¥
@Article{Joldes:2014:SSH,
author = "Mioara Joldes and Valentina Popescu and Warwick
Tucker",
title = "Searching for Sinks for the {H{\'e}non} Map using a
Multipleprecision {GPU} Arithmetic Library",
journal = jCOMPARCHNEWS,
volume = "42",
number = "4",
pages = "6368",
year = "2014",
CODEN = "CANED2",
DOI = "http://dx.doi.org/10.1145/2693714.2693726",
ISSN = ‰•v«m
@Article{Johnstone:1994:DAN,
author = "Paul Johnstone and Frederick E. Petry",
title = "Design and analysis of nonbinary radix floating point
representations",
journal = jCOMPUTELECTRENG,
volume = "20",
number = "1",
pages = "3950",
month = jan,
year = "1994",
CODEN = "CPEEBQ",
ISSN = "00457906",
ISSNL = "00457906",
bibdate = "Sat Feb 24 15:01:45 MST 1991’&¤M
@Article{Johnstone:1993:RNA,
author = "P. Johnstone and F. E. Petry",
title = "Rational number approximation in higher radix floating
point systems",
journal = jCOMPMATHAPPL,
volume = "25",
number = "6",
pages = "103108",
month = mar,
year = "1993",
CODEN = "CMAPDK",
ISSN = "08981221 (print), 18737668 (electronic)",
ISSNL = "08981221",
bibdate = "Tue Dec9…
Š
@Article{Johnson:1989:IMA,
author = "K. R. Johnson",
title = "An Iterative Method for Approximating Square Roots",
journal = jMATHMAG,
volume = "62",
number = "4",
pages = "253259",
month = oct,
year = "1989",
CODEN = "MAMGA8",
ISSN = "0025570X",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Mathematics Magazine",
journalURL = "http://www.maa.org/pubs/mathmag.html",
}»‡M
@Article{Johnson:1987:CES,
author = "Kenneth C. Johnson",
title = "Corrigendum: {``Algorithm 650: efficient square root
implementation on the 68000'' [ACM Trans. Math.
Software {\bf 13} (1987), no. 2, 138151]}",
journal = jTOMS,
volume = "13",
number = "3",
pages = "320320",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "http://doi.acm.org/10.1145/29380.356210",
ISSN = "00983500 (print), 15577295 (electronic)",
ISSNL = "00983500",
MRclass = "320. 65D15",
MRnumber = "918 582",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.",
acknowledgement = acknhfb,
fjournal = "ACM Transactions on Mathematical Software",
journalURL = "http://dl.acm.org/pub.cfm?id=J782",
}˜
ˆ
ãˆ
ˆW‚V#)S=!%E%;c/ES=‰Sæbookfparith.bibMaley:1964:MDCGerald A. Maley and Edward J. SkikoModern digital computerspubPHpubPH:adrxiv + 2161964QA76.5 .M192Thu Nov 18 10:04:00 MST 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.11.18 10:04:00 MSTPrenticeHall electrical engineering seriesbinary arithmeticElectronic digital computersacknhfbGerald A. Maley and Edward J. SkikoModern digital computers
@Book{Maley:1964:MDC,
author = "Gerald A. Maley and Edward J. Skiko",
title = "Modern digital computers",
publisher = pubPH,
address = pubPH: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 = "PrenticeHall electrical engineering series",
acknowledgement = acknhfb,
keywords = "binary arithmetic",
subject = "Electronic digital computers",
}Š‚Y #')'57E
;A=)‹articlefparith.bibLynn:1964:REMM. Stuart LynnOn the RoundOff Error in the Method of Successive OverRelaxationjMATHCOMPUT18853649jan11964MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknhfbhttp://www.ams.org/mcom/M. Stuart LynnOn the RoundOff Error in the Method of Successive OverRelaxation
@Article{Lynn:1964:REM,
author = "M. Stuart Lynn",
title = "On the RoundOff Error in the Method of Successive
OverRelaxation",
journal = jMATHCOMPUT,
volume = "18",
number = "85",
pages = "3649",
month = jan,
year = "1964",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}‹‚
W #++}=a7E‚;_+}Aarticlefparith.bibLamson:1964:DADRoger C. LamsonA Division Algorithm for a Digital Differential AnalyzerjIEEETRANSELECCOMPUTEC1315455feb21964IEECA8http://dx.doi.org/10.1109/PGEC.1964.26383803677508 OR 03677508Thu Jul 14 06:56:57 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:56:57 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038079IEEE Transactions on Electronic ComputersacknhfbRoger C. LamsonA Division Algorithm for a Digital Differential Analyzer
@Article{Lamson:1964:DAD,
author = "Roger C. Lamson",
title = "A Division Algorithm for a Digital Differential
Analyzer",
journal = jIEEETRANSELECCOMPUT,
volume = "EC13",
number = "1",
pages = "5455",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263838",
ISSN = "03677508",
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;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038079",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
™wnY #1'g[57E‚5;ˆ1?cˆ1'g˜Marticlefparith.bibGoldstein:1963:SADMax GoldsteinSignificance arithmetic on a digital computerjCACM63111117mar31963CACMA2http://dx.doi.org/10.1145/366274.36633900010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:45 MST 2005http://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.bib2005.11.25 18:19:45 MSTThe 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 floatingpoint arithmetic operations. The manner in which floatingpoint 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.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79The 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 floatingpoint arithmetic operations. The manner in which floatingpoint 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.Max GoldsteinSignificance arithmetic on a digital computer
@Article{Goldstein:1963:SAD,
author = "Max Goldstein",
title = "Significance arithmetic on a digital computer",
journal = jCACM,
volume = "6",
number = "3",
pages = "111117",
month = mar,
year = "1963",
CODEN = "CACMA2",
DOI = "http://dx.doi.org/10.1145/366274.366339",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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 floatingpoint arithmetic operations.
The manner in which floatingpoint 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 = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
ë ëŒ1pY #93=a7E‚;_3iarticlefparith.bibKrishnamurthy:1963:CMDE. V. KrishnamurthyOn Computer Multiplication and Division Using Binary LogarithmsjIEEETRANSELECCOMPUTEC123319320jun61963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26357203677508 OR 03677508Thu Jul 14 08:10:39 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:39 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037874IEEE Transactions on Electronic ComputersacknhfbE. V. KrishnamurthyOn Computer Multiplication and Division Using Binary Logarithms
@Article{Krishnamurthy:1963:CMD,
author = "E. V. Krishnamurthy",
title = "On Computer Multiplication and Division Using Binary
Logarithms",
journal = jIEEETRANSELECCOMPUT,
volume = "EC12",
number = "3",
pages = "319320",
month = jun,
year = "1963",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1963.263572",
ISSN = "03677508",
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 = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}‰\oY #)+5=S;=+AŠ+articlefparith.bibKnuth:1963:LEEDonald E. KnuthLetter to the Editor: Evaluation of polynomials by computerjCACM625151feb21963CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)Tue Dec 26 16:31:38 1995http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.26 16:31:38 ???See cite Knuth:1962:EPC.acknhfbDonald E. KnuthSee \cite{Knuth:1962:EPC}.Letter to the {Editor}: {Evaluation} of polynomials by computer
@Article{Knuth:1963:LEE,
author = "Donald E. Knuth",
title = "Letter to the {Editor}: {Evaluation} of polynomials by
computer",
journal = jCACM,
volume = "6",
number = "2",
pages = "5151",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
bibdate = "Tue Dec 26 16:31:38 1995",
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:1962:EPC}.",
acknowledgement = acknhfb,
}
"?~;"„?ˆ
@Article{Mar„\‰9
@Article{Manning:1996:FS,
author = "Evan Manning",
title = "Floatingpoint Summation",
journal = jCCCUJ,
volume = "14",
number = "9",
pages = "51??",
month = sep,
year = "1996",
CODEN = "CCUJEX",
ISSN = "10752838",
bibdate = "Wed Nov 6 07:30:58 MST 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "C/C++ Users Journal",
keywords = "accurate floatingpoint summation",
}
d‡ti
@Article{Mandelbaum:1995:DUL,
author = "D. M. Mandelbaum",
title = "Division using a logarithmicexponential transform to
form a short reciprocal",
journal = jIEEETRANSCOMPUT,
volume = "44",
number = "11",
pages = "13261330",
month = nov,
year = "1995",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.475129",
ISSN = "00189340 (print), 15579956 (electroni,‡?Ž
@Article{Mandelbaum:1993:SRS,
author = "D. M. Mandelbaum",
title = "Some results on a {SRT} type division scheme",
journal = jIEEETRANSCOMPUT,
volume = "42",
number = "1",
pages = "102106",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.192218",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Jul 7 07:58:46 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/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192218",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}x‡aC
@Article{Mandelbaum:1990:SMD,
author = "D. M. Mandelbaum",
title = "A systematic method for division with high average bit
skipping",
journal = jIEEETRANSCOMPUT,
volume = "39",
number = "1",
pages = "127130",
month = jan,
year = "1990",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.46287",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Jul 7 14:19:59 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/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=46287",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
} ]W
@Article{Mansfield‡C
@Article{Maniatakos:2013:LCC,
author = "Michail Maniatakos and Prabhakar Kudva and Bruce M.
Fleischer and Yiorgos Makris",
title = "LowCost Concurrent Error Detection for FloatingPoint
Unit ({FPU}) Controllers",
journal = jIEEETRANSCOMPUT,
volume = "62",
number = "7",
pages = "13761388",
month = jul,
year = "2013",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2012.81",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Mon Jun 17 15:07:53 2013",
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ê ÖêhrY #+%=a7E‚U;ƒ__%‘marticlefparith.bibLehmer:1963:RDOD. H. LehmerR6317 Division and Overflow Detection in Residue Number SystemsjIEEETRANSELECCOMPUTEC1213637feb21963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26349303677508 OR 03677508Thu Jul 14 08:10:36 MDT 2011http://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.bib2011.07.14 08:10:36 MDThttp://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=4037754IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemacknhfbD. H. Lehmer{R6317} Division and Overflow Detection in Residue Number Systems
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}Œ&qY #+!=a7E‚;_!]articlefparith.bibLehman:1963:MABM. LehmanThe Minimization of Assimilations in Binary CarryStorage Arithmetic UnitsjIEEETRANSELECCOMPUTEC124409410aug81963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26347903677508 OR 03677508Thu Jul 14 08:10:40 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:40 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037921IEEE Transactions on Electronic ComputersacknhfbM. LehmanThe Minimization of Assimilations in Binary CarryStorage Arithmetic Units
@Article{Lehman:1963:MAB,
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title = "The Minimization of Assimilations in Binary
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c csY#1Y#'O57E‚#;#C%Y#Ž7 articlefparith.bibLindamood:1963:MCOGeorge E. Lindamood and George ShapiroMagnitude Comparison and Overflow Detection in Modular Arithmetic ComputersjSIAMREVIEW543423501963SIREADhttp://dx.doi.org/10.1137/100509500361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 00361445Thu Mar 27 09:05:07 MDT 2014http://epubs.siam.org/toc/siread/5/4; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:05:07 MDTSIAM Reviewacknhfbhttp://epubs.siam.org/sirevOctober 1963George E. Lindamood and George ShapiroMagnitude Comparison and Overflow Detection in Modular Arithmetic Computers
@Article{Lindamood:1963:MCO,
author = "George E. Lindamood and George Shapiro",
title = "Magnitude Comparison and Overflow Detection in Modular
Arithmetic Computers",
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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
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ËËœ1tZ#3Qw=97Eƒ);‡a_M!‡aQw›s articlefparith.bibMetropolis:1963:BOUN. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic SystemjIEEETRANSELECCOMPUTEC126896904dec121963IEECA8http://dx.doi.org/10.1109/PGEC.1963.263593; http://dx.doi.org/10.1109/PGEC.1963.26359203677508 OR 03677508Thu Jul 14 08:10:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037A 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 multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.IEEE Transactions on Electronic ComputersCited in cite Sterbenz:1974:FPC.0124.07910acknhfbA 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 multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.N. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic System
@Article{Metropolis:1963:BOU,
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title = "Basic Operations in an Unnormalized Arithmetic
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University of Chicago Maniac III Computer. Each basic
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two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multiprecision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = acknhfb,
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Tw#{ŒŽdI
@InProceedings{Zimmermann:1999:EVI,
author = "Reto Zimmermann",
title = "Efficient {VLSI} Implementation of Modulo $ (2^n \pm
1) $ Addition and Multiplication",
crossref = "Koren:1999:ISC",
pages = "158167",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper127.pdf;
$‡&ŽM
@InProceedings{Zhuo:2005:DSF,
author = "Ling Zhuo and G. R. Morris and V. K. Prasanna",
booktitle = "Proceedings. 19th IEEE International Parallel and
Distributed Processing Symposium, 0408 April 2005",
title = "Designing Scalable {FPGA}Based Reduction Circuits
Using Pipelined FloatingPoint Cores",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "147a147a",
year = "2005",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The use of pipelined floatingpoint arithmetic cores
to create highperformance FPGAbased computational
kernels has introduced a new class of problems that do
not exist when using singlecycle arithmetic cores.
\ldots{}",
acknowledgement = acknhfb,
}¶„R‰%
@InProceedings{Zhuo:2004:SMA,
author = "L. Zhuo and V. K. Prasanna",
booktitle = "Proceedings. 18th International Parallel and
Distributed Processing Symposium, 2630 April 2004",
title = "Scalable and modular algorithms for floatingpoint
matrix mult