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National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA,
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Tera Computer Company,
2815 Eastlake East,
Seattle, WA 98102,
USA,
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acknjNorbert Juffa, 2445 Mission College Blvd. Santa Clara, CA 95054 USA email: path =norbert@iit.com=@String{acknj = "Norbert Juffa,
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Santa Clara, CA 95054
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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,
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: \pathbeebe@math.utah.edu,
\pathbeebe@acm.org,
\pathbeebe@computer.org (Internet),
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IBM UK (MP5),
PO Box 31,
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Warwick, CV34 5JL,
UK,
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National Institute of Standards and Technology,
Building 820, Room 365,
Gaithersburg, MD 20899, USA,
Tel: +1 301 9755119,
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email: \pathkarin@cam.nist.gov"}ƒ‚„ackjrJon Rokne, Department of Computer Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada@String{ackjr = "Jon Rokne,
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2500 University Drive N.W.,
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Tera Computer Company,
2815 Eastlake East,
Seattle, WA 98102,
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@String{acknj = "Norbert Juffa,
2445 Mission College Blvd.
Santa Clara, CA 95054
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email: \path=norbert@iit.com="}„0ˆc@String{acknhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 841120090, USA,
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@Article{Miller:1981:RGU,
author = "W. Miller",
title = "A Remark on Gradual Underflow",þ†qc
@Article{Lozier:1992:RPC,
author = "D. W. Lozier and P. R. Turner",
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{SLI} Arithmetic. {Robuste ParallelVerarbeitung in
Gleitkommaund SLIArithmetik}",
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acknowledgement = acknhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journalURL = "http://link.springer.com/journal/607",
}
ï¬‡F
@Article{Watanabe:1999:NVM,
author = "Y. Watanabe and N. Yamamoto and M. T. Nakao",
title = "A Numerical Verification Method of Solutions for the
{NavierStokes} Equations",
journal = jRELIABLECOMPUTING,
volume = "5",
number = "3",
pages = "347357",
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.",
}qªƒA‡
@InProceedings{Simcoe:1986:MFP,
author = "R. J. Simcoe and A. Fisher and B. M. Leary and W. R.
Bidermann and W. R. Wheeler",
title = "The {MicroVAX} 78132 Floating Point Chip",
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bibdate = "Wed Sep 07 23:14:42 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
}wqŸc
@InProceedings{Fandrianto:1987:AHS,
author = "Jan Fandrianto",
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Radix 4 SquareRoot",
crossref = "Irwin:1987:PSC",
pages = "7379",
‡F
@Article{Watanabe:1999:NVM,
author = "Y. Watanabe and N. Yamamoto and M. T. Nakao",
title = "A Numerical Verification Method of Solutions for the
{NavierStokes} Equations",
journal = jRELIABLECOMPUTING,
volume = "5",
number = "3",
pages = "347357",
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.",
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acknowledgement = acknhfb,
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88“E_ #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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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,
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;G%!‹articlefparith.bibBarrow:1924:QDDD. F. BarrowQuestions and Discussions: Discussions: On Taking Square Roots of IntegersjAMERMATHMONTHLY3110482484dec121924AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:37:29 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:37:29 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlD. F. BarrowQuestions and Discussions: Discussions: On Taking Square Roots of Integers
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}Ž] #;3‚Y=7=m;k7‚}ŽQarticlefparith.bibTorresyQuevedo:1915:EASL. Torres y QuevedoEssais sur l'automatique. Sa definition. Etendue theorique de ses applications (French) [Essays on automation. Its definition. Theoretical extent of its applications]jREVGENSCIPURESAPPL60161115nov11191503707431 OR 03707431Wed Oct 13 11:15:08 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:15:08 ???Reprinted in cite [ 2.5]Randell:1982:ODC. Translated by Mr. R. Basu.Revue Generale des Sciences Pures et AppliqueesFrenchacknhfbL. {Torres y Quevedo}Reprinted in \cite[\S 2.5]{Randell:1982:ODC}. Translated by Mr. R. Basu.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]
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author = "L. {Torres y Quevedo}",
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¥†Y #/;?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
@Book{Karpinski:1925:HA,
author = "Louis Charles Karpinski",
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}ŒX[ #)1e57Eƒ;Qo1iŽarticlefparith.bibSmith:1924:FPADavid Eugene SmithThe First Printed Arithmetic (Treviso, 1478)jISIS633113311924ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:57:26 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211087; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1920.bib2013.07.30 21:57:26 MDThttp://www.jstor.org/stable/224315Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlDavid Eugene SmithThe First Printed Arithmetic ({Treviso}, 1478)
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@Article{Anonymous:1977:CAF,
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@Article{Anonymous:1898:OFA,
author = "Anonymous",
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journal = jSCIAMER,
volume = "79",
number = "17",
pages = "265266",
day = "22",
month = oct,
year = "1898",
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http://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
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acknowledgement = acknhfb,
fjournal = "Scientific American",
journalURL = "http://www.nature.com/scientificamerican",
}‡Ž+
@Article{Anonymous:1893:IDb,
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@Article{Anonymous:1879:TRA,
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÷ 6÷Œ<[ #)1W57Eƒ;Qo1Ww articlefparith.bibSmith:1926:FGCDavid Eugene SmithThe First Great Commercial ArithmeticjISIS814149feb21926ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:57:36 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211094; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1920.bib2013.07.30 21:57:36 MDThttp://www.jstor.org/stable/223673Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlDavid Eugene SmithThe First Great Commercial Arithmetic
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}G] #+)#57Eƒ;Qo)/Žoarticlefparith.bibCajori:1926:BRBFlorian CajoriBook Review: booktitle The History of Arithmetic by Louis Charles KarpinskijISIS81231232feb21926ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:57:36 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211094; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1920.bib2013.07.30 21:57:36 MDThttp://www.jstor.org/stable/223706Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlFlorian CajoriBook Review: {{\booktitle{The History of Arithmetic}} by Louis Charles Karpinski}
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author = "Florian Cajori",
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by Louis Charles Karpinski}",
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à9õ9ø¨ƒ:†u
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¼‹!] #)+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
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author = "Raymond Garver",
title = "Questions, Discussions, and Notes: a Square Root
Method and Continued Fractions",
journal = jAMERMATHMONTHLY,
volume = "39",
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pages = "533535",
month = nov,
year = "1932",
CODEN = "AMMYAE",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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«‹] #/)!357E
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title = "Les machines {\`a} calculer, leurs principes, leur
{\'e}volution. ({French}) [{Calculating} machines,
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language = "French",
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Õ
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author = "Jerome T. Coonen",
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\cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
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author = "Jerome Coonen and William Kahan and John Palmer and
Tom Pittman and David Stevenson",
title = "A Proposed Standard for Binary Floating Point
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number = "3S (Special issue)",
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year = "1979",
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author = "R. Conway and J. Nelson",
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}vŠ”
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4 œ¬4Šu[ #'‚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]
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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.",
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language = "German",
}‡mY #)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
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}Œa[ #'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
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author = "H. R. Calvert",
title = "Decimal Division of Scales before the Metric System",
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year = "1936",
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ISSN = "00211753 (print), 15456994 (electronic)",
ISSNL = "00211753",
bibdate = "Tue Jul 30 21:21:25 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211115;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/225380",
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fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}
”
k”‰T]#/g#=m;[g‰Ibookfparith.bibMillikan:1937:MMPRobert A. Millikan and Duane E. Roller and Earnest C. WatsonMechanics, Molecular Physics, Heat, and SoundpubMITpubMIT:adr1937Mon May 21 17:16:04 2018http://www.math.utah.edu/pub/tex/bib/fparith.bib2018.05.21 17:16:04 ???See Appendix: Significant Figures and Notations by Powers of Ten.Cited in cite [ref. 22]Carter:2013:ESF.acknhfbRobert A. Millikan and Duane E. Roller and Earnest C. WatsonSee Appendix: Significant Figures and Notations by Powers of Ten.Mechanics, Molecular Physics, Heat, and Sound
@Book{Millikan:1937:MMP,
author = "Robert A. Millikan and Duane E. Roller and Earnest C.
Watson",
title = "Mechanics, Molecular Physics, Heat, and Sound",
publisher = pubMIT,
address = pubMIT:adr,
pages = "????",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Appendix: Significant Figures and Notations by
Powers of Ten.",
acknowledgement = acknhfb,
remark = "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}‹] #+%%357E
;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.''",
}
66G [ '#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.",
}!
pË
šéåp†sg
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volume = "C28",
number = "3",
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CODEN = "ITCOB4",
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}3&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.",
}
mmÓ!_ #'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%
Q Q‡=#[#)]!)!=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,
}l"] #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",
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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
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landmark in that it helped to change digital circuit
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}$
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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;
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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.''",
}
¸ ¸ŠW&\ ##
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Z†ÈJZ *Z '#)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. T/†{)Y !#)'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
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author = "G. R. Stibitz",
title = "Computer",
type = "Unpublished memorandum",
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address = "New York, NY, USA",
year = "1940",
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author = "V. Bush",
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author = "J. V. Atanasoff",
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type = "Unpublished memorandum",
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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.",
}*he 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.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",
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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.",
}
ž~ž
E4‰k Ú9
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note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
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}*+[ #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",
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ISSN = "01621459 (print), 1537274X (electronic)",
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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",
}
'
Ž'Œd/] !#3+WQ7=m;‚9+[Qtechreportfparith.bibRademacher:1943:MTIHans RademacherMathematical Topics of Interest in PX, Part Two: Summary of Articles Dealing with Rounding off ErrorsPX Report14Moore School of Electrical Engineering, Office of the Director Records, University of PennsylvaniaPhiladelphia, PA, USA19019130nov111943Fri Jun 15 17:39:28 2018http://www.math.utah.edu/pub/tex/bib/fparith.bib2018.06.15 17:39:28 ???Cited on page 34 of Haigh, Priestley, and Rope, booktitle ENIAC in Action (2016) (ISBN 0262033984) as an annotated bibliography of rounding errors.acknhfbHans RademacherMathematical Topics of Interest in {PX}, Part Two: Summary of Articles Dealing with Rounding off Errors
@TechReport{Rademacher:1943:MTI,
author = "Hans Rademacher",
title = "Mathematical Topics of Interest in {PX}, Part Two:
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type = "{PX} Report",
number = "14",
institution = "Moore School of Electrical Engineering, Office of the
Director Records, University of Pennsylvania",
address = "Philadelphia, PA, USA",
day = "30",
month = nov,
year = "1943",
bibdate = "Fri Jun 15 17:39:28 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited on page 34 of Haigh, Priestley, and Rope,
\booktitle{ENIAC in Action} (2016) (ISBN 0262033984)
as an annotated bibliography of rounding errors.",
}Šo.] #//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",
}0
žž”_0]#/IuM57=m;
„ysW„yIu”;articlefparith.bibGoudsmit:1944:SFNS. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical TablesjNATURE154392180080123dec121944NATUAShttps://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",
journal = jNATURE,
volume = "154",
number = "3921",
pages = "800801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/154800a0",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "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",
}
> Œ>ŽK2[ !#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}.",
}Œq1]#)GM57=m;
sWGŽ#articlefparith.bibFurry:1945:DNDW. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant FiguresjNATURE155525313jan11945NATUAShttps://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 = "https://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}.",
}2
lal‡r5Y #+!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",
}« 4a!#)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'  multipl9‰q3Z#)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
Electrical Engineers)",
}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.''",
}4icative 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.''",
}
¿‹#7[#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>6]!#+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",
}
^M<
‚ Ç^+‰’=
@Article{Singer:2003:REP,
author = "Sanja Singer and Sa{\v{s}}a Singer",
title = "Rounding error and perturbation bounds for the
symplectic {QR} factorization",
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volume = "358",
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pages = "255279",
day = "1",
month = jan,
year = "2003",
CODEN = "LAAPAW",
ISSN = "00243795 (print), 18731856 (electronic)",
ISSNL = ®Ž@
@Article{Silverman:1990:PPA,
author = "Robert D. Silverman",
title = "Parallel polynomial arithmetic over finite rings",
journal = jJPARDISTCOMP,
volume = "10",
number = "3",
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month = nov,
year = "1990",
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ISSNL = "07437315",
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@Article{Simar:1992:FPP,
author = "Ray {Simar, Jr.} and Peter Koeppen and Jerald Leach
and Steve Marshall and Dave Francis and Greg Mekras and
Jeffrey Rosenstrauch and Scott Anderson",
title = "FloatingPoint Processors Join Forces in Parallel
Processing Architectures",
journal = jIEEEMICRO,
volume = "12",
number = "4",
pages = "6069",
month = aug,
year = "19
Û‡Ž5
@Article{Singh:1973:MOA,
author = "S. Singh and R. Waxman",
title = "Multiple Operand Addition and Multiplication",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "2",
pages = "113120",
month = feb,
year = "1973",
CODEN = "ITCOB4",
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the sum of $m$ products of two $s$digit numbers is
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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}.",
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acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}…}‹{
@Article{Waterhouse:1986:TMW,
author = "William C. Waterhouse",
title = "The Teaching of Mathematics: Why Square Roots are
Irrational",
journal = jAMERMATHMONTHLY,
volume = "93",
number = "3",
pages = "213214",
month = mar,
year = "1986",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:38:15 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",
}†N¡
@Article{Watanuki:1983:EAC,
author = "Osaaki Watanuki and Milo{\v{s}} D. Ercegovac",
title = "Error analysis of certain floatingpoint online
algorithms",
journal = jIEEETRANSCOMPUT,
volume = "C32",
number = "4",
pages = "352358",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676236",
ISSN = "00189340 (print), 15579956R
•••‰}BZ#/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/",
}’hA\ #+%[C773!=„;+gy!%/[—
articlefparith.bibTuring:1948:REMA. M. TuringRoundingOff Errors in Matrix ProcessesjQUARTJMECHAPPLIEDMATH1287308sep91948QJMMAV00335614 OR 0033561400335614 OR 0033561465.0XMR0028100 (10,405c)E. BodewigSat Nov 19 12:09:58 2005http://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.bib2005.11.19 12:09:58 ???Reprinted in cite Turing:1992:PM with summary and notes (including corrections)http://turing.ecs.soton.ac.uk/browse.php/B/18Quarterly Journal of Mechanics and Applied Mathematics0033.28501acknhfbA. M. TuringReprinted in \cite{Turing:1992:PM} with summary and notes (including corrections)RoundingOff Errors in Matrix Processes
@Article{Turing:1948:REM,
author = "A. M. Turing",
title = "RoundingOff Errors in Matrix Processes",
journal = jQUARTJMECHAPPLIEDMATH,
volume = "1",
pages = "287308",
month = sep,
year = "1948",
CODEN = "QJMMAV",
ISSN = "00335614",
ISSNL = "00335614",
MRclass = "65.0X",
MRnumber = "MR0028100 (10,405c)",
MRreviewer = "E. Bodewig",
bibdate = "Sat Nov 19 12:09:58 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/a/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.",
}
–üò–ˆYEZ!#)K7)1=m;K‰techreportfparith.bibTukey:1949:TRAJohn W. Tukey and M. F. FreemanTransformation related to the angular and the squarerootSRG Memorandum report24instPRINCETONinstPRINCETON:adr1949Tue May 15 08:00:09 2012http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2012.05.15 08:00:09 ???acknhfbJohn W. Tukey and M. F. FreemanTransformation related to the angular and the squareroot
@TechReport{Tukey:1949:TRA,
author = "John W. Tukey and M. F. Freeman",
title = "Transformation related to the angular and the
squareroot",
type = "SRG Memorandum report",
number = "24",
institution = instPRINCETON,
address = instPRINCETON:adr,
pages = "??",
year = "1949",
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/fparith.bib",
acknowledgement = acknhfb,
}ˆD[ #+%
97=m;M%
ˆiarticlefparith.bibHuskey:1949:PCPH. D. HuskeyOn the Precision of a Certain Procedure of Numerical IntegrationjJRESNATLBURSTAND4257621949JRNBAG00910635 OR 00910635Fri Aug 20 09:32:34 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:32:34 ???Cited in cite Sterbenz:1974:FPC.acknhfbH. D. HuskeyOn the Precision of a Certain Procedure of Numerical Integration
@Article{Huskey:1949:PCP,
author = "H. D. Huskey",
title = "On the Precision of a Certain Procedure of Numerical
Integration",
journal = jJRESNATLBURSTAND,
volume = "42",
number = "??",
pages = "5762",
year = "1949",
CODEN = "JRNBAG",
ISSN = "00910635",
bibdate = "Fri Aug 20 09:32:34 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}ˆC[ #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,
}
¶ Û å„[3
@Book{Anonymous:1996:SROb,
author = "Anonymous",
tit„ˆ)
@Book{Alt:1960:AC,
editor = "Franz L. Alt and Andrew Donald Booth and Robert Emmet
Meagher",
booktitle = "Advances in Computers",
title = "Advances in Computers",
publisher = pubACADEMIC,
address = pubACADEMIC:adr,
pages = "x + 316",
year = "1960",
ISSN = "00652458",
LCCN = "QA76 .A3",
bibdate = "Sat Nov 29 11:05:31 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}c/3
@Book{Anonymous:1996:SROa,
author = „*ˆU
@Book{Alt:1965:AC,
editor = "Franz L. Alt and Morris Rubinoff and Andrew Donald
Booth and Robert Emmet Meagher",
booktitle = "Advances in Computers",
title = "Advances in Computers",
publisher = pubACADEMIC,
address = pubACADEMIC:adr,
pages = "xiv + 310",
year = "1965",
ISSN = "00652458",
LCCN = "QA76 .A3",
bibdate = "Sat Nov 29 11:06:34 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}n
c
@Bo„g‰O
@Book{Anbar:1987:CM,
editor = "Michael Anbar",
booktitle = "Computers in medicine",
title = "Computers in medicine",
publisher = "Computer Science Press, Inc.",
address = "Rockville, MD, USA",
pages = "314",
year = "1987",
ISBN = "0881750808",
ISBN13 = "9780881750805",
LCCN = "????",
bibdate = "Sat Nov 29 11:19:13 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$32.95",
series = "Applications of computer science series",
acknowledgement = acknhfb,
}Ç„U‰+
@Book{Anonymous:1993:SRT,
author = "Anonymous",
title = "The Square Root of Two to 100,000 digits",
volume = "52",
publisher = pubPROJECTGUTENBERG,
address = pubPROJECTGUTENBERG:adr,
year = "1993",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = serPROJECTGUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext93/2sqrt10.zip",
acknowledgement = acknhfb # " and " # ackst,
subject = "Mathematical constants.",
}L…"ŠG
@Book{Alt:1957:EDC,
editor = "Franz L. Alt",
title = "Electronic Digital Computers: Their Use in Science and
Engineering",
publisher = pubACADEMIC,
address = pubACADEMIC:adr,
pages = "x + 335",
year = "1957",
bibdate = "Sun Jun 17 18:53:23 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Section 2.3 discusses number representation and
decimal versus binary arithmetic.",
xxnote = "Check page count: incomplete view in Google books. Price bibliography says 1958.",
tableofcontents = "
",
}’
@Book{Albrecht:1993:VNT,
editor = "R. (Rudolf F.) Albrecht and G. (G{\"o}tz) Alefeld and
H. (Hans) J. Stetter",
title = "Validation numerics: theory and applications",
volume = "9",
publisher = pubSV,
address = pubSV:adr,
pages =„Y‰3
@Book{Anonymous:1996:SROc,
author = "Anonymous",
title = "The Square Root of 6 to onª(ÔQ
@Book{Alefeld:2001:SAM,
editor = "G{\"o}tz Alefeld and Ji{\v{r}}i Rohn and Siegfried
Rump and Tetsuro Yamamoto",
title = "Symbolic algebraic methods and verification methods",
publisher = pubSV,
address = pubSV:adr,
pages = "ix + 266",
year = "2001",
ISBN = "3211835938",
ISBN13 = "9783211835937",
LCCN = "QA76.9.M35 S92 2001",
bibdate = "Thu May 09 07:34:15 2002",
bibsourU
Ãî‰WH[ '#+'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,
}‰RG['#'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
Calculating Machines, 2225 June 1949}",
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,
}Œ:F[ #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",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6ONR240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}
²ƒ `K^ #'i?7=m;9'„Ci’1
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
computing machine",
journal = jPROCCAMBRIDGEPHILSOC,
volume = "47",
pages = "96108",
year = "1951",
CODEN = "PCPSA4",
ISSN = "00081981",
bibdate = "Tue Aug 28 05:54:12 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
keywords = "accurate floatingpoint summation; floatingpoint
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a RungeKutta code in a program library for the
EDSAC computer.''",
}†,JY %#)#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",
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}ˆKIY #)#]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",
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",
}b/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
keywords = "accurate floatingpoint summation; floatingpoint
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a RungeKutta code in a program library for the
EDSAC computer.''",
}K
$Mã eMx‰‡U+
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author = "A. F. Tenca and C. K. Koc",
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pages = "12151221",
month = sep,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1228516",
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ISSNL = "00189340",
bibdate = "Tue Jul 5 08:52:54 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1228516",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}Ôe%
@Article{Thomas:1995:IFC,
author = "Jim Thomas and Jerome T. Coonen",
title = –9¬s
@Article{Thapliyal:2006:CIF,
author = "Himanshu Thapliyal and Hamid R. Arabnia and A. P
Vinod",
title = "Combined Integer and Floating Point Multiplication
Architecture ({CIFM}) for {FPGAs} and Its Reversible
Logic Implementation",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "????",
day = "14",
month = oct,
year = "2006",
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@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = jMATHCOMPUT,
volume = "15",
number = "76",
pages = "399403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
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bibdate = "Tue Oct 13 08:06:19 MDT 1998",
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JSTOR database",
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fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}Ó†y
@Article{Tenca:2001:HRD,
author = "A. F. Tenca and G. Todorov and {\c{C}}.K. Ko{\c{c}}",
title = "HighRadix Design of a Scalable Modular Multiplier",
journal = jLECTNOTESCOMPSCI,
volume = "2162",
pages = "185??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Sat Feb 2 13:06:06 MST 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2162.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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http://link.springerny.com/link/service/series/0558/papers/2162/21620185.pdf",
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fjournal = "Lecture Notes in Computer Science",
}¦†Œ7
@Article{Teachey:1982:SRX,
author = "R. D. Teachey",
title = "SquareRoot{X} Comparison  New Results
Discovered",
journal = jIEEEMICRO,
volume = "2",
number = "4",
pages = "55",
month = nov,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.290929",
ISSN = "02721732 (print), 19374143 (electronic)",
ISSNL = "02721732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (19802000)",
acknowledgement = acknhfb,
fjournal = "IEEE Micro",
journalURL = "http://www.computer.org/csdl/mags/mi/index.html",
}²ÇŸÀ
CSŸHf
€‡C
@Article{Anonymous:1997:SIS,
author = "Anonymous",
title = P†"ŒE
@Article{Andrews:1982:SRX,
author = "M. Andrews",
title = "SquareRoot{X} Comparison  New Results Discovered
 Reply",
journal = jIEEEMICRO,
volume = "2",
number = "4",
pages = "56",
month = nov,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.291010",
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month = jan,
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reviewer = "D. Bini",
}
À‰9M] '#3+E#+=m;+E‰
inproceedingsfparith.bibRademacher:1951:AEPHans RademacherProceedings of a Symposium on Largescale Digital Calculating MachineryOn the accumulation of errors in processes of integration on highspeed calculating machinespubHARVARDpubHARVARD:adr1761851951Mon Jun 18 06:50:41 2018http://www.math.utah.edu/pub/tex/bib/fparith.bib2018.06.18 06:50:41 ???acknhfbHans RademacherProceedings of a Symposium on Largescale Digital Calculating MachineryOn the accumulation of errors in processes of integration on highspeed calculating machines
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author = "Hans Rademacher",
booktitle = "Proceedings of a Symposium on Largescale Digital
Calculating Machinery",
title = "On the accumulation of errors in processes of
integration on highspeed calculating machines",
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address = pubHARVARD:adr,
pages = "176185",
year = "1951",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = jPROCAMMATHSOC,
volume = "2",
pages = "188202",
year = "1951",
CODEN = "PAMYAR",
ISSN = "00029939 (print), 10886826 (electronic)",
ISSNL = "00029939",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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in \cite[Paper~15, pp.~558572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
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fjournal = "Proceedings of the American Mathematical Society",
}ith.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",
}N
ÐÐ”N] #+MO57m…{Co…{+Q“Uarticlefparith.bibShirley:1951:BNBJohn W. ShirleyBinary Numeration before LeibnizjAMERJPHYSICS1984524541951AJPIAShttps://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 = "https://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",
}pubACM,
address = pubACM:adr,
bookpages = "vi + 114",
pages = "101105",
year = "1952",
DOI = "https://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,
keywords = "Bell Laboratories Model 15 relay computers; complex
fixedpoint decimal arithmetic; complex floatingpoint
decimal arithmetic",
}O
©©ˆjPY#)]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,
author = "K. Davis and R. Biddulph and S. Balashek",
title = "Automatic Recognition of Spoken Digits",
journal = jJACOUSTSOCAM,
volume = "24",
number = "6",
pages = "637642",
month = nov,
year = "1952",
CODEN = "JASMAN",
ISSN = "00014966",
ISSNL = "00014966",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
fjournal = "Journal of the Acoustical Society of America",
}gO^ '#'+ƒ
#[=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:adr1011051952https://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
discussions presented at the December 1012, 1951,
joint AIEEIRE computer conference, Philadelphia, PA:
Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
publisher = pubACM,
address = pubACM:adr,
bookpages = "vi + 114",
pages = "101105",
year = "1952",
DOI = "https://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,
keywords = "Bell Laboratories Model 15 relay computers; complex
fixedpoint decimal arithmetic; complex floatingpoint
decimal arithmetic",
}
"
g¢"Š}S['#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",
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note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
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}‰BR[#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 = "????",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
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fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}‹QZ #1/!K77E‚#;SGc/articlefparith.bibMichaelson:1952:BAR. L. MichaelsonBinary ArithmeticjINCSTAT313540feb21952https://doi.org/10.2307/298659114669404 OR 1466940414669404 OR 14669404Thu Jan 22 18:10:18 MST 2015http://www.jstor.org/stable/i349863; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrssd1950.bib2015.01.22 18:10:18 MSThttp://www.jstor.org/stable/2986591The Incorporated Statisticianacknhfbhttp://www.jstor.org/journals/14669404.htmlR. L. MichaelsonBinary Arithmetic
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = jINCSTAT,
volume = "3",
number = "1",
pages = "3540",
month = feb,
year = "1952",
CODEN = "????",
DOI = "https://doi.org/10.2307/2986591",
ISSN = "14669404",
ISSNL = "14669404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrssd1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = acknhfb,
fjournal = "The Incorporated Statistician",
journalURL = "http://www.jstor.org/journals/14669404.html",
}U8916837 (print), 23264853 (electronic)",
ISSNL = "08916837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
abstract = "The difficulties which arise when programming
calculations for large automatic calculating machines
which have a fixed decimal point are discussed. This
leads to a consideration of the possibility of using
floating decimal arithmetic for certain kinds of
calculations. A method by which floating decimal
arithmetic can be carried out with any fixed
decimalpoint machine is outlined and the scheme
adopted for use with the EDSAC is described in
detail.",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
keywords = "floatingpoint decimal arithmetic",
remark01 = "From page 38: ``The problem [of programmercontrolled
numeric scaling] does not arise with machines designed
to operate directly with numbers expressed in the
floating radix form. Numbers in this form are
represented by $a \cdot r^p$. The first machine of this
kind was the Bell Telephone Laboratories Relay Computer
Model V(1). This is a decimal machine (that is, $r =
10$) in which $1 > a > 0.1$, $19 > p > 19$ and $a$
is expressed to an accuracy of seven significant
figures. Since this was completed all important relay
machines have been equipped with similar facilities. No
electronic machine of this kind has yet been built but
we would remark that in our opinion an electronic
machine provided with a floating point arithmetical
unit would be a powerful computing instrument even if
it had a relatively slow store, a magnetic drum, for
example.''",
remark02 = "From page 39: ``Two long and two short storage
locations are set aside to form a kind of `arithmetical
unit.' One long location holds the numerical part of a
number and one short location holds the exponent.
Together they form the {\em floating decimal
accumulator}. In a similar fashion the other long
location and the other short location form the {\em
floating decimal register}.''",
remark03 = "From page 40: ``the floating decimal accumulator is
then `cleared' by replacing the number held in it by
zero, that is, by the special number $010^{63}$.''",
remark04 = "From page 40: `The use of two separate storage
locations for the floating decimal accumulator allows
the range and accuracy of numbers held therein to be
greater than those held in a single storage location
elsewhere. This enables products to be accumulated
without loss of accuracy due to intermediate
roundingoff errors.''",
remark05 = "From the conclusion on page 46: ``From a direct
comparison it would seem that the floating 'orders,'
other than those used for reading and writing, are
about 60 times as slow as the machine orders and hence
that a programme using the interpretive subroutine
would be slower by the same factor. This is not
altogether true because in such a programme fewer
orders' are needed than would otherwise be necessary as
there are no scale factors to deal with and the
techniques for counting and for the modification of
orders' have been streamlined. Moreover, the time taken
by the C auxiliaries is about the same as that taken by
the corresponding subroutine in fixed decimalpoint
working. These factors vary from problem to problem but
our experience has shown that the reduction in speed
varies from about 20 to 1 to about 4 to 1. The
reduction of the time taken to code a problem has to be
experienced to be believed!''",
}T
?
Ô
¼Í÷.?h›Q
@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",
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ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Sat Dec 03¿…G‹
@Article{Cowlishaw:2004:FFE,
author = "Mike Cowlishaw and Joshua Bloch and Joseph D. Darcy",
title = "Fixed, Floating, and Exact Computation in {Java}'s
{{\em BigDecimal\/}}: Calculations just got easier",
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volume = "29",
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pages = "22, 24, 2627",
month = jul,
year = "2004",
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ISSN = "1044789X",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "decimal floatingpoint arithmetic",
}ú…T‹)
@Article{Cowlishaw:2002:DPD,
author = "Michael F. Cowlishaw",
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journal = jIEEPROCCOMPUTDIGITTECH,
volume = "149",
number = "3",
pages = "102104",
year = "2002",
CODEN = "ICDTEA",
DOI = "https://doi.org/10.1049/ipcdt:20020407",
ISSN = "13502387 (print), 13597027 (electronic)",
ISSNL = "13502387",
bibdate = "Fri Jun 07 11:08:45 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "decimal floatingpoint arithmetic",
}â’X¥1
@Article{Cowlishaw:1984:DRL,
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ISSN = "00188670",
bibdate = "Wed Jan 08 16:35:07 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a BuiltIn Square Root Method",
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volume = "EC13",
number = "2",
pages = "156157",
month = apr,
year = "1964",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
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@Article{Coupe:1983:SPZ,
author = "B. Coupe",
title = "Superefficient programs for 8080 and {Z80} multiply",
journal = jELECTRONICS,
volume = "56",
number = "6",
pages = "142143",
month = mar,
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",
}×oating decimal arithmetic for certain kinds of
calculations. A method by which floating decimal
arithmetic can be carried out with any fixed
decimalpoint machine is outlined and the scheme
adopted for use with the EDSAC is described in
detail.",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
keywords = "floatingpoint decimal arithmetic",
remark01 = "From page 38: ``The problem [of programmercontrolled
numeric scaling] does not arise with machines designed
to operate directly with numbers expressed in the
floating radix form. Numbers in this form are
represented by $a \cdot r^p$. The first machine of this
kind was the Bell Telephone Laboratories Relay Computer
Model V(1). This is a decimal machine (that is, $r =
10$) in which $1 > a > 0.1$, $19 > p > 19$ and $a$
is expressed to an accuracy of seven significant
figures. Since this was completed all important relay
machines have been equipped with similar facilities. No
electronic machine of this kind has yet been built but
we would remark that in our opinion an electronic
machine provided with a floating point arithmetical
unit would be a powerful computing instrument even if
it had a relatively slow store, a magnetic drum, for
example.''",
remark02 = "From page 39: ``Two long and two short storage
locations are set aside to form a kind of `arithmetical
unit.' One long location holds the numerical part of a
number and one short location holds the exponent.
Together they form the {\em floating decimal
accumulator}. In a similar fashion the other long
location and the other short location form the {\em
floating decimal register}.''",
remark03 = "From page 40: ``the floating decimal accumulator is
then `cleared' by replacing the number held in it by
zero, that is, by the special number $010^{63}$.''",
remark04 = "From page 40: `The use of two separate storage
locations for the floating decimal accumulator allows
the range and accuracy of numbers held therein to be
greater than those held in a single storage location
elsewhere. This enables products to be accumulated
without loss of accuracy due to intermediate
roundingoff errors.''",
remark05 = "From the conclusion on page 46: ``From a direct
comparison it would seem that the floating 'orders,'
other than those used for reading and writing, are
about 60 times as slow as the machine orders and hence
that a programme using the interpretive subroutine
would be slower by the same factor. This is not
altogether true because in such a programme fewer
orders' are needed than would otherwise be necessary as
there are no scale factors to deal with and the
techniques for counting and for the modification of
orders' have been streamlined. Moreover, the time taken
by the C auxiliaries is about the same as that taken by
the corresponding subroutine in fixed decimalpoint
working. These factors vary from problem to problem but
our experience has shown that the reduction in speed
varies from about 20 to 1 to about 4 to 1. The
reduction of the time taken to code a problem has to be
experienced to be believed!''",
}
ÍïÍ†U[ #%+#=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,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
Equipment",
publisher = pubIBM,
address = pubIBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}¶T_#KKo57E{;‡oO=‡K1Ðkarticlefparith.bibBrooker:1953:FOER. A. Brooker and D. J. WheelerFloating Operations on the EDSAC (in Automatic Computing Machinery; Discussions)jMATHTABLESOTHERAIDSCOMPUT7413747jan11953MTTCAShttps://doi.org/10.1090/S0025571819530052901308916837 (print), 23264853 (electronic) OR 08916837 (print), 23264853 (electronic)08916837 OR 08916837Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database1998.10.13 08:06:19 MDTThe difficulties which arise when programming calculations for large automatic calculating machines which have a fixed decimal point are discussed. This leads to a consideration of the possibility of using floating decimal arithmetic for certain kinds of calculations. A method by which floating decimal arithmetic can be carried out with any fixed decimalpoint machine is outlined and the scheme adopted for use with the EDSAC is described in detail.Mathematical Tables and Other Aids to Computationfloatingpoint decimal arithmeticacknhfbhttp://www.ams.org/mcom/The difficulties which arise when programming calculations for large automatic calculating machines which have a fixed decimal point are discussed. This leads to a consideration of the possibility of using floating decimal arithmetic for certain kinds of calculations. A method by which floating decimal arithmetic can be carried out with any fixed decimalpoint machine is outlined and the scheme adopted for use with the EDSAC is described in detail.R. A. Brooker and D. J. WheelerFloating Operations on the {EDSAC} (in Automatic Computing Machinery; Discussions)
@Article{Brooker:1953:FOE,
author = "R. A. Brooker and D. J. Wheeler",
title = "Floating Operations on the {EDSAC} (in Automatic
Computing Machinery; Discussions)",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "7",
number = "41",
pages = "3747",
month = jan,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S00255718195300529013",
ISSN = "08916837 (print), 23264853 (electronic)",
ISSNL = "08916837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
abstract = "The difficulties which arise when programming
calculations for large automatic calculating machines
which have a fixed decimal point are discussed. This
leads to a consideration of the possibility of using
flW",
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",
}V
TT™)V] #+%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",
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",
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",
}d 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.",
}W
R±RŒ\X\#?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.",
}ŽLWZ #/O1%/Em;3†WS1manualfparith.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.",
}
ÅC‡Å‰?[Z#)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;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‰9Z[#+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
Electronic Computers",
}‰:Y\ #'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",
}
}
~s}P†
Œ
@Article{Goodman:1978:ITD,
auth#s
@Article{Goodwin:1977:CUO,
author = "D. T. Goodwin",
title = "Conditions for Underflow and Overflow of an Arithmetic
Stack",
journal = jCOMPJ,
volume = "20",
number = "1",
pages = "5662",
month = feb,
year = …t‹i
@Article{Goodman:1990:SMR,
author = "R. H. Goodman",
title = "Some Models of Relative Error in Products",
journal = jAPPLNUMMATH,
volume = "6",
number = "3",
pages = "209220",
month = mar,
year = "1990",
CODEN = "ANMAEL",
ISSN = "01689274 (print), 18735460 (electronic)",
ISSNL = "01689274",
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",
acknowledgement = acknj,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journalURL = "http://www.sciencedirect.com/science/journal/01689274",
} h† Œ
@Article{Goodman:1985:REF,
author = "R. H. Goodman and A. Feldstein and J. Bustoz",
title = "Relative error in floatingpoint multiplication",
journal = jCOMPUTING,
volume = "35",
number = "2",
pages = "127139",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
MRclass = "65G05",
MRnumber = "87d:65052",
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 = "Luciano Biasini",
}Ë†
Œ
@Article{Goodman:1978:ITD,
author = "R. Goodman and J. Bustoz and A. Feldstein",
title = "Improved Trailing Digits Estimates Applied to Optimal
Computer Arithmetic",
journal = jSIAMREVIEW,
volume = "20",
number = "3",
pages = "625625",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "00361445 (print), 10957200 (electronic)",
ISSNL = "00361445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "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",
}‡Ž
@Article{Goodman:1977:EGD,
author = "R. Goodman and A. Feldstein",
title = "Effect of Guard Digits and Normalization Options on
Floating Point Multiplication",
journal = jCOMPUTING,
volume = "18",
number = "2",
pages = "93106",
month = "????",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
MRclass = "65G05",
MRnumber = "55 11596",
bibdate = "Fri Dec 08 12:02:42 1995",
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",
reviewer = "N. N. Abdelmalek",
}Áˆn‘]
@Article{Goodman:1976:REF,
author = "Richard Goodman",
title = "On roundoff error in fixedpoint multiplication",
journal = jBIT,
volume = "16",
number = "1",
pages = "4151",
month = mar,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940776",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Wed Jan 4
ÄA]\ #/)cKo57=[;o‚y=)g‘9articlefparith.bibClenshaw:1955:NSCC. W. ClenshawA note on the summation of Chebyshev seriesjMATHTABLESOTHERAIDSCOMPUT9511181201955MTTCAShttps://doi.org/10.1090/S0025571819550071856008916837 (print), 23264853 (electronic) OR 08916837 (print), 23264853 (electronic)08916837 OR 0891683765.0X0071856Thu Feb 08 16:17:25 2018http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib2018.02.08 16:17:25 ???Mathematical Tables and Other Aids to ComputationHidden inside cite Brenner:1955:TNS, but important in its own right for commentary on the recursive algorithm for summation of Chebyshev series, and a brief analysis of its accuracy.acknhfbhttp://www.ams.org/mcom/C. W. ClenshawA note on the summation of {Chebyshev} series
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A note on the summation of {Chebyshev} series",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "9",
number = "51",
pages = "118120",
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S00255718195500718560",
ISSN = "08916837 (print), 23264853 (electronic)",
ISSNL = "08916837",
MRclass = "65.0X",
MRnumber = "0071856",
bibdate = "Thu Feb 08 16:17:25 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
remark = "Hidden inside \cite{Brenner:1955:TNS}, but important
in its own right for commentary on the recursive
algorithm for summation of Chebyshev series, and a
brief analysis of its accuracy.",
}Š9\\ #%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",
}"65.0X",
MRnumber = "0071856",
bibdate = "Thu Feb 08 16:17:25 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
remark = "Hidden inside \cite{Brenner:1955:TNS}, but important
in its own right for commentary on the recursive
algorithm for summation of Chebyshev series, and a
brief analysis of its accuracy.",
}]
˜`Þ˜ˆC`\#/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,
}Š_\#+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
Jones",
title = "Faster, faster; a simple description of a giant
electronic calculator and the problems it solves",
publisher = pubIBM,
address = pubIBM:adr,
pages = "160",
year = "1955",
LCCN = "QA76 .E25",
bibdate = "Fri Aug 20 08:57:56 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
authordates = "19021971",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Computers",
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}‰^Z#/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
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P¨P†UcY #/;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
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author = "Richard Kohler Richards",
title = "Arithmetic Operations in Digital Computers",
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}Šjb\ #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
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}‡haZ #/)=)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,
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number = "??",
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@Book{StDenis:2006:BMH,
author = "Tom {St Denis} and Greg Rose",
title = "{BigNum} Math: Implementing Cryptographic Multiple
Precision Arithmetic",
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year = "2006",
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ISBN13 = "9781597491129",
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pages = "viii + 295",
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melvyl.cdlib.org:210/CDL90",
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subject = "Electronic digital computers; Arithmetic",
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@Book{Steele:1984:CLL,
author = "Guy L†+ŒW
@Book{StDenis:2006:BMI,
author = "Tom {St.Denis}",
title = "{BigNum} Math: Implementing Cryptographic Multiple
Precision Arithmetic",
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acknowledgement = acknhfb,
keywords = "Karatsuba multiplication; modular exponentiation;
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@Book{Startz:1988:IPC,
author = "Richard Startz",
title = "8087\slash 80287\slash 80387 for the {IBM PC} and
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{Intel}'s Math Coprocessors",
publisher = pubBRADY,
address = pubBRADY:adr,
edition = "Third",
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year = "1988",
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ISBN13 = "9780132466042",
LCCN = "QA76.8.I2923 S79 1988",
bibdate = "Wed Sep 14 20:23:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
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author = "Otto Spaniol",
title = "Computer Arithmetic: Logic and Design",
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pages = "280",
year = "1981",
ISBN = "0471279269",
ISBN13 = "9780471279266",
LCCN = "QA76.6 .S6613, TK7888.3.S7",
bibdate = "Thu Sep 01 22:26:58 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation of \cite{Spaniol:1976:AR}.",
acknowledgement = acknhfb,
}[† Œ
@Book{Spaniol:1976:AR,
author = "Otto Spaniol",
title = "{Arithmetik in Rechenanlagen: Logik und Entwurf}
\toenglish {Computer Arithmetic: Logic and Design}
\endtoenglish",
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address = pubTEUBNER:adr,
pages = "208",
year = "1976",
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ISBN13 = "9783519023326",
LCCN = "QA76.6 .S66",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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\cite{Spaniol:1981:CAL}.",
price = "DM24.80",
acknowledgement = acknj,
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@InProceedings{Teufel:1984:HAO,
author = "Thomas Teufel",
title = "A hardware architecture of an optimal
{BCD}floatingpoint processor",
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pages = "553560",
year = "1984",
MRclass = "65G05",
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}“™7
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author = "H. Thapliyal and S. Kotiyal and M. B. Srinivas",
title = "Novel {BCD} adders and their reversible logic
implementation for {IEEE 754R} format",
crossref = "IEEE:2006:ICV",
year = "2006",
DOI = "https://doi.org/10.1109/VLSID.2006.122",
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@InProceedings{Thistle:1988:PAH,
author = "M. R. Thistle and B. J. Smith",
title = "A processor architecture for {Horizon}",
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pages = "3541",
year = "1988",
bibdate = "Thu Apr 16 07:55:03 MDT 1998",
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classification = "C5220 (Computer architecture); C5440 (Multiprocessor
VƒI‡
@InProceedings{Teufel:1992:IFP,
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accurate scalar product for digital signal processing",
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}0‰5’k
@InProceedings{Tenca:2009:MOF,
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of multiple floatingpoint (FP) operands is explored in
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@InProceedings{Thapliyal:2006:DNR,
author = "Himanshu Thapliyal and Sumedha K. Gupta",
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crossref = "Mohanty:2006:IIC",
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abstract = "IEEE 754r ib‘v£m
@InProceedings{Thakkar:2006:PDP,
author = "Anuja J. Thakkar and Abdel Ejnioui",
title = "Pipelining of double precision floating point division
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crossref = "Menezes:2006:PAS",
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abstract = ]‹`—A
@InProceedings{Thomas:2003:IMF,
author = "James W. Thomas",
title = "Inlining of mathematical functions in {HPUX} for
{Itanium 2}",
crossref = "IEEE:2003:PCI",
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F
F‹Qe[ #+gc;]7Ea;]gcŒ_articlefparith.bibEstrin:1956:NHSG. Estrin and B. Gilchrist and J. H. PomereneA Note on HighSpeed Digital MultiplicationjIRETRANSELECCOMPUTEC53140140sep91956IRELAOhttps://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 = "https://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",
}‹cd] #1+;e7Ea;]+articlefparith.bibRobertson:1955:TCMJ. E. RobertsonTwo's Complement Multiplication in Binary Parallel Digital ComputersjIRETRANSELECCOMPUTEC43118119sep91955IRELAOhttps://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 = "https://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",
} pure and applied mathematics",
acknowledgement = acknhfb,
remark = "See also second edition
\cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
subject = "Numerical analysis",
tableofcontents = "1. Introduction (significant figures, random
errors, error bounds, etc.) \\
2. Interpolation with divided differences \\
3. Lagrangian methods \\
4. Finitedifference interpolation \\
5. Operations with finite differences \\
6. Numerical solution of ordinary differential
equations \\
7. Leastsquares polynomial approximation \\
8. Gaussian quadrature and related topics \\
9. Approximations of various types \\
10. Numerical solution of equations \\
Appendix: Justification of the Crout reduction",
}f
nn—f] #3AQ+3E%;u1‡5AQ‡q–)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 analysis1. Introduction (significant figures, random errors, error bounds, etc.) 2. Interpolation with divided differences 3. Lagrangian methods 4. Finitedifference interpolation 5. Operations with finite differences 6. Numerical solution of ordinary differential equations 7. Leastsquares polynomial approximation 8. Gaussian quadrature and related topics 9. Approximations of various types 10. Numerical solution of equations Appendix: Justification of the Crout reductionacknhfbFrancis Begnaud HildebrandIntroduction to Numerical Analysis1. Introduction (significant figures, random errors, error bounds, etc.) \\ 2. Interpolation with divided differences \\ 3. Lagrangian methods \\ 4. Finitedifference interpolation \\ 5. Operations with finite differences \\ 6. Numerical solution of ordinary differential equations \\ 7. Leastsquares polynomial approximation \\ 8. Gaussian quadrature and related topics \\ 9. Approximations of various types \\ 10. Numerical solution of equations \\ Appendix: Justification of the Crout reduction
@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",
tableofcontents = "1. Introduction (significant figures, random
errors, error bounds, etc.) \\
2. Interpolation with divided differences \\
3. Lagrangian methods \\
4. Finitedifference interpolation \\
5. Operations with finite differences \\
6. Numerical solution of ordinary differential
equations \\
7. Leastsquares polynomial approximation \\
8. Gaussian quadrature and related topics \\
9. Approximations of various types \\
10. Numerical solution of equations \\
Appendix: Justification of the Crout reduction",
}
³ÃÚ‡
] #++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,
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title = "An Improved Decimal Redundancy Check",
journal = jCACM,
volume = "1",
number = "5",
pages = "1012",
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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,
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a7a‹R[ #)#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,
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bibdate = "Wed Jul 14 15:48:22 MDT 2004",
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}‰E[ #+%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",
}
,,—P
]#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",
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.",
}Ž
èóèŒ[ #'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)",
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",
}Ž ] #//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.",
}
ú ,úˆ.Y #'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",
}P[ %#%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,
bookpages = "????",
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,
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",
}
@ QnŽ\9
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}’ˆ0a
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@Article{Hegland:1994:SSP,
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@Article{Hecker:1996:LGF,
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‰’5
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R R*]#+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,
author = "Paolo Ercoli and Roberto Vacca",
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pages = "1315",
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ISSNL = "00010782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#ErcoliV59;
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 = "ErcoliV59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
}r = "MR0099119 (20 \#5563)",
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http://www.math.utah.edu/pub/bibnet/authors/f/forsythegeorgeelmer.bib;
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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ZMnumber = "0168.14002",
acknowledgement = acknhfb,
fjournal = "SIAM Review",
journalURL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis; random roundingoff procedure",
onlinedate = "January 1959",
received = "7 February 1958",
remark = "From a footnote on the cover page: ``This note was
written in June 1950 at the National Bureau of
Standards, Los Angeles, and a few copies were
distributed in multilithed form by that organization as
an appendix to a reproduction of a wellknown article
by Rademacher [1]. The note was abstracted in Math.
Reviews, Vol. 12 (1951), p. 208. Because he receives
frequent requests for copies of the note, which are
unavailable, the author has asked the editors to
reprint it in essentially its original form.''",
}“
ƒƒšy\ #/1]'K577E…I;#oˆ!C%1]Ÿ
articlefparith.bibForsythe:1959:RNRGeorge E. ForsytheReprint of a Note on RoundingOff ErrorsjSIAMREVIEW116667jan11959SIREADhttps://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 analysis; random roundingoff procedureFrom a footnote on the cover page: ``This note was written in June 1950 at the National Bureau of Standards, Los Angeles, and a few copies were distributed in multilithed form by that organization as an appendix to a reproduction of a wellknown article by Rademacher [1]. The note was abstracted in Math. Reviews, Vol. 12 (1951), p. 208. Because he receives frequent requests for copies of the note, which are unavailable, the author has asked the editors to reprint it in essentially its original form.''0168.14002acknhfbhttp://epubs.siam.org/sirevJanuary 1959George E. ForsytheReprint of a Note on RoundingOff Errors
@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 = jan,
year = "1959",
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DOI = "https://doi.org/10.1137/1001011",
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MRclass = "65.00",
MRnumber = "MR0099119 (20 \#5563)",
bibdate = "Thu Mar 27 09:04:24 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/1/1;
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.bib",
ZMnumber = "0168.14002",
acknowledgement = acknhfb,
fjournal = "SIAM Review",
journalURL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis; random roundingoff procedure",
onlinedate = "January 1959",
received = "7 February 1958",
remark = "From a footnote on the cover page: ``This note was
written in June 1950 at the National Bureau of
Standards, Los Angeles, and a few copies were
distributed in multilithed form by that organization as
an appendix to a reproduction of a wellknown article
by Rademacher [1]. The note was abstracted in Math.
Reviews, Vol. 12 (1951), p. 208. Because he receives
frequent requests for copies of the note, which are
unavailable, the author has asked the editors to
reprint it in essentially its original form.''",
}
é
1éŠD[ #+?;]7Ea;]?Œarticlefparith.bibGarner:1959:RNSHarvey L. GarnerThe Residue Number SystemjIRETRANSELECCOMPUTEC82140147jun61959IRELAOhttps://doi.org/10.1109/TEC.1959.521951503679950 OR 03679950Thu Jul 14 15:56:44 MDT 2011http://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 = "https://doi.org/10.1109/TEC.1959.5219515",
ISSN = "03679950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515",
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volume = "17",
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author = "Thomas D. Wilbanks",
title = "Microcoding floatingpoint instructions for a
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type = "Thesis ({M.S.})",
school = "University of South Carolina",
address = "Columbia, SC, USA",
pages = "vi + 131",
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
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acknowledgement = acknhfb,
keywords = "Bit slice microprocessors.; Microprocessors 
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}•„‰y
@MastersThesis{Wong:1990:PFP,
author = "Karpang Wong",
title = "The precision of floating point computation in digital
computer",
type = "Thesis ({M.S. in Computer Science})",
school = "University of Wisconsin, Milwaukee",
address = "Milwaukee, WI, USA",
pages = "vii + 45",
year = "1990",
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acknowledgement = acknhfb,
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@MastersThesis{Wong:1980:IOF,
author = "Clement SauFai Wong",
title = "Input\slash output and floatingpoint arithmetic
package",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
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year = "1980",
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@MastersThesis{Wittman:1989:SCU,
author = "Susan Jean Wittman",
title = "Servo compensation using a floating point digital
signal processor",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology, Dept. of
Aeronautics and Astronautics",
address = "Cambridge, MA, USA",
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year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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} B„B‰
@MastersThesis{Williams:1987:FPL,
author = "Robert Leslie Williams",
title = "A floating point loop engine architecture using
pattern generation",
type = "Thesis ({M.S.})",
school = "University of New Mexico",
address = "Albuquerque, NM, USA",
pages = "ix + 92",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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acknowledgement = acknhfb,
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@MastersThesis{Williams:1983:BFP,
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school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "x + 97",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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acknowledgement = acknhfb,
keywords = "Computer architecture.; Floatingpoint arithmetic.;
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@Article{Bockstaele:1960:NFA,
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@MastersThesis{Young:1959:SSM,
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month = dec,
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volume = "39",
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@Article{Chang:1983:HSN,
author = "TungLiang Chang and P. Fisher",
title = "Highspeed normalization and rounding circuits for
pipelined floatingpoint processors",
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{Fourier} transforms implemented with logarithmic
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)¹Šl)[ #'%e;]7Ea;]%eŒarticlefparith.bibCroy:1960:IADJohn E. CroyImproved Arrangement of a Decimal MultiplierjIRETRANSELECCOMPUTEC92263263jun61960IRELAOhttps://doi.org/10.1109/TEC.1960.521983003679950 OR 03679950Thu Jul 14 15:34:11 MDT 2011http://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
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author = "John E. Croy",
title = "Improved Arrangement of a Decimal Multiplier",
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volume = "EC9",
number = "2",
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month = jun,
year = "1960",
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author = "David T. Brown",
title = "Error Detecting and Correcting Binary Codes for
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journal = jIRETRANSELECCOMPUT,
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À ŸÀ[+[ #)!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,
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}Œ]*] #+%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,
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‹,\ !#+%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
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MathSciNet database",
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(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.",
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›_ #)+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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MathSciNet database",
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’*[‡K0[ #+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
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month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}rce = "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",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}¹
`(`‹D:[ #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,
author = "J. H. Wilkinson",
title = "Error Analysis of FloatingPoint Computation",
journal = jNUMMATH,
volume = "2",
pages = "319340",
month = dec,
year = "1960",
CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
ISSNL = "0029599X",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Numerische Mathematik",
journalURL = "http://link.springer.com/journal/211",
}“T9\ #'#A57'=m;…)1Me…)#A”
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",
title = "FloatingPoint Arithmetics",
journal = jJACM,
volume = "7",
number = "2",
pages = "129139",
month = apr,
year = "1960",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
MRclass = "65.00 (68.00)",
MRnumber = "22\#6090",
bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Three types of 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",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}), 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=3;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
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xxpages = "220221??",
}»
v+v‡1] #+5{;]7Ea;Š=]Š=5{šWarticlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number SystemjIRETRANSELECCOMPUTEC1016370mar31961IRELAOhttps://doi.org/10.1109/TEC.1961.521915403679950 OR 03679950Thu Jul 14 14:45:02 MDT 2011http://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 = "https://doi.org/10.1109/TEC.1961.5219154",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:02 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=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",
}
WW‰%?Z #/)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",
} 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",
}À
))S@] #%I[W57=ƒ;Š?cŠI[›Qarticlefparith.bibCox:1961:NMPAlbert G. Cox and H. A. LutherA Note on Multiple Precision ArithmeticjCACM48353353aug81961CACMA2https://doi.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 = "https://doi.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;
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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",
}
c Æcˆ_B[ #'!=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.",
}Œ6A] #'%];]7Ea;]%]7articlefparith.bibCroy:1961:RTMJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix ArithmeticjIRETRANSELECCOMPUTEC104777777dec121961IRELAOhttps://doi.org/10.1109/TEC.1961.521928603679950 OR 03679950Thu Jul 14 14:45:05 MDT 2011http://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 = "https://doi.org/10.1109/TEC.1961.5219286",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:05 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=5219286",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}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..",
}ÃHis 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..",
}
‰‰°kC`!#+[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. Ã "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",
}Ä
¨E] #'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",
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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",
}
ù‡YKY #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",
}ŒJ]#+9#;]7Ea;]9#articlefparith.bibLehman:1961:STHM. Lehman and N. BurlaSkip Techniques for HighSpeed CarryPropagation in Binary Arithmetic UnitsjIRETRANSELECCOMPUTEC104691698dec121961IRELAOhttps://doi.org/10.1109/TEC.1961.521927403679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://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 = "https://doi.org/10.1109/TEC.1961.5219274",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 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=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",
}Ì
üüŽL] #+' 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",
}th.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}.",
}Íal 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 (print), 21688990 (electronic)",
ISSNL = "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}.",
}
Ë@ËˆqNZ #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",
}µ4M^ #k+!57=m;CŽmOsŽ7Žuk´1articlefparith.bibPinkham:1961:DFSRoger S. PinkhamOn the Distribution of First Significant DigitsjANNMATHSTAT32412231230dec121961AASTAD00034851 (print), 21688990 (electronic) OR 00034851 (print), 21688990 (electronic)00034851 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 constants with low order first significant digits than high. ActuÒ
Pû î P‡N
@Article{Revol:2014:NRP,
author = "Nathalie Revol and Philippe Theveny",
title = "Numerical Reproducibility and Parallel Computations:
Issues for Interval Algorithms",
journal = jIEEETRANSCOMPUT,
volume = "63",
number = "8",
pages = "19151924",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2322593",
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",
keywords = "floatingpoint arithmetic; reproducible arithmetic",
}IŽD
@Article{Revol:2005:TMF,
author = "N. Revol and K. Makino and M. Berz",
title = "{Taylor} models and floatingpoint arithmetic: proof
that arithmetic operations are validated in {COSY}",
journal = jJLOGICALGPROG,
volume = "64",
number = "1",
pages = "135154",
month = "????",
year = "2005",
CODEN = "????",
ISSN = "15678326",
ISSNL = "15678326",
MRclass = ‰‡];
@Article{Renner:1974:RRN,
author = "K. Renner and S. Gupta",
title = "Reduction of roundoff noise in wave digital filters",
journal = jIEEETRANSCIRCUITSSYST,
volume = "21",
number = "2",
pages = "305310",
month = mar,
year = "1974",
CODEN = "ICSYBT",
ISSN = "00984094 (print), 15581276 (electronic)",
ISSNL = "00984094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Roundoff noise generated by arithmetic operations in a
digitalfilter computational sequence is undesirable in
that it serves to distort the true signal at the
output. Furthermore, coefficient wordlength is directly
related to the generated noise. \ldots{}",
}†Œ
@Article{Reiser:1975:EDFb,
author = "John F. Reiser and Donald E. Knuth",
title = "Erratum: ``{Evading} the drift in floatingpoint
addition''",
journal = jINFOPROCLETT,
volume = "3",
number = "5",
pages = "164164",
month = may,
year = "1975",
CODEN = "IFPLAT",
ISSN = "00200190 (print), 18726119 (electronic)",
ISSNL = "00200190",
bibdate = "Sun Dec 04 12:21:42 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Reiser:1975:EDFa}.",
acknowledgement = acknhfb,
fjournal = "Information Processing Letters",
journalURL = "http://www.sciencedirect.com/science/journal/00200190",
}U†Œ
@Article{Reiser:1975:EDFa,
author = "John F. Reiser and Donald E. Knuth",
title = "Evading the drift in floatingpoint addition",
journal = jINFOPROCLETT,
volume = "3",
number = "3",
pages = "8487",
month = jan,
year = "1975",
CODEN = "IFPLAT",
ISSN = "00200190 (print), 18726119 (electronic)",
ISSNL = "00200190",
bibdate = "Sun Dec 04 12:21:37 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Reiser:1975:EDFb}.",
acknowledgement = acknhfb # "\slash " # acknj,
fjournal = "Information Processing Letters",
journalURL = "http://www.sciencedirect.com/science/journal/00200190",
}T
œ
Oœ‹/P] #1)'57Ek;A=)ŒM articlefparith.bibSpielberg:1961:ECFKurt SpielbergEfficient Continued Fraction Approximations To Elementary FunctionsjMATHCOMPUT1576409417oct101961MCMPAF00255718 (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 SpielbergEfficient Continued Fraction Approximations To Elementary Functions
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = jMATHCOMPUT,
volume = "15",
number = "76",
pages = "409417",
month = oct,
year = "1961",
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;
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/",
}‹O[ #){;]7Ea;]){Œ_articlefparith.bibSaltman:1961:RCTRoy G. SaltmanReducing Computing Time for Synchronous Binary DivisionjIRETRANSELECCOMPUTEC102169174jun61961IRELAOhttps://doi.org/10.1109/TEC.1961.521918603679950 OR 03679950Thu Jul 14 14:45:03 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:03 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186IRE Transactions on Electronic ComputersacknhfbRoy G. SaltmanReducing Computing Time for Synchronous Binary Division
@Article{Saltman:1961:RCT,
author = "Roy G. Saltman",
title = "Reducing Computing Time for Synchronous Binary
Division",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "2",
pages = "169174",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219186",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:03 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=5219186",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
’R\ #'!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
@Book{Taub:1961:JNC,
editor = "A. H. Taub",
title = "{John von Neumann}: Collected Works",
publisher = pubPERGAMON,
address = pubPERGAMON:adr,
pages = "??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol.
4), ??? (vol. 5), ??? (vol. 6)",
year = "19611963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Six volumes. Volume I: Logic, Theory of Sets and
Quantum Mechanics (1961); Volume II: Operators, Ergodic
Theory and Almost Periodic Functions in a Group (1961);
Volume III: Rings of Operators (1961); Volume IV:
Continuous Geometry and Other Topics (1962); Volume V:
Design of Computers, Theory of Automata and Numerical
Analysis (1963); Volume VI: Theory of Games,
Astrophysics, Hydrodynamics and Meteorology (1963).",
acknowledgement = acknhfb,
}‹`Q] #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
@Article{Spielberg:1961:RPS,
author = "K. Spielberg",
title = "Representation of Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
journal = jJACM,
volume = "8",
number = "4",
pages = "613627",
month = oct,
year = "1961",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Sat Dec 09 14:01:44 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}x volumes. Volume I: Logic, Theory of Sets and
Quantum Mechanics (1961); Volume II: Operators, Ergodic
Theory and Almost Periodic Functions in a Group (1961);
Volume III: Rings of Operators (1961); Volume IV:
Continuous Geometry and Other Topics (1962); Volume V:
Design of Computers, Theory of Automata and Numerical
Analysis (1963); Volume VI: Theory of Games,
Astrophysics, Hydrodynamics and Meteorology (1963).",
acknowledgement = acknhfb,
}Ò
ßSBS
û^ø†Œ)
@Book{Stevenson:1981:PSBb,
aßS
@Book{Stone:1975:ICA,
editor = "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
and Samuel H. Fuller and others",
title = "Introduction to computer architecture",
publisher = "Science Research Associates",
address = Àvk
@Book{Sterbenz:1974:FPC,
author = "Pat H. Sterbenz",
title = "Floating Point Computation",
publisher = pubPH,
address = pubPH:adr,
pages = "xiv + 316",
year = "1974",
ISBN = "0133224953",
ISBN13 = "9780133224955",
LCCN = "QA76.8.I12 S771 1974",
MRclass = "68A05 (65G05)",
MRnumber = "50 1556",
bibdate = "Sat May 29 08:01:36 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc]„ˆ5
@Book{Stein:1971:IMA,
author = "Marvin L. Stein and William D. Munro",
title = "Introduction to machine arithmetic",
publisher = pubAW,
address = pubAW:adr,
pages = "viii + 295",
year = "1971",
LCCN = "QA76.5 .S752",
bibdate = "Fri Nov 9 19:20:08 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = acknhfb,
subject = "Electronic digital computers; Arithmetic",
}[†Ž
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "Highspeed computing devices",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "xiii + 451",
year = "1950",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6ONR240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}F
ç)
@Book{Stevenson:19‹r—e
@Book{Stine:2004:DCA,
author = "James E. Stine",
title = "Digital computer arithmetic datapath design using
{Verilog HDL}",
publisher = pubKLUWER,
address = pubKLUWER:adr,
pages = "xi + 180",
year = "2004",
ISBN = "1402077106",
ISBN13 = "9781402077104",
LCCN = "TK7868.D5 S75 2004",
bibdate = "Thu Nov 18 09:03:42 MST 2010",
bibsource = "http://www.math.utah.edu/pub/tex…Q
@Book{Stone:1†Œ)
@Book{Stevenson:1981:PSBb,
author = "David Stevenson",
title = "A proposed standard for binary floatingpoint
arithmetic: draft 8.0 of {IEEE} Task {P754}",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "36",
year = "1981",
bibdate = "Sun May 02 09:22:07 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = acknhfb,
keywords = "Compiling (Electronic computers).; Floatingpoint
arithmetic.",
remark = "Reprinted from: Computer, v. 14, no. 3 (Mar. 1981):
5187. Includes articles by W.J. Cody, David Hough,
and Jerome T. Coonen.",
}^µXë1
@Book{Stewart:1996:ANA,
author = "G. W. (Gilbert W.) Stewart",
title = "Afternotes on numerical analysis: a series of lectures
on elementary numerical analysis presented at the
{University of Maryland at College Park} and recorded
after the fact",
publisher = pubSIAM,
address = pubSIAM:adr,
pages = "x + 200",
year = "1996",
DOI = "https://doi.org/10.1137/1.9781611971491o
…
…ŠwS] #75'57E
;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
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = jMATHCOMPUT,
volume = "15",
number = "76",
pages = "399403",
month = oct,
year = "1961",
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/",
}tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
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
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ackmfc # " and " # acknhfb,
}Ô
nnT] !#')KM=m;Œ]Œ])™atechreportfparith.bibWeik:1961:TSDMartin H. WeikA Third Survey of Domestic Electronic Digital Computing SystemsReport1115Ballistic Research LaboratoriesAberdeen Proving Ground, MD, USA1131mar31961Fri Nov 28 19:37:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 19:37:51 ???Based on the results of a third survey, the engineering and programming characteristics of two 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 comparative tables, a discussion of trends, a revised bibliography, and a complete glossary of computer engineering and programming terminology are included.ackmfcBased on the results of a third survey, the engineering and programming characteristics of two 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 comparative tables, a discussion of trends, a revised bibliography, and a complete glossary of computer engineering and programming terminology are included.Martin H. WeikA Third Survey of Domestic Electronic Digital Computing Systems
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title = "A Third Survey of Domestic Electronic Digital
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abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
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
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ackmfc # " and " # acknhfb,
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ô
fô‰%XZ %#/)+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
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
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title = "FloatingPoint Operation",
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address = pubMCGRAWHILL:adr,
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}‚¢uWa #/+c+3!Eƒ{;{µC7ñ%+{gü‚”eSbookfparith.bibBuchholz:1962:PCSWerner BuchholzPlanning a computer system: Project StretchpubMCGRAWHILLpubMCGRAWHILL:adrxvii + 32219621876Fri Nov 19 10:02:31 MST 2010http://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; lâ…SVY '#3M)=m;Q…cinproceedingsfparith.bibAshenhurst:1962:MIAR. L. AshenhurstThe Maniac III Arithmetic SystemAFIPS:1962:APS1922021962Wed Feb 14 17:14:21 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 17:14:21 ???acknhfbR. L. AshenhurstThe {Maniac III} Arithmetic System
@InProceedings{Ashenhurst:1962:MIA,
author = "R. L. Ashenhurst",
title = "The {Maniac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}‹U[#+GY;]7Ea;]GYŒ7 articlefparith.bibWilson:1961:ARBJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary DivisionjIRETRANSELECCOMPUTEC104662670dec121961IRELAOhttps://doi.org/10.1109/TEC.1961.521927103679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://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",
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CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219271",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 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=5219271",
acknowledgement = acknhfb,
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}Þ
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
ß 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 \à\
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 \\
á 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",
}×ãibrary.ox.ac.uk:210/ADVANCE2010.11.19 10:02:31 MSTThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.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.ä 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 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 11.1å6. 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}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. Pærocedures 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 18ç3 \\ 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
@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 detail on page 102,
which states:
``By definition oèf 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
significanceé.)''",
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 Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmeêtical 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",
}
0ý6
v0Š5”k
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The concepts real and integer, however, are taken from
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language = "German",
}