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@Article{Owens:1987:AC,
author = "Robert Michael Owens and Mary Jane Irwin",
title = "The Arithmetic Cube",
journal = jIEEETRANSCOMPUT,
volume = "C36",
number = "11",
pages = "13421348",
month = nov,
year = "1987",
CODEN = "ITCOB4",
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acknowledgement = acknhfb,
authordates = "Johan Vilhelm Nystr{\"o}m (18241885)",
remark = "Thanks for Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicodecompatible fonts to represent the additional
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subject = "Weights and measures; Numeration; base16 arithmetic;
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<<“A[ #I‚=7E%;e„O%QI‚•bookfparith.bibNystrom:1862:PNSJohn W. (John William) NystromProject of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the baseJ. B. Lippincott and Co.Philadelphia, PA, USA1061862QC96 .N95Sat Oct 29 10:28:27 MDT 2016http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2016.10.29 10:28:27 MDThttp://unifoundry.com/tonal/; https://catalog.hathitrust.org/Record/011602816; https://lccn.loc.gov/04025433Thanks for Paul Hardy of Unifoundry in San Diego, CA, USA, for information about Nystrom's promotion of hexadecimal arithmetic, and for creating a Web site about Nystrom's tonal system, as well as developing Unicodecompatible fonts to represent the additional digits needed by the system.Weights and measures; Numeration; base16 arithmetic; hexadecimal arithmeticacknhfbJohan Vilhelm Nystrom (18241885)John W. (John William) NystromProject of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the base
@Book{Nystrom:1862:PNS,
author = "John W. (John William) Nystrom",
title = "Project of a new system of arithmetic, weight, measure
and coins, proposed to be called the tonal system, with
sixteen to the base",
publisher = "J. B. Lippincott and Co.",
address = "Philadelphia, PA, USA",
pages = "106",
year = "1862",
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bibdate = "Sat Oct 29 10:28:27 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = acknhfb,
authordates = "Johan Vilhelm Nystr{\"o}m (18241885)",
remark = "Thanks for Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicodecompatible fonts to represent the additional
digits needed by the system.",
subject = "Weights and measures; Numeration; base16 arithmetic;
hexadecimal arithmetic",
}
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• ©•†U #/;?9/=m;;?†OÓbookfparith.bibKarpinski:1925:HALouis Charles KarpinskiThe History of ArithmeticRand McNally & CompanyNew York, NY, USAxi + 2001925Fri Nov 28 18:09:05 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:09:05 ???ackmfcLouis Charles KarpinskiThe History of Arithmetic
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÷ ±÷‹7Y ##;357E
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*"
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@ ´@ŠqW #'‚c=m;_Og‚wŠ?#miscfparith.bibZuse:1936:VSDK. ZuseVerfahren zur selbsttatigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen. (German) [Procedure for automatic execution of calculations by calculating machines]18722111apr41936Wed Oct 13 11:22:03 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:22:03 ???Reprinted in cite [ 4.1]Randell:1982:ODC.GermanacknhfbGerman patent application Z23624.K. ZuseReprinted in \cite[\S 4.1]{Randell:1982:ODC}.{Verfahren zur selbstt{\"a}tigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen}. ({German}) [{Procedure} for automatic execution of calculations by calculating machines]
@Misc{Zuse:1936:VSD,
author = "K. Zuse",
title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
[{Procedure} for automatic execution of calculations by
calculating machines]",
howpublished = "German patent application Z23624.",
day = "11",
month = apr,
year = "1936",
bibdate = "Wed Oct 13 11:22:03 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
language = "German",
}‡iU #)117=m;_W)g1ˆA#articlefparith.bibPhillips:1936:BCE. W. PhillipsBinary calculationjJINSTACTUARIES67187221193600202681 OR 00202681Wed Oct 13 11:33:16 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:33:16 ???Reprinted in cite [ 7.1]Randell:1982:ODC.Journal of the Institute of ActuariesacknhfbE. W. PhillipsReprinted in \cite[\S 7.1]{Randell:1982:ODC}.Binary calculation
@Article{Phillips:1936:BC,
author = "E. W. Phillips",
title = "Binary calculation",
journal = jJINSTACTUARIES,
volume = "67",
number = "??",
pages = "187221",
year = "1936",
ISSN = "00202681",
bibdate = "Wed Oct 13 11:33:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Journal of the Institute of Actuaries",
}Œ]W #'s57Eƒ;Qo'sŽarticlefparith.bibCalvert:1936:DDSH. R. CalvertDecimal Division of Scales before the Metric SystemjISIS252433436sep91936ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:21:25 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211115; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1930.bib2013.07.30 21:21:25 MDThttp://www.jstor.org/stable/225380Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlH. R. CalvertDecimal Division of Scales before the Metric System
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division of Scales before the Metric System",
journal = jISIS,
volume = "25",
number = "2",
pages = "433436",
month = sep,
year = "1936",
CODEN = "ISISA4",
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",
acknowledgement = acknhfb,
fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}
o
o‹Y #+%%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.''",
}
::CW '#7s/_1=m;=
=O7=s¡%mastersthesisfparith.bibShannon:1937:SARClaude Elwood ShannonA Symbolic Analysis of Relay and Switching CircuitsMaster of ScienceDepartment of Electrical Engineering, MITCambridge, MA, USA7210aug81937Thu Nov 18 10:35:20 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 10:35:20 ???Not submitted until 1940http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdfSmiley cite [p. 91]Smiley:2010:MWI claims: ``He [Shannon] also had the insight, like Atanasoff, that the binary arithmetic that relay switches represented would simplify information systems. His master's thesis, written when he as twentyone and published when he was twentytwo, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 5961 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 6268, ``A Factor Table Machine'', describe a machine that will print a table of factors and primes of all the integers from 1 to 100,000,000. Shannon notes on page 68: ``As to the practicality of such a device, it might be said that J. P. Kulik spent 20 years in constructing a table of primes up to 100,000,000 and when finished it was found to contain so many errors that it was not worth publishing. The machine described here could probably be made to handle 5 numbers per second so that the table would require only about 2 months to construct.''acknhfbApril 30, 1916February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = acknhfb,
authordates = "April 30, 1916February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twentyone and published
when he was twentytwo, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 5961 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 6268,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}umbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution lawhence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multidigit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
º"
3H\º… ŠA
@Article{Andrews:1978:IAN,
author = "M. Andrews",
title = "Influence of architecture on numerical algorithms",
journal = jMICROPROCMICROSYS,
volume = "2",
number = "3",
pages = "130137",
month = jun,
year = "1978",
CODEN = "MIMID5",
ISSN = "01419331 (print), 18729436 (electronic)",
ISSNL = "01419331",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Microprocessors and Microsystems",
}Þ…j‹U
@Article{Andrews:1978:EFM,
author = "M. Andrews and S. F. McCormick and G. D. Taylor",
title = "Evaluation of Functions on Microcomputers: Square
Root",
journal = jCOMPUTMATHAPPL,
volume = "4",
number = "4",
pages = "359367",
year = "1978",
CODEN = "CMAPDK",
ISSN = "08981221 (print), 18737668 (electronic)",
ISSNL = "08981221",
bibdate = "Thu Sep 15 18:40:29 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Computers and Mathematics with Applications",
xxmonth = "(none)",
}Ý‡iS
@Article{Anderson:2017:EMF,
author = "Andrew Anderson and Servesh Muralidharan and David
Gregg",
title = "Efficient Multibyte Floating Point Data Formats Using
Vectorization",
journal = jIEEETRANSCOMPUT,
volume = "66",
number = "12",
pages = "20812096",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2716355",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7950938/",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}±Ž œA
@Article{Anderson:1999:DAF,
author = "I. J. Anderson",
title = "A Distillation Algorithm for FloatingPoint
Summation",
journal = jSIAMJSCICOMP,
volume = "20",
number = "5",
pages = "17971806",
month = sep,
year = "1999",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596314200",
ISSN = "10648275 (print), 10957197 (electronic)",
ISSNL = "10kŽ>œ}
@Article{Anderson:1967:ISMb,
author = "S. F. Anderson and J. G. Earle and R. E. Goldschmidt
and D. M. Powers",
title = "The {IBM System\slash 360 Model 91}: Floatingpoint
execution unit",
journal = jIBMJRD,
volume = "11",
number = "1",
pages = "3453",
month = jan,
year = "1967",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.111.0034",
ISSN = tˆq‘c
@Article{An:1988:CRE,
author = "S. H. An and K. Yao",
title = "Convergent and roundoff error properties of reflection
coefficients in adaptive spatial recursive least
squares lattice algorithm",
journal = jIEEETRANSCIRCUITSSYST,
volume = "35",
number = "2",
pages = "241246",
month = feb,
year = "1988",
CODEN = "ICSYBT",
ISSN = "00984094 (print), 1558127 &e Law of Anomalous Numbers is thus a general probability law of widespread application.Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledgeBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom cite Logan:1978:FDP: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 573585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] containing an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography cite Hurlimann:2006:BLB cites 325 publications about Benford's Law.acknhfbhttp://www.jstor.org/journal/procamerphilsociIt has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution lawhence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multidigit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.Frank BenfordThe Law of Anomalous Numbers
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = jPROCAMERPHILSOC,
volume = "78",
number = "4",
pages = "551572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003049X (print), 23269243 (electronic)",
ISSNL = "0003049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution lawhence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multidigit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
qqÓ[ #'E557=m;CŸ]WsŽEgŸe'EÌSarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous NumbersjPROCAMERPHILSOC784551572mar31938PAPCAA0003049X (print), 23269243 (electronic) OR 0003049X (print), 23269243 (electronic)0003049X OR 0003049XThu Feb 15 16:28:28 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 16:28:28 ???http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2GIt has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution lawhence the name ``Anomalous Numbers.''par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.par The equation also gives the frequency of digits in the second, third + place of a multidigit number, and it is shown that the same law applies to reciprocals.par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. Th%
Y Y‡9 W#)]!)!=m;]‡I£bookfparith.bibHardy:1938:ITNG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of NumberspubOXFORDpubOXFORD:adrxvi + 4031938QA241 .H28Fri Nov 30 06:49:15 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.30 06:49:15 ???acknhfbG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numbers
@Book{Hardy:1938:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pubOXFORD,
address = pubOXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}hY #3'ƒ7G'=m;''/ƒ_ phdthesisfparith.bibCouffignal:1938:AMAL. CouffignalSur l'analyse mecanique. Application aux machines a calculer et aux calculs de la mecanique celeste. (French) [On mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]GauthierVillarsFaculte des Sciences de ParisParis, France5515721938Wed Oct 13 11:17:22 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:17:22 ???Extracts reprinted in cite [ 2.7]Randell:1982:ODC. Translated by Mr. R. Basu.FrenchacknhfbL. CouffignalExtracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.Sur l'analyse m{\'e}canique. Application aux machines {\`a} calculer et aux calculs de la m{\'e}canique c{\'e}leste. ({French}) [{On} mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
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Application to calculating machines and to calculation
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Translated by Mr. R. Basu.",
acknowledgement = acknhfb,
language = "French",
} http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = acknhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}!
ùù”!Y #/sA7=]; ‡}/s–Uarticlefparith.bibShannon:1938:SARClaude E. ShannonA Symbolic Analysis of Relay and Switching CircuitsjTRANSAMERINSTELECENG57713723dec121938TAEEA500963860 OR 00963860Sat Nov 20 08:54:12 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www2.research.att.com/~njas/doc/shannonbio.html2010.11.20 08:54:12 ???Transactions of the American Institute of Electrical EngineersThis is Shannon's first published paper (his Master's thesis). In 1940, it received the Alfred Noble Prize of the combined engineering societies of the United States, an award given each year to a person not over thirty for a paper published in one of the journals of the participating societies. H. H. Goldstine cite Goldstine:1972:CPN called this work ``one of the most important master's theses ever written ... a landmark in that it helped to change digital circuit design from an art to a science.''acknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714Claude E. ShannonA Symbolic Analysis of Relay and Switching Circuits
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
journal = jTRANSAMERINSTELECENG,
volume = "57",
number = "??",
pages = "713723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "00963860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = acknhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
À ÀŠS#X ##
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author = "Robert Jager and Boyd C. Patterson",
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author = "G. W. Gerrity",
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author = "Alexander Gelbukh and Grigori Sidorov",
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Language",
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@Article{Gemignani:2004:REA,
author = "Luca Gemignani and Grazia Lotti",
title = "Rounding Error Analysis in Solving {$M$}Matrix Linear
Systems of Block {Hessenberg} Form",
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fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH2",
}š‡Ž
@Article{Gelbukh:2001:ZHL,
author = "Alexander Gelbukh and Grigori Sidorov",
title = "{Zipf} and {Heaps Laws}' Coefficients Depend on
Language",
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fŠÐVf x'V '#)7#1'=m;‡!7³kmastersthesisfparith.bibBerry:1941:DEDClifford Edward BerryDesign of electrical data recording and reading mechanismM.S. thesisIowa State CollegeAmes, IA, USA321941Thu Nov 18 11:18:18 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 11:18:18 ???This thesis may be one of the earliest surviving records of the ABC computer built by John Atanasoff and Clifford Berry in the late 1930s. The o/†w&U !#)'9C/=m;_'g‡techreportfparith.bibStibitz:1940:CG. R. StibitzComputerUnpublished memorandumBell Telephone LaboratoriesNew York, NY, USA2993001940Wed Oct 13 11:30:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:30:38 ???Reprinted in cite [ 6.1]Randell:1982:ODC.acknhfbG. R. StibitzReprinted in \cite[\S 6.1]{Randell:1982:ODC}.Computer
@TechReport{Stibitz:1940:C,
author = "G. R. Stibitz",
title = "Computer",
type = "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}‰7%X #%5=m;‚#‚+5ˆ}miscfparith.bibBush:1940:AMV. BushArithmetical Machine2993001940Wed Oct 13 11:37:32 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:37:32 ???Reprinted in cite [ 7.3]Randell:1982:ODC. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.acknhfbVannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 19391940V. BushReprinted in \cite[\S 7.3]{Randell:1982:ODC}. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.Arithmetical Machine
@Misc{Bush:1940:AM,
author = "V. Bush",
title = "Arithmetical Machine",
howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 19391940",
year = "1940",
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Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
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}ˆs$W !#1+/91'=m;_+g/ˆqtechreportfparith.bibAtanasoff:1940:CMSJ. V. AtanasoffComputing machine for the solution of large systems of linear algebraic equationsUnpublished memorandumIowa State CollegeAmes, IA, USA299300aug81940Wed Oct 13 11:36:11 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:36:11 ???Reprinted in cite [ 7.2]Randell:1982:ODC.acknhfbJ. V. AtanasoffReprinted in \cite[\S 7.2]{Randell:1982:ODC}.Computing machine for the solution of large systems of linear algebraic equations
@TechReport{Atanasoff:1940:CMS,
author = "J. V. Atanasoff",
title = "Computing machine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}"19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of WisconsinMadison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the AtanasoffBerry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 19671973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the AtanasoffBerry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50bit word.",
}'neofakind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 19301966'', (found in http://discover.lib.umn.edu/): CWB as an attorney for the group retained by Honeywell in the Honeywell v. Sperry Rand ENIAC trial. The ABC had a 50bit word.acknhfb19181963Clifford Edward BerryDesign of electrical data recording and reading mechanism
@MastersThesis{Berry:1941:DED,
author = "Clifford Edward Berry",
title = "Design of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
authordates = "19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of WisconsinMadison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the AtanasoffBerry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 19671973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the AtanasoffBerry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50bit word.",
}
¡ÓÈ†ÂÓ
Ù‡q…D‹
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bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}&(W #1/i/57Eƒ;SkW/iŽ]articlefparith.bibLancaster:1942:MMEOtis E. LancasterMachine Method for the Extraction of Cube RootjJAMSTATASSOC37217112115mar31942JSTNAL01621459 (print), 1537274X (electronic) OR 01621459 (print), 1537274X (electronic)01621459 OR 01621459Wed Jan 25 08:05:24 MST 2012http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314096; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib2012.01.25 08:05:24 MSThttp://www.jstor.org/stable/2279437Journal of the American Statistical Associationacknhfbhttp://www.tandfonline.com/loi/uasa20Otis E. LancasterMachine Method for the Extraction of Cube Root
@Article{Lancaster:1942:MME,
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title = "Machine Method for the Extraction of Cube Root",
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number = "217",
pages = "112115",
month = mar,
year = "1942",
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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;
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URL = "http://www.jstor.org/stable/2279437",
acknowledgement = acknhfb,
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}
4
’4”[,Y#/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,
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title = "Significant Figures of Numbers in Statistical Tables",
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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,
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;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
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month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
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bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
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} "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",
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F FŽG.W !#3UA=‚ ;_‚ugY‘utechreportfparith.bibvonNeumann:1945:FDRJohn von NeumannFirst Draft of a Report on the EDVACUniversity of Pennsylvania525330jun61945Mon Jun 06 19:17:03 2005ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.06 19:17:03 ???Reprinted in cite [ 8.2]Randell:1982:ODC.This is the report that got von Neumann's name associated with the serial, storedprogram, general purpose, digital architecture upon which 99.99% of all computers today are based.acknhfbJohn von NeumannReprinted in \cite[\S 8.2]{Randell:1982:ODC}.First Draft of a Report on the {EDVAC}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
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bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
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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}.",
}ŒmY#)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
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journal = jNATURE,
volume = "155",
number = "??",
pages = "5253",
day = "13",
month = jan,
year = "1945",
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DOI = "https://doi.org/10.1038/155052a0",
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bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}n \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, storedprogram, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W670ORD4926. Reprinted in
\cite[pp.~177246]{Stern:1981:EUA},
\cite[pp.~399413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}.
xix‡n1U #+!917=m;_=!g9ˆ[articlefparith.bibCesareo:1946:RIO. CesareoThe Relay InterpolatorjBELLLABSRECORD234574601946BLRCAB00058564 OR 00058564Wed Oct 13 11:31:47 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:31:47 ???Reprinted in cite [ 6.2]Randell:1982:ODC.Bell Laboratories RecordacknhfbO. CesareoReprinted in \cite[\S 6.2]{Randell:1982:ODC}.The Relay Interpolator
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = jBELLLABSRECORD,
volume = "23",
number = "??",
pages = "457460",
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CODEN = "BLRCAB",
ISSN = "00058564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Bell Laboratories Record",
}«0]!#)13;=„q;‚Y•U‚i1®]techreportfparith.bibBurks:1946:PDLArthur W. Burks and Herman H. Goldstine and John von NeumannPreliminary discussion of the logical design of an electronic computing instrumentinstINSTADVSTUDYinstINSTADVSTUDY:adr4228jun61946Wed Oct 13 08:17:48 2004ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.10.13 08:17:48 ???Report to the U.S. Army Ordnance Department. Reprinted in cite [pp.~221259]Swartzlander:1976:CDD, cite [ 8.3]Randell:1982:ODC, and cite [pp.~97146]Aspray:1987:PJNDiscusses floatingpoint versus fixedpoint computation, and concludes that floatingpoint is probably not justifiable. They wrote:par ``There appear to be two major purposes in a `floating' decimal point system both of which arise from the fact that the number of digits in a word is a constant fixed by design considerations for each particular machine. The first of these purposes is to retain in a sum or product as many significant digits as possible and the second of these is to free the human operator from the burden of estimating and inserting into a problem `scale factors'  multipl8‰m/V#)Ee%E7=m;_EgiŠAarticlefparith.bibAiken:1946:ASCH. H. Aiken and G. M. HopperThe Automatic Sequence Controlled CalculatorjELECTRENG65384391, 449454, 5225281946ELENAC00959197 OR 00959197Wed Oct 13 11:26:29 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:26:29 ???Reprinted in cite [ 5.2]Randell:1982:ODC.Electrical Engineering (American Institute of Electrical Engineers)acknhfbH. H. Aiken and G. M. HopperReprinted in \cite[\S 5.2]{Randell:1982:ODC}.The {Automatic Sequence Controlled Calculator}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = jELECTRENG,
volume = "65",
number = "??",
pages = "384391, 449454, 522528",
year = "1946",
CODEN = "ELENAC",
ISSN = "00959197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
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ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors'  multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}0icative constants which serve to keep numbers within the limits of the machine.par There is, of course, no denying the fact that human time is consumed in arranging for the introduction of suitable scale factors. We only argue that the time so consumed is a very small percentage of the total time we will spend in preparing an interesting problem for our machine. The first advantage of the floating point is, we feel, somewhat illusory. In order to have such a floating point, one must waste memory capacity which could otherwise be used for carrying more digits per word. It would therefore seem to us not at all clear whether the modest advantages of a floating binary point offset the loss of memory capacity and the increased complexity of the arithmetic and control circuits.''acknhfbArthur W. Burks and Herman H. Goldstine and John von NeumannReport to the U.S. Army Ordnance Department. Reprinted in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S 8.3]{Randell:1982:ODC}, and \cite[pp.~97146]{Aspray:1987:PJN}Preliminary discussion of the logical design of an electronic computing instrument
@TechReport{Burks:1946:PDL,
author = "Arthur W. Burks and Herman H. Goldstine and John von
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title = "Preliminary discussion of the logical design of an
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pages = "42",
day = "28",
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bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors'  multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}
!Ã!‹3W#1S}K7E
;_o=SgŒarticlefparith.bibGoldstine:1946:ENIH. H. Goldstine and Adele GoldstineThe Electronic Numerical Integrator and Computer (ENIAC)jMATHTABLESOTHERAIDSCOMPUT21597110jul71946MTTCAS08916837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 7.7]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationacknhfbhttp://www.ams.org/mcom/H. H. Goldstine and Adele GoldstineReprinted in \cite[\S 7.7]{Randell:1982:ODC}.The {Electronic Numerical Integrator and Computer (ENIAC)}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
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journal = jMATHTABLESOTHERAIDSCOMPUT,
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number = "15",
pages = "97110",
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bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
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journalURL = "http://www.ams.org/mcom/",
}Ž:2Y!#+Cƒ;=m;'C/ƒŽ#techreportfparith.bibDreyer:1946:REMH.J. Dreyer and A. WaltherDer Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945. (German) [The Ipm Calculator. The development of mathematical instruments in Germany 19391945]BerichtA3Institut fur Praktische Mathematik, Technische HochschuleDarmstadt, West Germany45746019aug81946Wed Oct 13 11:20:15 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:20:15 ???Reprinted in cite [ 3.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. JonesGermanacknhfbH.J. Dreyer and A. WaltherReprinted in \cite[\S 3.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones{Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945}. ({German}) [{The} {Ipm} Calculator. {The} development of mathematical instruments in {Germany} 19391945]
@TechReport{Dreyer:1946:REM,
author = "H.J. Dreyer and A. Walther",
title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 19391945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
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address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = acknhfb,
language = "German",
}
ú‡\5U #'917=m;_=g9ˆKarticlefparith.bibJuley:1947:BCJ. JuleyThe Ballistic ComputerjBELLLABSRECORD24591947BLRCAB00058564 OR 00058564Wed Oct 13 11:32:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:32:38 ???Reprinted in cite [ 6.3]Randell:1982:ODC.Bell Laboratories RecordacknhfbJ. JuleyReprinted in \cite[\S 6.3]{Randell:1982:ODC}.The Ballistic Computer
@Article{Juley:1947:BC,
author = "J. Juley",
title = "The Ballistic Computer",
journal = jBELLLABSRECORD,
volume = "24",
number = "??",
pages = "59",
year = "1947",
CODEN = "BLRCAB",
ISSN = "00058564",
bibdate = "Wed Oct 13 11:32:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Bell Laboratories Record",
}4Y!#1]3;=m;„;]„Ctechreportfparith.bibGoldstine:1947:PCPHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrumentTechnical report1instINSTADVSTUDYinstINSTADVSTUDY:adr691apr41947Wed Jun 01 17:41:33 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 17:41:33 ???Report prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in cite [80151]Taub:1963:JNCa. Knuth cite [p.~278]Knuth:1997:SA cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.acknhfbHerman H. Goldstine and John von NeumannReport prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in \cite[80151]{Taub:1963:JNCa}. Knuth \cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.Planning and coding of problems for an electronic computing instrument
@TechReport{Goldstine:1947:PCP,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
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type = "Technical report",
number = "1",
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address = instINSTADVSTUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W36034OKD7481. Reprinted in
\cite[80151]{Taub:1963:JNCa}. Knuth
\cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this
report as the first published treatment of
doubleprecision arithmetic on digital computers.",
acknowledgement = acknhfb,
}
l ³lŒD7W #/)[57Eƒ;Qo)_Ž
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
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fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
} 2005",
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notes (including corrections)",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
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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.",
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}Œ6AW #1E+3!E%;„I5EŽÐbookfparith.bibStifler:1950:HSCW. W. Stifler, Jr.Highspeed computing devicespubMCGRAWHILLpubMCGRAWHILL:adrxiii + 4511950QA75 .E5Fri Aug 20 10:18:44 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:18:44 MDTSupervised by Charles Brown Tompkins and C. H. Wakelin, Engineering Research Associates. The contents of this volume were first assembled in the form of a report to the Office of Naval Research, prepared under a provision of contract N6ONR240, Task 1. Cited in cite Sterbenz:1974:FPC.computersacknhfbW. W. {Stifler, Jr.}Highspeed computing devices
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "Highspeed computing devices",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
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acknowledgement = acknhfb,
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\cite{Sterbenz:1974:FPC}.",
subject = "computers",
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articlefparith.bibGill:1951:PSSS. GillA process for the stepbystep integration of differential equations in an automatic digital computing machinejPROCCAMBRIDGEPHILSOC47961081951PCPSA400081981 OR 00081981Tue Aug 28 05:54:12 2001http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.08.28 05:54:12 ???Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciencesaccurate floatingpoint summation; floatingpoint arithmetic; rounding errorsHigham cite Higham:1993:AFP comments ``In 1951 Gill [8] noticed that the rounding error in the sum of two numbers could be estimated by subtracting one of the numbers from the sum, and he made use of this estimate in a RungeKutta code in a program library for the EDSAC computer.''acknhfbS. GillA process for the stepbystep integration of differential equations in an automatic digital computing machine
@Article{Gill:1951:PSS,
author = "S. Gill",
title = "A process for the stepbystep integration of
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}†(EU %#)#K5=m;g#O†Wincollectionfparith.bibBrown:1951:HRRG. W. BrownHistory of RAND's random digitsHouseholder:1951:MCM31321951Sun Sep 18 12:02:43 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:02:43 ???http://www.rand.org/pubs/papers/2008/P113.pdfacknhfbG. W. BrownHistory of {RAND}'s random digits
@InCollection{Brown:1951:HRR,
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title = "History of {RAND}'s random digits",
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bibdate = "Sun Sep 18 12:02:43 2011",
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}ˆGDU #)#]C77;m;y#]‰{articlefparith.bibBooth:1951:SBMA. D. BoothA signed binary multiplication techniquejQUARTJMECHAPPLIEDMATH422362401951QJMMAV00335614 OR 0033561400335614 OR 00335614Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied MathematicsacksfoA. D. BoothA signed binary multiplication technique
@Article{Booth:1951:SBM,
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title = "A signed binary multiplication technique",
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acknowledgement = acksfo # " and " # acknhfb,
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@Book{Menninger:1992:NWN,
author = "Karl Menninger",
title = "Number Words and Number Symbols: a Cultural History of
Numbers",
publisher = pubDOVER,
address = pubDOVER:adr,
pages = "xiii + 480",
year = "1992",
ISBN = "0486270963",
ISBN13 = "9780486270968",
LCCN = "QA141.2 .M4513 1992",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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@Book{Mead:1980:IVS,
author = "Carver Mead and Lynn Conway",
title = "Introduction to {VLSI} systems",
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year = "1980",
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bibdate = "Mon Sep 16 16:25:00 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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author = "{Motorola, Inc.}",
title = "{MC68881\slash MC68882} floatingpoint coprocessor
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publisher = pubPH,
address = pubPH:adr,
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year = "1987",
ISBN = "0135669367 (pbk.)",
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
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keywords = "Floatingpoint arithmetic.; Motorola 68881
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}½…Š
@Book{McCracken:1964:NMF,
author = "Daniel D. McCracken and William S. Dorn",
title = "Numerical methods and {FORTRAN} programming, with
applications in engineering and science",
publisher = pubWILEY,
address = pubWILEY:adr,
pages = "xii + 457",
year = "1964",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
keywords = "Numerical analysis  Data processing.; {Fortran}
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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@Book{McCalla:1967:INM,
author = "Thomas Richard McCalla",
title = "Introduction to Numerical Methods and {Fortran}
Programming",
publisher = pubWILEY,
address = pubWILEY:adr,
pages = "xiii + 359",
month = jan,
year = "1967",
ISBN = "0471581259",
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@Book{Markstein:2000:IEF,
author = "Peter Markstein",
title = "{IA64} and elementary functions: speed and
precision",
publisher = pubPH,
address = pubPH:adr,
pages = "xix + 298",
year = "2000",
ISBN = "0130183482",
ISBN13 = "9780130183484",
LCCN = "QA76.9.A73 M365 2000",
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ó„@‰
@Article{Anuta:1996:MMC,
author = "M. A. Anuta and Daniel W. Lozier and P. R. Turner",
title = "The {MasPar MP1} as a Computer Arithmetic
Laboratory",
journal = jJRESNATLBURSTAND,
volume = "101",
number = "2",
pages = "165174",
month = î„O‰
@Article{Anonymous:1992:FPc,
author = "Anonymous",
title = "Floating Point",
journal = jCOMPUTAIDEDENG,
volume = "11",
number = "10",
pages = "101??",
month = oct,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "07333536",
ISSNL = "07333536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A Helping Hand for FEA.",
acknowledgement = acknhfb,
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‹â‡o_
@Article{Anonymous:1982:ARBf,
author = "Anonymous",
title = "Article Review: {{\booktitle{Ada model arithmetic:
costs and benefits}}: Wallis, P. J. L. \booktitle{IEE
Proc.E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
pp 7580}",
journal = jMICROPROCMICROSYS,
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number = "9",
pages = "497498",
month = nov,
year = "1982",
CODEN = "MIMID57Ý‡Ž+
@Article{Anonymous:1893:IDb,
author = "Anonymous",
title = "The Instantaneous Divider",
journal = jSCIAMER,
volume = "68",
number = "21",
pages = "325325",
day = "27",
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year = "1893",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican05271893325a",
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bibdate = "Wed May 22 19:04:00 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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@Article{Anguita:2013:EES,
author = "D. Anguita and A. Ghio and L. Oneto and X. Parra and
J. L. ReyesOrtiz",
title = "Energy Efficient {Smartphone}Based Activity
Recognition using FixedPoint Arithmetic",
journal = jJUCS,
volume = "19",
number = "9",
pages = "1295??",
month = "????",
year = "2013",
CODEN = "????",
ISSN = "0948695X (print), 09486968 (electronic)",
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bibdate = "Fri Sep 13 11:19:07 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jucs.bib",
URL = "http://www.jucs.org/jucs_19_9/energy_efficient_smartphone_based",
acknowledgement = acknhfb,
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@Article{Andrews:1978:UEF,
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title = "Unified elementary function generator",
journal = jMICROPROCMICROSYS,
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number = "5",
pages = "270273",
month = oct,
year = "1978",
CODEN = "MIMID5",
ISSN = "01419331 (print), 18729436 (electronic)",
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bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a RungeKutta code in a program library for the
EDSAC computer.''",
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ÄÄŽ9GX#1]o1573%;m;Qym]YsŽ}articlefparith.bibGoldstine:1951:NIMHerman H. Goldstine and John von NeumannNumerical Inverting of Matrices of High Order. IIjPROCAMMATHSOC21882021951PAMYAR00029939 (print), 10886826 (electronic) OR 00029939 (print), 10886826 (electronic)00029939 OR 0002993965.0XMR0041539 (12,861b)F. J. MurrayThu Nov 8 14:49:46 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:46 ???See cite vonNeumann:1947:NIM for Part I. Reprinted in cite [Paper~15, pp.~558572]Taub:1963:JNCa.http://www.jstor.org/view/00029939/di970628/97p0185x/0Proceedings of the American Mathematical Society043.12301acknhfbHerman H. Goldstine and John von NeumannSee \cite{vonNeumann:1947:NIM} for Part I. Reprinted in \cite[Paper~15, pp.~558572]{Taub:1963:JNCa}.Numerical Inverting of Matrices of High Order. {II}
@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = jPROCAMMATHSOC,
volume = "2",
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year = "1951",
CODEN = "PAMYAR",
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MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper~15, pp.~558572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
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}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",
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~„<ˆy
@Book{Omondi:1994:CAS,
author = "Amos R. Omondi",
title = "Computer Arithmetic Systems: Algorithms, Architecture,
and Implementation",
publisher = pubPH,
address = pubPH:adr,
pages = "xvi + 520",
year = "1994",
ISBN = "0133343014",
ISBN13 = "9780133343014",
LCCN = "QA76.9.C62 O46 1994",
bibdate = "Sat Dec 09 11:57:03 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$40.00",
acknowledgement = acknhfb,
}E…G‹
@Book{Oberman:1979:DCB,
author = "R. M. M. (Roelof Maarten Marie) Oberman",
title = "Digital circuits for binary arithmetic",
publisher = pubWILEY,
address = pubWILEY:adr,
pages = "xii + 340",
year = "1979",
ISBN = "0470263733",
ISBN13 = "9780470263730",
LCCN = "TK7868.L6 O23 1979",
bibdate = "Wed Nov 14 17:33:15 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
remark = "A Halsted Press book.",
subject = "logic circuits; digital integrated circuits; switching
theory",
}kš=
@Book{P754:2008:ISF,
author = "{IEEE Task P754}",
title = "{IEEE 7542008, Standard for FloatingPoint
Arithmetic}",
publisher = pubIEEESTD,
address = pubIEEESTD:adr,
pages = "58",
day = "29",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1109/IEEESTD.2008.4610935",
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ISBN13 = "9780738157535 (pa”ˆ
@Book{Overton:2002:CNC,
author = "Michael L. Overton",
title = "{C}{\'o}mputo num{\'e}rico con aritm{\'e}tica de punto
flotante {IEEE}",
volume = "19",
publisher = "Sociedad Matem{\'a}tica Mexicana",
address = "M{\'e}xico",
pages = "xii + 123",
year = "2002",
ISBN = "9703200869",
ISBN13 = "9789703200863",
MRclass = "6502 (65Bxx 65G30)",
MRnumber = "MR1925397 (2003g:6500p‡Ž#
@Book{Overton:2001:NCI,
author = "Michael L. Overton",
title = "Numerical Computing with {IEEE} Floating Point
Arithmetic, Including One Theorem, One Rule of Thumb,
and One Hundred and One Exercises",
publisher = pubSIAM,
address = pubSIAM:adr,
pages = "xiv + 104",
year = "2001",
ISBN = "0898714826",
ISBN13 = "9780898714821",
LCCN = "QA76.9.M35 O94 2001",
MRclass = "6502 (65G30 68M07 68N99)",
MRnumber = "MR1828597 (2003b:65002)",
MRreviewer = "Jesse L. Barlow",
bibdate = "Fri Apr 27 16:50:46 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$40.00",
URL = "http://www.cs.nyu.edu/cs/faculty/overton/book/;
http://www.siam.org/catalog/mcc07/ot76.htm",
acknowledgement = acknhfb,
}\
ÔÔ”)HY #+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",
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ISSNL = "00029505",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (15601621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = acknhfb,
fjournal = "American Journal of Physics",
journalURL = "http://scitation.aip.org/content/aapt/journal/ajp",
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LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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±±ˆfJU#)]Y/77=m;e]Y‰earticlefparith.bibDavis:1952:ARSK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken DigitsjJACOUSTSOCAM246637642nov111952JASMAN00014966 OR 0001496600014966 OR 00014966Fri Nov 28 16:38:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 16:38:51 ???Journal of the Acoustical Society of AmericaackmfcK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken Digits
@Article{Davis:1952:ARS,
author = "K. Davis and R. Biddulph and S. Balashek",
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#[=m;‚'ƒ+inproceedingsfparith.bibAndrews:1952:RBLE. G. AndrewsJ. C. McPhersonProceedings of the AIEEIRE '51: Papers and discussions presented at the December 1012, 1951, joint AIEEIRE computer conference, Philadelphia, PA: Review of electronic digital computersA review of the Bell Laboratories' digital computer developmentspubACMpubACM: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
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bibdate = "Fri Dec 03 09:17:58 2010",
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acknowledgement = acknhfb,
keywords = "Bell Laboratories Model 15 relay computers; complex
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@ˆ+
@Article{Nedialkov:1999:IHO,
author = "N. S. Nedialkov and K. R. Jackson",
title = "An Interval HermiteObreschkoff Method for Computing
Rigorous Bounds on the Solution of an Initial Value
Problem for an Ordinary Differential Equation",
journal = jRELIABLECOMPUTING,
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author = "J. W. Backus",
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abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
threeaddress floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
builtin checking.",
acknowledgement = acknhfb,
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abstract = "The IBM 701 Speedcoding System is a set of
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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",
}Od coding manual  Datatron
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Paper tape system handbook  Card converter Model 500
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Cardatron system handbook  Model 560 DATAFILE
handbook  Control console and consolette handbook
 Floating point control unit handbook  External
switching unit handbook  Tape preparation unit
handbook.",
}P
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author = "H. Freeman and E. Parsons",
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}ŽHPV #/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
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organization = "The Division",
address = "Pasadena, CA, USA",
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note = "12 volumes in 1.",
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Paper tape system handbook  Card converter Model 500
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Cardatron system handbook  Model 560 DATAFILE
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 Floating point control unit handbook  External
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author = "W. J. (Wallace John) Eckert and Rebecca Bradley
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title = "Faster, faster; a simple description of a giant
electronic calculator and the problems it solves",
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address = pubIBM:adr,
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fjournal = "Pacific Journal of Mathematics",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}Š5UX #%57=m;1Oe%‹=articlefparith.bibMoshman:1954:GPRJack MoshmanThe Generation of PseudoRandom Numbers on a Decimal CalculatorjJACM128891apr41954JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???Journal of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Jack MoshmanThe Generation of PseudoRandom Numbers on a Decimal Calculator
@Article{Moshman:1954:GPR,
author = "Jack Moshman",
title = "The Generation of PseudoRandom Numbers on a Decimal
Calculator",
journal = jJACM,
volume = "1",
number = "2",
pages = "8891",
month = apr,
year = "1954",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
}
n¾×nŠfZX #1W57=m;1e1W‹articlefparith.bibParsons:1955:SDCFrances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic OperationsjJACM23205207jul71955JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Wed Nov 09 01:00:34 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.09 01:00:34 ???Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Frances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic Operations
@Article{Parsons:1955:SDC,
author = "Frances L. Parsons",
title = "A Simple DeskCalculator Method for Checking Binary
Results of Digital Computer Arithmetic Operations",
journal = jJACM,
volume = "2",
number = "3",
pages = "205207",
month = jul,
year = "1955",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Wed Nov 09 01:00:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}‡dYV #/)=)7;K;9)=‰articlefparith.bibLenaerts:1955:ASRE. H. LenaertsAutomatic Square RootingjELECTRONENG27287289jul71955ELEGAP00134902 OR 00134902Thu Sep 1 10:15:41 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:41 ???Electronic EngineeringacknjE. H. LenaertsAutomatic Square Rooting
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author = "E. H. Lenaerts",
title = "Automatic Square Rooting",
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volume = "27",
number = "??",
pages = "287289",
month = jul,
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CODEN = "ELEGAP",
ISSN = "00134902",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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}ˆ?XX#/U'/!=K;Uˆ_Ñbookfparith.bibHastings:1955:ADCCecil B. Hastings, Jr. and Jeanne T. Hayward and James P. Wong, Jr.Approximations for Digital ComputerspubPRINCETONpubPRINCETON:adrviii + 2011955QA76 .H33Mon Sep 30 14:51:50 1996ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.09.30 14:51:50 ???acknjCecil B. {Hastings, Jr.} and Jeanne T. Hayward and James P. {Wong, Jr.}Approximations for Digital Computers
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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",
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}
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author = "Joseph F. Grcar",
title = "{John von Neumann}'s Analysis of {Gaussian}
Elimination and the Origins of Modern Numerical
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month = "????",
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author = "Robert T. Gregory",
title = "On the Design of the Arithmetic Unit of a
FixedWordLength Computer from the Standpoint of
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pages = "255257",
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year = "1966",
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fjournal = "IEEE Transactions on Electronic Computers",
}V…0Ša
@Article{Gregory:1964:FAN,
author = "Robert T. Gregory and James L. Raney",
title = "Floatingpoint arithmetic with $ 84 $bit numbers",
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volume = "7",
pages = "1013",
year = "1964",
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ISSNL = "00010782",
MRclass = "68.00",
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journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}‘9¢s
@Article{Green:1973:NTF,
author = "D. H. Green and R. G. Kelsch",
title = "Nonlinear Ternary Feedback Shift Registers",
journal = jCOMPJ,
volume = "16",
number = "4",
pages = "360367",
month = nov,
year = "1973",
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@Article{Grcar:1991:IAS,
author = "Joe Grcar",
title = "{IEEE} Arithmetic Stinks",
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volume = "91",
number = "33",
day = "18",
month = aug,
year = "1991",
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note = "See rebuttal \cite{Demmel:1991:OIA}.",
URL = "http://www.netlib.org/nadigest/91/v91n33",
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fjournal = "NA Digest",
} ú„H‰
@Article{Gray:1992:UMF,
author = "A. Gray and R. Knill",
title = "Using {Mathematica} to Find Closed Form Expressions
for Approximations to the Square Root of $x$",
journal = jMATHEMATICAEDUC,
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number = "4",
pages = "1213",
month = "Summer",
year = "1992",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "Mathematica in Education",
}
°
ú¬Êú‹M]W #+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",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936",
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fjournal = "IRE Transactions on Electronic Computers",
}‹_\Y #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
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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",
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ISSN = "03679950",
bibdate = "Thu Jun 30 15:10:39 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911",
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fjournal = "IRE Transactions on Electronic Computers",
}†Q[U #/;a+/'=m;;a†}‘bookfparith.bibRichards:1955:AODRichard Kohler RichardsArithmetic Operations in Digital ComputersD. Van NostrandNew York, NY, USAiv + 3971955QA75 .R5 1955Fri Nov 28 18:46:37 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:46:37 ???acknhfbRichard Kohler RichardsArithmetic Operations in Digital Computers
@Book{Richards:1955:AOD,
author = "Richard Kohler Richards",
title = "Arithmetic Operations in Digital Computers",
publisher = "D. Van Nostrand",
address = "New York, NY, USA",
pages = "iv + 397",
year = "1955",
LCCN = "QA75 .R5 1955",
bibdate = "Fri Nov 28 18:46:37 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}
k"D
3†Zkš;´w
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author = "M. J. Jamieson",
title = "Short Notes: Rapidly Converging Iterative Formulae for
Finding Square Roots and their Computational
Efficiencies",
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month = feb,
year = "1989",
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ISSN = "0010
¿„*ˆU
@Article{James:1983:RDB,
author = "F. V. James",
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@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
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author = "F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and
J. Villalba and E. L. Zapata",
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@Article{Jain:1991:CSN,
author = "Suneel Jain",
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de convergents de fractions continues. ({French})
[Arithmetic distributions of the denominators of
continued fractions]",
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van Wetenschappen, Series A, Indagationes
mathematicae",

×Ç×¢`X #)?57=m;Ž1OqeŽ)Gžgarticlefparith.bibPerkins:1956:EPCRobert PerkinsEASIAC, A PseudoComputerjJACM326572apr41956JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 23:46:26 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 23:46:26 ???One of the primary functions of the MIDAC installation at the University of Michigan is the instru^ŠF_W #//A;]7Ea;]/AŒ articlefparith.bibLilamand:1956:TDMM. Lejet LilamandA TimeDivision MultiplierjIRETRANSELECCOMPUTEC512634mar31956IRELAOhttps://doi.org/10.1109/TEC.1956.521978903679950 OR 03679950Thu Jun 30 15:46:18 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:18 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789IRE Transactions on Electronic ComputersacknhfbM. Lejet LilamandA TimeDivision Multiplier
@Article{Lilamand:1956:TDM,
author = "M. Lejet Lilamand",
title = "A TimeDivision Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC5",
number = "1",
pages = "2634",
month = mar,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219789",
ISSN = "03679950",
bibdate = "Thu Jun 30 15:46:18 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‰m^W #3AQ+3E%;u1AQŠ}bookfparith.bibHildebrand:1956:INAFrancis Begnaud HildebrandIntroduction to numerical analysispubMCGRAWHILLpubMCGRAWHILL:adr5111956QA300 .H5Fri Aug 20 09:19:58 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 09:19:58 MDTInternational series in pure and applied mathematicsSee also second edition cite Hildebrand:1974:INA,Hildebrand:1987:INA.Numerical analysisacknhfbFrancis Begnaud HildebrandIntroduction to numerical analysis
@Book{Hildebrand:1956:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "511",
year = "1956",
LCCN = "QA300 .H5",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = acknhfb,
remark = "See also second edition
\cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
subject = "Numerical analysis",
}ib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}`ction of beginners in the various aspects of digital machine use including programming and coding. ldots In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. ldots To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Journal of the ACMdecimal floatingpoint arithmeticEarly example of a decimal floatingpoint machine.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401One of the primary functions of the MIDAC installation at the University of Michigan is the instruction of beginners in the various aspects of digital machine use including programming and coding. \ldots{} In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. \ldots{} To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Robert Perkins{EASIAC}, {A} PseudoComputer
@Article{Perkins:1956:EPC,
author = "Robert Perkins",
title = "{EASIAC}, {A} PseudoComputer",
journal = jJACM,
volume = "3",
number = "2",
pages = "6572",
month = apr,
year = "1956",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Fri Nov 04 23:46:26 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}
J`JŒcY#+k;]7Ea;]k!articlefparith.bibSydnor:1956:AMSR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid ModulatorjIRETRANSELECCOMPUTEC528285jun61956IRELAOhttps://doi.org/10.1109/TEC.1956.521980403679950 OR 03679950Thu Jun 30 15:46:21 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:21 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804IRE Transactions on Electronic ComputersacknhfbR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulator
@Article{Sydnor:1956:AMS,
author = "R. L. Sydnor and T. R. O'Meara and J. Strathman",
title = "Analog Multipliers and Squarers Using a Multigrid
Modulator",
journal = jIRETRANSELECCOMPUT,
volume = "EC5",
number = "2",
pages = "8285",
month = jun,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219804",
ISSN = "03679950",
bibdate = "Thu Jun 30 15:46:21 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex dataprocessing machines.",
acknowledgement = acknhfb,
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articlefparith.bibMurphy:1957:PIAR. W. MurphyA PositiveInteger Arithmetic for Data ProcessingjIBMJRD12158170apr41957IBMJAEhttps://doi.org/10.1147/rd.12.015800188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 0018864668.0X18,939dTue Sep 11 15:35:33 MDT 2012http://ieeexplore.ieee.org/servlet/opac?punumber=5288520; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; http://www.research.ibm.com/journal/2012.09.11 15:35:33 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735; http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdfIt is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield nonnegative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex dataprocessing machines.IBM Journal of Research and Developmentacknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520C. C. GotliebIt is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield nonnegative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex dataprocessing machines.R. W. MurphyA PositiveInteger Arithmetic for Data Processing
@Article{Murphy:1957:PIA,
author = "R. W. Murphy",
title = "A PositiveInteger Arithmetic for Data Processing",
journal = jIBMJRD,
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number = "2",
pages = "158170",
month = apr,
year = "1957",
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http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf",
abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
nonnegative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex dataprocessing machines.",
acknowledgement = acknhfb,
bookURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
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}‡noW #+/Y=m;'/ˆAarticlefparith.bibPawlak:1957:UENZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computerBull. Acad. Pol. Sci., Ser. Sci. Tech.52322361957Thu Nov 06 05:56:32 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:56:32 ???negative baseacknhfbZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computer
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journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
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pages = "232236",
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year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
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acknowledgement = acknhfb,
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abstract = "An experimental 50megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50megacycle
pulserepetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
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provides a 3.125megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a highspeed shift register, a
highspeed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variablephase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of highspeed computing and measurements
applications.",
acknowledgement = acknhfb,
bookURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}rbe used advantageously to provide features such as the variablephase clock system used in the arithmetic unit.\par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of highspeed computing and measurements applications.R. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50Megacycle Arithmetic Unit
@Article{Walker:1957:EMA,
author = "R. M. Walker and D. E. Rosenheim and P. A. Lewis and
A. G. Anderson",
title = "An Experimental 50Megacycle Arithmetic Unit",
journal = jIBMJRD,
volume = "1",
number = "3",
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CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.13.0257",
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bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://ieeexplore.ieee.org/servlet/opac?punumber=5288520;
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abstract = "An experimental 50megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50megacycle
pulserepetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phaselocked frequency divider which
provides a 3.125megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a highspeed shift register, a
highspeed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variablephase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of highspeed computing and measurements
applications.",
acknowledgement = acknhfb,
bookURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
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bb½r^#+eQ57Eƒ;‚™S[™Ye¶Uarticlefparith.bibWalker:1957:EMAR. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50Megacycle Arithmetic UnitjIBMJRD13257278jul71957IBMJAEhttps://doi.org/10.1147/rd.13.025700188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Tue Sep 11 15:35:35 MDT 2012http://ieeexplore.ieee.org/servlet/opac?punumber=5288520; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; http://www.research.ibm.com/journal/2012.09.11 15:35:35 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687; http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdfAn experimental 50megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50megacycle pulserepetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phaselocked frequency divider which provides a 3.125megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a highspeed shift register, a highspeed indicator register, and a binary word generator.par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.par In a 50megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may be used advantageously to provide features such as the variablephase clock system used in the arithmetic unit.par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of highspeed computing and measurements applications.IBM Journal of Research and Developmentacknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520An experimental 50megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50megacycle pulserepetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phaselocked frequency divider which provides a 3.125megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a highspeed shift register, a highspeed indicator register, and a binary word generator.\par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.\par In a 50megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may m
…#Š uW #)+e57=K;?c+e‹
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author = "Anonymous",
title = "Analysis and research memorandum 294",
type = "{AR} Memo",
number = "294 (AD 207929)",
institution = "Massachusetts Institute of Technology, Naval
Supersonic Laboratory",
address = "Cambridge, MA, USA",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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keywords = "Error functions.; Floatingpoint arithmetic.",
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00—LY#3eY577+={;†3q!e†3eY—articlefparith.bibAshenhurst:1959:UFPRobert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point ArithmeticjJACM63415428jul71959JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541168.00MR0105833 (21 \#4568)H. H. GoldstineFri Dec 08 13:06:24 1995http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:06:24 ???Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Journal of the Association for Computing Machinery0121.12102acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Robert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point Arithmetic
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = jJACM,
volume = "6",
number = "3",
pages = "415428",
month = jul,
year = "1959",
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MRnumber = "MR0105833 (21 \#4568)",
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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
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}…
ð÷ðŒW #'c57E‚;?c1cŽ!articlefparith.bibCarr:1959:EAFJohn W. Carr IIIError Analysis in Floating Point ArithmeticjCACM251015may51959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:23 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:23 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79John W. {Carr III}Error Analysis in Floating Point Arithmetic
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = jCACM,
volume = "2",
number = "5",
pages = "1015",
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year = "1959",
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}ŽY #//57Eo;?Oc/‘ articlefparith.bibBuchholz:1959:FFCWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)jCACM2123111959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Mon Jan 22 06:28:45 MST 2001http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 06:28:45 MSTCommunications of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Wilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
title = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = jCACM,
volume = "2",
number = "12",
pages = "311",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
0ˆ*U #'U;7=m;]O'Y‰?articlefparith.bibDaggett:1959:DBCD. H. DaggettDecimalBinary Conversions in CORDICjIRETRANSELECCOMPUTEC85335339sep91959IRELAO03679950 OR 03679950Thu Sep 08 08:14:00 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:00 ???IRE Transactions on Electronic Computersdecimal floatingpoint arithmeticacknjD. H. DaggettDecimalBinary Conversions in {CORDIC}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
title = "DecimalBinary Conversions in {CORDIC}",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "5",
pages = "335339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floatingpoint arithmetic",
}LW %#%ym9'!=%;!‚;{1my!9Ž[incollectionfparith.bibCarr:1959:PCJohn W. Carr IIIEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeHandbook of Automation, Computation, and ControlProgramming and CodingpubWILEYpubWILEY:adr10151959TJ213 .G72Fri Aug 20 08:41:16 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 08:41:16 ???Chapter 2.19581961: Volume 1. Control fundamentals. Volume 2. Computers and data processing. Volume 3. Systems and components. Cited in cite Sterbenz:1974:FPC.automation; mathematics; computers; operations researchacknhfbJohn W. {Carr III}Handbook of Automation, Computation, and ControlEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeChapter 2.Programming and Coding
@InCollection{Carr:1959:PC,
author = "John W. {Carr III}",
editor = "Eugene M. Grabbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pubWILEY,
address = pubWILEY:adr,
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",
}
µ
1“É¤µ
¸Ú‡ti
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ISSN = "00189340 (print), 15579956 (electronic)",
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Sato and A. Suga and G. Goto",
title = "A 64bit FloatingPoint Processing Unit with a
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} aˆx‘q
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author = "S. Kawahito and M. Ishida and T. Nakamura and M.
Kameyama and T. Higuchi",
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multiplevalued currentmode circuits",
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volume = "43",
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pages = "3442",
month = jan,
year = "1994",
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@Article{Katti:1994:CDC,
author = "R. Katti",
title = "Comments on {``Decomposition of Complex Multipliers
Using Polynomial Encoding''}",
journal = jIEEETRANSCOMPUT,
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number = "3",
pages = "381383",
month = mar,
year = "1994",
CODEN = "ITCOB4",
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ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL =Y„w‰o
@Article{Kawabata:1984:SFP,
author = "Hugh M. Kawabata",
title = "{Savage} Floating Point Benchmark in {Fortran} in
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "Dr. Dobb's Journal of Software Tools",
}W…M‹
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author = "W. J. Karplus and D. Cohen",
title = "Architectural and Software Issues in the Design of
Peripheral Array Processors",
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volume = "??",
number = "??",
pages = "????",
month = sep,
year = "1981",
CODEN = "CPTRB4",
ISSN = "00189162 (print), 15580814 (electronic)",
ISSNL = "00189162",
bibdate = "Fri Nov 09 19:01:34 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Computer",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
ã Vão
W #/1]'K577E…I;#1!C%1]“=articlefparith.bibForsythe:1959:RNRGeorge E. ForsytheReprint of a Note on RoundingOff ErrorsjSIAMREVIEW1166671959SIREADhttps://doi.org/10.1137/100101100361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 0036144565.00MR0099119 (20 \#5563)Thu Mar 27 09:04:24 MDT 2014http://epubs.siam.org/toc/siread/1/1; http://www.math.utah.edu/pub/bibnet/authors/f/forsythegeorgeelmer.bib; http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:04:24 MDTSIAM Reviewnumerical analysis0168.14002acknhfbhttp://epubs.siam.org/sirevJanuary 1959George E. ForsytheReprint of a Note on RoundingOff Errors
@Article{Forsythe:1959:RNR,
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title = "Reprint of a Note on RoundingOff Errors",
journal = jSIAMREVIEW,
volume = "1",
number = "1",
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month = "????",
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http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib;
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fjournal = "SIAM Review",
journalURL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis",
onlinedate = "January 1959",
}& Y#+I!57E‚;?cI!)articlefparith.bibErcoli:1959:BADPaolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial ComputerjCACM241315apr41959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#ErcoliV59; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Paolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial Computer
@Article{Ercoli:1959:BAD,
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title = "Binary Arithmetic for Discretely Variable Word Length
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journal = jCACM,
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month = apr,
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[ ê[‹W #+?;]7E‚;]?Œ]articlefparith.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.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515IRE Transactions on Electronic ComputersacknhfbHarvey L. GarnerThe Residue Number System
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "2",
pages = "140147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219515",
ISSN = "03679950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
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acknowledgement = acknhfb,
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}ŒY #+;]7E‚;]Karticlefparith.bibGarner:1959:RMSHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement CodesjIRETRANSELECCOMPUTEC812530mar31959IRELAOhttps://doi.org/10.1109/TEC.1959.522275703679950 OR 03679950Thu Jul 14 15:56:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757IRE Transactions on Electronic ComputersacknhfbHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement Codes
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "1",
pages = "2530",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222757",
ISSN = "03679950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
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acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
ŒY '#''‚U=m;M''‚UŒinproceedingsfparith.bibHenrici:1959:TESPeter HenriciProceedings of the International Conference on Information Processing, UNESCOTheoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations36431959Fri Aug 20 09:11:32 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:11:32 ???Cited in cite Sterbenz:1974:FPC.acknhfbPeter HenriciProceedings of the International Conference on Information Processing, UNESCOTheoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations
@InProceedings{Henrici:1959:TES,
author = "Peter Henrici",
editor = "????",
booktitle = "Proceedings of the International Conference on
Information Processing, UNESCO",
title = "Theoretical and Experimental Studies on the
Accumulation of Error in the Numerical Solution of
Initial Value Problems for Systems of Ordinary
Differential Equations",
publisher = "????",
address = "????",
pages = "3643",
year = "1959",
LCCN = "????",
bibdate = "Fri Aug 20 09:11:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}‰e
Y'#'A7'%=m;A7‰einproceedingsfparith.bibGray:1959:NFPH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, MA, December 13, 1959Normalized floatingpoint arithmetic with an index of significance16pubAFIPSpubAFIPS:adr2442481959TK7885.A1 J6Tue Oct 09 09:43:31 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.10.09 09:43:31 ???acknhfbH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, MA, December 13, 1959Normalized floatingpoint arithmetic with an index of significance
@InProceedings{Gray:1959:NFP,
author = "H. L. Gray and C. Harrison",
booktitle = "Proceedings of the Eastern Joint Computer Conference,
Boston, MA, December 13, 1959",
title = "Normalized floatingpoint arithmetic with an index of
significance",
volume = "16",
publisher = pubAFIPS,
address = pubAFIPS:adr,
pages = "244248",
year = "1959",
LCCN = "TK7885.A1 J6",
bibdate = "Tue Oct 09 09:43:31 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}
— à—ŒEY #)+1;]7E‚;]+1m
articlefparith.bibLucal:1959:AODHarold M. LucalArithmetic Operations for Digital Computers Using a Modified Reflected Binary CodejIRETRANSELECCOMPUTEC84449458dec121959IRELAOhttps://doi.org/10.1109/TEC.1959.522205703679950 OR 03679950Thu Jul 14 15:56:45 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:45 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057IRE Transactions on Electronic ComputersacknhfbHarold M. LucalArithmetic Operations for Digital Computers Using a Modified Reflected Binary Code
@Article{Lucal:1959:AOD,
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title = "Arithmetic Operations for Digital Computers Using a
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journal = jIRETRANSELECCOMPUT,
volume = "EC8",
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square root.",
abstract = "For centuries the decimal number system reigned
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until the advent of digital computers brought the
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introduces another number system which may prove useful
for manipulating complex numbers on machines.",
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€€š"[ #)+A57Eƒ[;‚7„q?c„q+‚WAœarticlefparith.bibKnuth:1960:INSDonald E. KnuthAn Imaginary Number SystemjCACM34245247apr41960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.9923\#B554C. B. HaselgroveFri Nov 25 18:19:26 MST 2005http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Knuth60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database2005.11.25 18:19:26 MSTErrata, sl Communications of the ACM bf 4 (August 1961), 355 cite Knuth:1961:EIN. See cite Nadler:1961:DSR for extension to division and square root.For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.Donald E. KnuthErrata, {\sl Commun\i\ca\tions of the ACM\/ \bf 4} (August 1961), 355 \cite{Knuth:1961:EIN}. See \cite{Nadler:1961:DSR} for extension to division and square root.An Imaginary Number System
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MathSciNet database",
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note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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((TY #)#S57Eƒ1;C?c#GW‘karticlefparith.bibTraub:1960:CNMJ. F. TraubComments on a recent paper [``A New Method of Computation of Square Roots Without Using Division'']jCACM328686feb21960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:25 MST 2005http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:25 MSTSee cite Sarafyan:1959:NMC.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79J. F. TraubSee \cite{Sarafyan:1959:NMC}.Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]
@Article{Traub:1960:CNM,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = jCACM,
volume = "3",
number = "2",
pages = "8686",
month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Traub60;
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
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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}.",
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xxmonth = "none",
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h,h‹@/W #1+e!577=;7U+eŒmarticlefparith.bibWilkinson:1960:EAFJ. H. WilkinsonError Analysis of FloatingPoint ComputationjNUMMATH2319340dec121960NUMMA70029599X (print), 09453245 (electronic) OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599X65.00MR0116477 (22 \#7264)C. B. HaselgroveFri May 14 17:18:08 2010http://www.math.utah.edu/pub/bibnet/authors/w/wilkinsonjameshardy.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.05.14 17:18:08 ???Numerische Mathematikacknhfbhttp://link.springer.com/journal/211J. H. WilkinsonError Analysis of FloatingPoint Computation
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articlefparith.bibWadey:1960:FAW. G. WadeyFloatingPoint ArithmeticsjJACM72129139apr41960JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541165.00 (68.00)22\#6090Fri Dec 08 14:44:46 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 14:44:46 ???Three types of floatingpoint arithmetics with error control are discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.Journal of the ACMCited in cite Sterbenz:1974:FPC.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401C. B. HaselgroveThree types of floatingpoint arithmetics with error control are discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.W. G. WadeyFloatingPoint Arithmetics
@Article{Wadey:1960:FA,
author = "W. G. Wadey",
title = "FloatingPoint Arithmetics",
journal = jJACM,
volume = "7",
number = "2",
pages = "129139",
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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.",
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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",
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acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
xxpages = "220221??",
}°
~/~‡1U !#1==E[=m;M=ˆ techreportfparith.bibAnonymous:1961:MCMAnonymousModern Computing MethodsNotes on Applied Science16National Physical LaboratoryHer Majesty's Stationery Office, London2202221961Fri Aug 20 10:05:25 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 10:05:25 ???Cited in cite Sterbenz:1974:FPC.acknhfbAnonymousModern Computing Methods
@TechReport{Anonymous:1961:MCM,
author = "Anonymous",
title = "Modern Computing Methods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
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}‘M0Z#)C#I)Q57C‚;cKqYCg’warticlefparith.bibAmble:1961:AFPO. Amble and Jan V. GarwickOn the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp. 8788]jNORDISKTIDSKRINFORMBEHAND13220222sep91961BITTEL, NBITABhttps://doi.org/10.1007/BF0193343400063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=3; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee cite Garwick:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543O. Amble and Jan V. GarwickSee \cite{Garwick:1961:AFP,Garwick:1961:RAF}.On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 8788]}
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author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
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journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "3",
pages = "220222",
month = sep,
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CODEN = "BITTEL, NBITAB",
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keywords = "floatingpoint accuracy; floatingpoint arithmetic",
xxpages = "220221??",
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acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}Ú`†9Œs
@Article{Black:1984:NIS,
author = "Cheryl M. Black and Robert P. Burton and Thomas M.
Miller",
title = "The Need for an Industry Standard of Accuracy for
ElementaryFunction Programs",
journal = jTOMS,
volume = "10",
number = "4",
pages = "361366",
month = dec,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2701.356101",
ISSN = "00983500 (print), 15577295 (electronic)",
ISSNL = "00983500",
bibdate = "Sun Sep 04 20:32:29 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "ACM Transactions on Mathematical Software",
journalURL = "http://dl.acm.org/pub.cfm?id=J782",
}3L„=ˆ{
@Article{Campbell:1986:SS,
author = "R. A. Campbell",
title = "In Search of a Sine",
journal = jDDJ,
volume = "11",
number = "12",
pages = "3032",
month = dec,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044789X",
bibdate = "Thu Sep 1 10:15:57 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
Ï ÏŒ2Y #11
;]7E‚;]=
earticlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSignedDigit Number Representations for Fast Parallel ArithmeticjIRETRANSELECCOMPUTEC103389400sep91961IRELAOhttps://doi.org/10.1109/TEC.1961.521922703679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227IRE Transactions on Electronic ComputersacknhfbAlgirdas Avi{\v{z}}ienisSignedDigit Number Representations for Fast Parallel Arithmetic
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
title = "SignedDigit Number Representations for Fast Parallel
Arithmetic",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "3",
pages = "389400",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219227",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}³
QQ+3Y #+5{;]7E‚;Š=]Š=5{›3articlefparith.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.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:02 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154A system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.IRE Transactions on Electronic ComputersacknhfbA system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.Philip Warren CheneyA Digital Correlator Based on the Residue Number System
@Article{Cheney:1961:DCB,
author = "Philip Warren Cheney",
title = "A Digital Correlator Based on the Residue Number
System",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "1",
pages = "6370",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219154",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
[[‰!4V #/)c57=m;?c)cŠarticlefparith.bibClarkson:1961:DMIW. K. ClarksonA Divisionless Method of Integer ConversionjCACM47315316jul71961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 08:14:59 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:59 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79W. K. ClarksonA Divisionless Method of Integer Conversion
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Method of Integer Conversion",
journal = jCACM,
volume = "4",
number = "7",
pages = "315316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision additionsubtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}µ
O5Y #%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;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision additionsubtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
ˆ[7W #'!=m;+'‹
articlefparith.bibFreiman:1961:SACC. V. FreimanStatistical analysis of certain binary division algorithmsjIREPROC49191103jan11961Mon Sep 16 16:12:21 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.09.16 16:12:21 ???IRE ProceedingsacksfoC. V. FreimanStatistical analysis of certain binary division algorithms
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = jIREPROC,
volume = "49",
number = "1",
pages = "91103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}Œ}6Y #'%];]7E‚;]%]Žarticlefparith.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.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:05 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286IRE Transactions on Electronic ComputersacknhfbJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix Arithmetic
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine BinarytoDecimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "777777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219286",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
Ýÿÿî"
3Ýg‰+’W
@Article{Grehan:1988:FPCa,
author = "Rick Grehan",
title = "FloatingPoint Without a Coprocessor",
journal = jBYTE,
volume = "13",
number = …R‹%
@Article{Groeger:1989:DRG,
author = "Detlef Gr{\"o}ger",
title = "{Zur Division mit Rest auf Gleitkommarechnern.
(German)} [On division with remainder on floating point
co‰B“
@Article{Gregory:1977:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base conversion in residue number systems",
journal = jBIT,
volume = "17",
number = "3",
pages = "286302",
month = sep,
year = "1977",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932149",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
MRclas/ˆ[
@Article{Gregory:1979:EFC,
author = "Robert Todd Gregory",
title = "Errorfree computation with finite number systems",
journal = jSIGNUM,
volume = "14",
number = "3",
pages = "916",
month = sep,
year = "1979",
CODEN = "SNEWD6",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "http://portal.ac
#O
@Article{Griffin:1991:REA,
author = "C. Griffin and P. Rao and F. Taylor",
title = "Roundoff error analysis of the discrete {Wigner}
distribution using fixedpoint arithmetic",
journal = jIEEETRANSSIGPROC,
volume = "39",
number = "9",
pages = "20962098",
month = sep,
year = "1991",
CODEN = "ITPRED",
ISSN = "1053587X (print), 19410476 (electronic)",
ISSNL = "105j„e‰K
@Article{Grehan:1989:FPR,
author = "R„1ˆc
@Article{Gregory:1972:URA,
author = "Robert Todd Gregory",
title = "The use of residue arithmetic with automatic digital
computers",
journal = "Delta (Waukesha)",
volume = "3",
number = "2",
pages = "127",
year = "1972\slash 1973",
MRclass = "68A10",
MRnumber = "MR0321348 (47 \#9881)",
MRreviewer = "A. D. Booth",
bibdate = "Thu Nov 8 14:50:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}b‰{“w
@Article{Grehan:1988:FPCb,
author = "R. Grehan",
title = "FloatingPoint Without a Coprocessor, Part 2",
journal = jBYTE,
volume = "13",
number = "10",
pages = "293297 (or 293298??)",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "03605280 (print), 10827838 (electronic)",
ISSNL = "03605280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "ftp://garbo.u ×‰+’W
@Article{Grehan:1988:FPCa,
author = "Rick Grehan",
title = "FloatingPoint Without a Coprocessor",
journal = jBYTE,
volume = "13",
number = "9",
pages = "313319",
month = sep,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "03605280 (print), 10827838 (electronic)",
ISSNL = "03605280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CDROM database Õ‹–?
@Article{Grehan:1988:BBL,
author = "R. Grehan and T. Thompson",
title = "{Borland} beefs up its languages",
journal = jBYTE,
volume = "13",
number = "10",
pages = "151154",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "03605280 (print), 10827838 (electronic)",
ISSNL = "03605280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "http://www.math.utah.edu/p Òibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = acknhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}¸His work was supported by this contract, and led to the Ph.D..acknhfbThe purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.H. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computers
@TechReport{Garner:1961:RNS,
author = "H. L. Garner and R. F. Arnold and B. C. Benson and C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = acknhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}
°g8\!#+[U51=m;#Žy‹Žy[Uw
techreportfparith.bibGarner:1961:RNSH. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computersASD Technical Report61483Electronic Technology Laboratory, The University of MichiganAnn Arbor, MI, USA91103oct101961Thu Nov 18 09:27:06 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:27:06 ???http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txtThe purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.This report represents the results of research performed by the group at The University of Michigan under the direction of Professor H. L. Garner. Concurrently, research on the same subject was being conducted at Harvard University under the direction of Professor Howard Aiken, and at the Lockheed Missile System Division under the direction of Dr. Richard Tanaka. There was a considerable exchange of information among the above groups during the course of the research effort. The efforts attained exhibit little overlap, rather they are complementary. A portion of this report was extracted from the doctoral dissertation of D. P. Rozenberg. ¸ "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}¹
¬:Y #'AI)57=I;_qY'cK[articlefparith.bibGarwick:1961:RAFJ. V. GarwickReply to ``On the Accuracy of Floating Point Computers'' [BIT bf 1(3), 1961, pp. 220221]jNORDISKTIDSKRINFORMBEHAND132222221961BITTEL, NBITAB00063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Mon Nov 16 14:36:22 1998http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.11.16 14:36:22 ???See cite Garwick:1961:AFP,Amble:1961:AFP.floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543J. V. GarwickSee \cite{Garwick:1961:AFP,Amble:1961:AFP}.Reply to {``On the Accuracy of Floating Point Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "3",
pages = "222222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}P9Z #)]I)Q57C‚;
IqY)]‘warticlefparith.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point ComputersjNORDISKTIDSKRINFORMBEHAND128788jun61961BITTEL, NBITABhttps://doi.org/10.1007/BF0193922100063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee also comment and reply cite Amble:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543Jan V. GarwickSee also comment and reply \cite{Amble:1961:AFP,Garwick:1961:RAF}.The Accuracy of Floating Point Computers
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "2",
pages = "8788",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939221",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}b",
abstract = "Error checking codes based on residues have the
advantage over paritybased codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect bursttype errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
singledigit error in a decimal operation.",
acknowledgement = acknhfb,
keywords = "decimal arithmetic",
}»
[;[‹\W#EO;]7E‚;]ES
articlefparith.bibKovatch:1961:HEAG. Kovatch and W. E. MeserveThe HallEffect Analog MultiplierjIRETRANSELECCOMPUTEC103512515sep91961IRELAOhttps://doi.org/10.1109/TEC.1961.521924003679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240IRE Transactions on Electronic ComputersacknhfbG. Kovatch and W. E. MeserveThe {HallEffect} Analog Multiplier
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {HallEffect} Analog Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "3",
pages = "512515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219240",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Šo=W #)+Y57=S;=?c+A]‹warticlefparith.bibKnuth:1961:EINDonald E. KnuthErrata: ``An imaginary number system''jCACM48355355aug81961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Tue Jan 09 07:10:22 1996http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.01.09 07:10:22 ???See cite Knuth:1960:INS.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Donald E. KnuthSee \cite{Knuth:1960:INS}.Errata: {``An imaginary number system''}
@Article{Knuth:1961:EIN,
author = "Donald E. Knuth",
title = "Errata: {``An imaginary number system''}",
journal = jCACM,
volume = "4",
number = "8",
pages = "355355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
Ù ²Ù‡U@U #1+_!=m;]++a_ˆarticlefparith.bibMacSorley:1961:HSAO. L. MacSorleyHighspeed arithmetic in binary computersjIREPROC496791jan11961Sat May 18 14:34:55 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:34:55 ???Reprinted in cite Swartzlander:1976:CDD.IRE ProceedingsacknhfbO. L. MacSorleyReprinted in \cite{Swartzlander:1976:CDD}.Highspeed arithmetic in binary computers
@Article{MacSorley:1961:HSA,
author = "O. L. MacSorley",
title = "Highspeed arithmetic in binary computers",
journal = jIREPROC,
volume = "49",
number = "??",
pages = "6791",
month = jan,
year = "1961",
bibdate = "Sat May 18 14:34:55 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = acknhfb,
fjournal = "IRE Proceedings",
}ŒJ?Y#+9#;]7E‚;]9#qarticlefparith.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.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274IRE Transactions on Electronic ComputersacknhfbM. Lehman and N. BurlaSkip Techniques for HighSpeed CarryPropagation in Binary Arithmetic Units
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for HighSpeed CarryPropagation in
Binary Arithmetic Units",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "691698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219274",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}date = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}Á
AY #+' 57E‚5;=?Mc'A qarticlefparith.bibNadler:1961:DSRMorton NadlerDivision and square root in the quaterimaginary number systemjCACM44192193apr41961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.9923\#B555Fri Nov 25 18:19:32 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:32 MSTSee cite Knuth:1960:INS.Communications of the ACM$sqrt (x)$; elementary functionsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Morton NadlerSee \cite{Knuth:1960:INS}.Division and square root in the quaterimaginary number system
@Article{Nadler:1961:DSR,
author = "Morton Nadler",
title = "Division and square root in the quaterimaginary
number system",
journal = jCACM,
volume = "4",
number = "4",
pages = "192193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}/links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = acknhfb,
fjournal = "Annals of Mathematical Statistics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a nontrivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of roundoff in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}Âstants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ \log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.Roger S. PinkhamOn the Distribution of First Significant Digits
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = jANNMATHSTAT,
volume = "32",
number = "4",
pages = "12231230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "00034851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = acknhfb,
fjournal = "Annals of Mathematical Statistics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a nontrivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of roundoff in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
f×fˆmCV #3'C57=m;?c'C‰uarticlefparith.bibRabinowitz:1961:MPDP. RabinowitzMultiplePrecision DivisionjCACM429898feb21961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 00:29:25 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 00:29:25 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79P. RabinowitzMultiplePrecision Division
@Article{Rabinowitz:1961:MPD,
author = "P. Rabinowitz",
title = "MultiplePrecision Division",
journal = jCACM,
volume = "4",
number = "2",
pages = "9898",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}´BY #k+!7=m;CŽmOsŽ7Žuk³5articlefparith.bibPinkham:1961:DFSRoger S. PinkhamOn the Distribution of First Significant DigitsjANNMATHSTAT32412231230dec121961AASTAD00034851 OR 00034851Thu Feb 15 15:07:57 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 15:07:57 ???http://links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2TIt has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are more physical constants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ log _10(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ log _10(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.Annals of Mathematical StatisticsBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom p. 1223: ``ldots the proportion of these data with first significant digit $n$ or less is approximately $ log _10(n + 1) $.''par ldots ``The only distribution for first significant digits which is invariant under scale change of the underlying distribution is $ log _10(n + 1) $. Contrary to suspicion this is a nontrivial mathematical result, for the variable $n$ is discrete.''.par From p. 1230: ``The foregoing results bear on questions of roundoff in computing machines. Since $ d(u v) = u d v + v d u $, the error resulting from multiplying two rounded numbers will be governed primarily by the first significant digits of the two numbers being multiplied. Now the distribution of first significant digits, favoring as it does low order digits, tends to produce less error than would be the case if first significant digits were uniform as has sometimes been assumed.''par Cited in cite Sterbenz:1974:FPC.acknhfbIt has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are more physical conÄ
‘
®€‘o¿ ÐˆW‘/
@Article{Prado:1987:FSR,
author = "J. Prado and R. Alcantara",
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processor",
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month = feb,
year = "1987",
CODEN = "IEEPAD",
ISSN = "00189219 (print), 15582256 (electronic)",
ISSNL = "00189219",
bibdate = "Sat Jul 16 15:28:13 MDT ^‰L“
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author = "D. Pountain",
title = "{PROLOG} on Microcomputers",
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number = "13",
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month = dec,
year = "1984",
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author = "V. Pratt",
title = "Anatomy of the {Pentium} Bug",
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volume = "915",
pages = "97107",
year = "1995",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Sat May 11 13:45:32 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://boole.stanford.edu/pub/FDIV/anapent.ps.gz",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
keywords = "Intel Pentium divide flaw; Thomas R. Nicely",
}ðUŸ+
@Article{Prather:1988:CET,
author = "R. E. Prather",
title = "Comparison and Extension of Theories of {Zipf} and
{Halstead}",
journal = jCOMPJ,
volume = "31",
number = "3",
pages = "248252",
month = jun,
year = "1988",
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ISSNL = "00104620",
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bibsou
Ç/
@Article{Preston:1978:NAT,
author = "F. S. Preston",
title = "A New Algorithm for the Tangent",
journal = jIEEETRANSCOMPUT,
volume = "C27",
number = •"ªE
@Article{Preparata:1990:PCD,
author = "F. P. Preparata and J. E. Vuillemin",
title = "Practical cellular dividers",
journal = jIEEETRANSCOMPUT,
volume = "39",
number = "5",
pages = "605614",
month = may,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.53574",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "ThÇ‡pa
@Article{Preparata:1983:MCA,
author = "F. P. Preparata",
title = "A MeshConnected AreaTime Optimal {VLSI} Multiplier
of Large Integers",
journal = jIEEETRANSCOMPUT,
volume = "C32",
number = "2",
pages = "194198",
month = feb,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676203",
ISSN = "00189340 (print), 15579956 (electronic)",
„P‰!
@Article{Posnov:1969:FPR,
author = "N. N. Posnov and M. K. Buza and V. K. Kravcov",
title = "The floating point in a residue class number system.
({Russian})",
journal = "Vestnik Beloruss. Gos. Univ. Ser. I",
volume = "3",
pages = "2127",
year = "1969",
MRclass = "10A10",
MRnumber = "45 3303e",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
language = "Russian",
reviewer = "J. B. Roberts",
}Ñ
Y
Y‹+EY #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/",
}‹tDW #){;]7E‚;]){;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.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:03 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.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
’
GX #'!O%1%=m;†M!†MSEbookfparith.bibTaub:1961:JNCA. H. TaubJohn von Neumann: Collected WorkspubPERGAMONpubPERGAMON:adr??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol. 4), ??? (vol. 5), ??? (vol. 6)1961  1963Wed Jun 01 16:58:29 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 16:58:29 ???Six volumes. Volume I: Logic, Theory of Sets and Quantum Mechanics (1961); Volume II: Operators, Ergodic Theory and Almost Periodic Functions in a Group (1961); Volume III: Rings of Operators (1961); Volume IV: Continuous Geometry and Other Topics (1962); Volume V: Design of Computers, Theory of Automata and Numerical Analysis (1963); Volume VI: Theory of Games, Astrophysics, Hydrodynamics and Meteorology (1963).acknhfbA. H. TaubSix volumes. Volume I: Logic, Theory of Sets and Quantum Mechanics (1961); Volume II: Operators, Ergodic Theory and Almost Periodic Functions in a Group (1961); Volume III: Rings of Operators (1961); Volume IV: Continuous Geometry and Other Topics (1962); Volume V: Design of Computers, Theory of Automata and Numerical Analysis (1963); Volume VI: Theory of Games, Astrophysics, Hydrodynamics and Meteorology (1963).{John von Neumann}: Collected Works
@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,
}‹\FY #1%[57=K;1e%[ŒGarticlefparith.bibSpielberg:1961:RPSK. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued FractionsjJACM84613627oct101961JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Sat Dec 09 14:01:44 1995ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.09 14:01:44 ???Journal of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J401K. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractions
@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,
}Ç
‰
‰ŠsHY #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,
}É
rr
IY !#')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
@TechReport{Weik:1961:TSD,
author = "Martin H. Weik",
title = "A Third Survey of Domestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred 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,
}
Œ
xXMŒ—ƒ^‡=
@Book{Plauger:1992:SCL,
author = "P. J. Plauger",
title = "The {Standard C} Library",
publisher = pubPH,
address = pubPH:adr,
pages = "xiv + 498",
year = "1992",
ISBN = "013838‡?Ž
@Book{Patterson:2008:COD,
author = "David A. Patterson and John L. Hennessy",
booktitle = "Computer organization and design: the hardware\slash
software interface",
title = "Computer organization and design: the hardware\slash
software interface",
publisher = pubELSEVIERMORGANKAUFMANN,
address = pubELSEVIERMORGANKAUFMANN:adr,
edition = "Fourth",
bookpages = "xxv + 703 + A77 + B83 + I26",
pages = "xxv + 703 + A77 + B83 + I26",
year = "2008",
ISBN = "0123744938",
ISBN13 = "9780123744937",
LCCN = "QA76.9.C643",
bibdate = "Mon Nov 17 13:31:21 MST 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.gbv.de:20011/gvk",
acknowledgement = acknhfb,
subject = "computer organization; computer engineering; computer
interfaces",
}„ˆ[
@Book{Parker:1966:SNS,
author = "Francis D. Parker",
title = "The structure of number systems",
publisher = pubPH,
address = pubPH:adr,
pages = "xi + 137",
year = "1966",
LCCN = "QA241 .P3; QA241 .P239",
bibdate = "Fri Nov 9 19:10:47 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "Teachers' mathematics reference series",
acknowledgement = acknhfb,
subject = "Number theory",
}e§RÏ%
@Book{Parhami:2010:CAA,
author = "Behrooz Parhami",
title = "Computer arithmetic: algorithms and hardware designs",
publisher = pubOXFORD,
address = pubOXFORD:adr,
edition = "Second",
pages = "xxv + 641",
year = "2010",
ISBN = "0195328485 (hardcover)",
ISBN13 = "9780195328486 (hardcover)",
LCCN = "QA76.9.C62 P37 2010",
bibdate = "Sat Sep 20 16:57:27 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "The Oxford series in electrical and computer
engineering",
URL = "http://www.loc.gov/catdir/enhancements/fy1006/2009034155d.html;
http://www.loc.gov/catdir/enhancements/fy1006/2009034155t.html",
abstract = "Ideal for graduate and senior undergraduate courses in
computer arithmetic and advanced digital design,
å„ˆ=
@Book{Parhami:2000:CAA,
author = "Behrooz Parhami",
title = "Computer Arithmetic: Algorithms and Hardware Designs",
publisher = pubOXFORD,
address = pubOXFORD:adr,
pages = "xx + 490",
year = "2000",
ISBN = "0195125835",
ISBN13 = "9780195125832",
LCCN = "QA76.9.C62P37 1999",
bibdate = "Sat Jun 17 12:26:40 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$85.00",
acknowledgement = acknhfb,
}¼…Š
@Book{Palmer:1985:MGN,
author = "John F. Palmer and Stephen P. Morse",
title = "{Die mathematischen Grundlagen der NumerikProzessoren
8087\slash 80287}",
publisher = pubTEWI,
address = pubTEWI:adr,
pages = "240",
year = "1985",
ISBN = "3921803330",
ISBN13 = "9783921803332",
LCCN = "????",
bibdate = "Wed Sep 07 21:14:32 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "German translation of {\em The 8087 Primer}
\cite{Palmer:1984:P}.",
acknowledgement = acknj,
}ï
L»‰!MV %#/)+c=+3%=%;M)g+=Šincollectionfparith.bibCampbell:1962:FPOS. G. CampbellWerner BuchholzPlanning a Computer System: Project StretchFloatingPoint OperationpubMCGRAWHILLpubMCGRAWHILL:adr921211962QA76.8.I2 I5Wed Feb 14 17:24:27 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2007.02.14 17:24:27 ???IBM 7030 (Computer); IBM Stretchacknhfb322S. G. CampbellPlanning a Computer System: {Project Stretch}Werner BuchholzFloatingPoint Operation
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
editor = "Werner Buchholz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "FloatingPoint Operation",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
bookpages = "322",
pages = "92121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
subject = "IBM 7030 (Computer); IBM Stretch",
}älL\ #/+c+3!Eƒ{;{µC7ñ%+{g‚”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; library.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 architÔ…OKU '#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,
}‹]JW#+GY;]7E‚;]GY 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.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271IRE Transactions on Electronic ComputersacknhfbJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary Division
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "662670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219271",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Ð
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://edthelen.org/comphist/IBM7030PlanningMcJones.pdf",
acknowledgement = acknhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floatingpoint arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the ndigit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisymode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up  it
merely has a very high probability of showing up 
whereas builtin significance checks can be made
slightly pessimistic, so that actual significance loss
will not be greater than indicated. On the other hand,
little extra hardware and no extra storage are required
for the noisymode approach. Furthermore, significance
loss is relatively rare, so that running a problem
twice when Significance loss is suspected does not pose
a serious problem. What is serious is the possibility
of unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixedpoint arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
Ñ fixedpoint arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixedpoint arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixedpoint
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixedpoint operands do
give correct significance indications, the use of other
operations and of builtin scaling loops frequently
destroys entirely the leadingzeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. Highspeed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Indexarithmetic Unit 21 \\
3.10. Instruction Lookahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radixconversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Indexarithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. InputOutput Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
4.3. Data Hierarchies 39 \\
4.4. Classes of Operations 40 \\
5. Choosing a Number Base 42 \\
[by W. Buchholz] \\
5.1. Introduction 42 \\
5.2. Information Content 45 \\
5.3. Arithmetic Speed 49 \\
5.4. Numerical Data 50 \\
5.5. Nonnumerical Data 51 \\
5.6. Addresses 52 \\
5.7. Transformation 53 \\
5.8. Partitioning of Memory 54 \\
5.9. Program Interpretation 56 \\
5.10. Other Number Bases 58 \\
5.11. Conclusion 58 \\
6. Character Set 60 \\
[by R. W. Bemer and W. Buchholz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \Ò\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Taperecording Convention 71 \\
6.15. Cardpunching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variablefieldlength Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variablefieldlength Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radixconversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floatingpoint Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixedpoint Arithmetic 92 \\
8.2. Floatingpoint Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floatingpoint Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Roundoff Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floatingpoint Arithmetic 103 \\
8.9. Structure of Floatingpoint Data 104 \\
Floatingpoint Features of the 7030 \\
8.10. Floatingpoint Instruction Format 106 \\
8.11. Floatingpoint Data Formats 106 \\
8.12. Singular Floatingpoint Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floatingpointarithmetic Operations 114 \\
8.17. Fixedpoint Arithmetic Using Unnormalized \\
Floatingpoint Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multipleprecision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Singleaddress Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Programinterrupt System 136 \\
10.6. Components of the Programinterrupt System 137
\\
10.7. Examples of Programinterrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
Ó 11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Recordhandling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. InputOutput Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
InputOutput and External Storage 179 \\
12.2. InputOutput Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of InputOutput Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Lookahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timingsimulation Program 230 \\
15.3. Description of the Lookahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Lookback at the Lookahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Setup Mode 258 \\
17.3. Bytesequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTEBYBYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Lookup Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Storedprogram Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cuberoot Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floatingpoint Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}ÌÕects.http://edthelen.org/comphist/IBM7030PlanningMcJones.pdfThe text of the book is in the public domain, with the permission of the author in 2003. See cite MacKenzie:1991:IAL for a remark about the noisy mode for floatingpoint arithmetic in the IBM 7030 Stretch. That mode is first mentioned on page 25 of this book, and described in detail on page 102, which states: ``By definition of ordinary normalized FLP operations, numbers are frequently extended on the right by attaching zeros. During addition the ndigit operand that is not preshifted is extended with n zeros, so as to provide the extra positions to which the preshifted operand can be added. Any operand or result that is shifted left to be normalized requires a corresponding number of zeros to be shifted in at the right. Both sets of zeros tend to produce numbers smaller in absolute value than they would have been if more digits had been carried. In the noisy mode these numbers are simply extended with 1 s instead of zeros (1 s in a binary machine, 9s in a decimal machine). So all numbers tend to be too large in absolute value. The true value, if there had been no significance loss, should lie between these two extremes. Hence, two runs, one made without and one made with the noisy mode, should show differences in result that indicate which digits may have been affected by significance loss. The principal weakness of the noisymode procedure is that it requires two runs for the same problem. A much less important weakness is that the loss of significance cannot be guaranteed to show up  it merely has a very high probability of showing up  whereas builtin significance checks can be made slightly pessimistic, so that actual significance loss will not be greater than indicated. On the other hand, little extra hardware and no extra storage are required for the noisymode approach. Furthermore, significance loss is relatively rare, so that running a problem twice when Significance loss is suspected does not pose a serious problem. What is serious is the possibility of unsuspected significance loss. In discussions of significance two points are often overlooked. The first of these is trivial: the best way of ensuring significant results is to use an adequate number of fraction digits. The second is almost equally mundane: for a given procedure, normalized FLP arithmetic will ordinarily produce the greatest precision possible for the number of fraction digits used. Normalized FLP arithmetic has been criticized with respect to significance loss, because such loss is not indicated by the creation of leading zeros, as it is with fixedpoint arithmetic. In other words, the contention is not that normalized FLP arithmetic is more prone to significance loss than equivalent fixedpoint arithmetic, which would be untrue, but that an equivalent indication of such loss is not provided. Loss of significance, however, is also a serious problem in fixedpoint arithmetic; multiplication and division do not handle it at all correctly by means of leading zeros. (In particular, fixedpoint multiplication may lead to serious or even total significance loss, which would not have occurred with normalized FLP arithmetic: and although leading zeros in addition and subtraction of fixedpoint operands do give correct significance indications, the use of other operations and of builtin scaling loops frequently destroys entirely the leadingzeros method of counting significance.)''Computer architectureForeword v Preface vii 1. Project Stretch 1 [by W. Buchholz] 2. Architectural Philosophy 5 [by F. P. Brooks, Jr.] 2.1. The Two Objectives of Project Stretch 5 2.2. Resources 6 2.3. Guiding Principles 7 2.4. Contemporary Trends in Computer Architecture 10 2.5. Hindsight 15 3. System Summary of IBM 7030 17 [by W. Buchholz] 3.1. System Organization 17 3.2. Memory Units 17 3.3. Index Memory 19 3.4. Special Registers 19 3.5. Input and Output Facilities 19 3.6. Highspeed Disk Units 20 3.7. Central Processing Unit 20 3.8. Instruction Controls 21 3.9. Indexarithmetic Unit 21 3.10. InstrÖuction Lookahead 21 3.11. Arithmetic Unit 22 3.12. Instruction Set 24 3.13. Data Arithmetic 24 3.14. Radixconversion Operations 27 3.15. Connective Operations 27 3.16. Indexarithmetic Operations 27 3.17. Branching Operations 28 3.18. Transmission Operations 28 3.19. InputOutput Operations 29 3.20. New Features 29 3.21. Performance 32 4. Natural Data Units 33 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 4.1. Lengths and Structures of Natural Data Units 33 4.2. Procedures for Specifying Natural Data Units 36 4.3. Data Hierarchies 39 4.4. Classes of Operations 40 5. Choosing a Number Base 42 [by W. Buchholz] 5.1. Introduction 42 5.2. Information Content 45 5.3. Arithmetic Speed 49 5.4. Numerical Data 50 5.5. Nonnumerical Data 51 5.6. Addresses 52 5.7. Transformation 53 5.8. Partitioning of Memory 54 5.9. Program Interpretation 56 5.10. Other Number Bases 58 5.11. Conclusion 58 6. Character Set 60 [by R. W. Bemer and W. Buchholz] 6.1. Introduction 60 6.2. Size of Set 62 6.3. Subsets 62 6.4. Expansion of Set 63 6.5. Code 63 6.6. Parity Bit 66 6.7. Sequence 66 6.8. Blank 67 6.9. Decimal Digits 68 6.10. Typewriter Keyboard 68 6.11. Adjacency 69 6.12. Uniqueness 69 6.13. Signs 70 6.14. Taperecording Convention 71 6.15. Cardpunching Convention 71 6.16. List of 7030 Character Set 72 7. Variablefieldlength Operation 75 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 7.1. Introduction 75 7.2. Addressing of Variablefieldlength Data 76 7.3. Field Length 77 7.4. Byte Size 78 7.5. Universal Accumulator 79 7.6. Accumulator Operand 79 7.7. Binary and Decimal Arithmetic 80 7.8. Integer Arithmetic 81 7.9. Numerical Signs 82 7.10. Indicators 84 7.11. Arithmetical Operations 85 7.12. Radixconversion Operation 87 7.13. Logical Connectives of Two Variables 87 7.14. Connective Operations 89 8. Floatingpoint Operation 92 [by S. G. Campbell] General Discussion 8.1. Problems of Fixedpoint Arithmetic 92 8.2. Floatingpoint Arithmetic 94 8.3. Normalization 97 8.4. Floatingpoint Singularities 98 8.5. Range and Precision 99 8.6. Roundoff Error 100 8.7. Significance Checks 101 8.8. Forms of Floatingpoint Arithmetic 103 8.9. Structure of Floatingpoint Data 104 Floatingpoint Features of the 7030 8.10. Floatingpoint Instruction Format 106 8.11. Floatingpoint Data Formats 106 8.12. Singular Floatingpoint Numbers 108 8.13. Indicators 112 8.14. Universal Accumulator 113 8.15. Fraction Arithmetic 114 8.16. Floatingpointarithmetic Operations 114 8.17. Fixedpoint Arithmetic Using Unnormalized Floatingpoint Operations 118 8.18. Special Functions and Forms of Arithmetic 119 8.19. Multipleprecision Arithmetic 119 8.20. General Remarks 121 9. Instruction Formats 122 [by W. Buchholz] 9.1. Introduction 122 9.2. Earlier Instruction Languages 122 9.3. Evolution of the Singleaddress Instruction 124 9.4. Implied Addresses 125 9.5. Basic 7030 Instruction Formats 126 9.6. Instruction Efficiency 127 9.7. The Simplicity of Complexity 131 9.8. Relationship to Automatic Programming Languages 132 10. Instruction Sequencing 133 [by F. P. Brooks, Jr.] 10.1. Modes of Instruction Sequencing 133 10.2. Instruction Counter 134 10.3. Unconditional Branching 135 10.4. Conditional Branching 136 10.5. Programinterrupt System 136 10.6. Components of the Programinterrupt System 137 10.7. Examples of Programinterrupt Techniques 140 10.8. Execute Instructions 146 10.9. Execute Operations in the 7030 148 11. Indexing 150 [by G. P. Blaauw] 11.1. Introduction 150 11.2. Indexing Functions 151 11.3. Instruction Format for Indexing 155 11.4. Incrementing 157 11.5. Counting 159 11.6. Advancing by One 161 11.7. Progressive Indexing 161 11.8. Data Transmission 162 11.9. Data Ordering 163 11.10. Refilling 165 11.11. Indirect Addressing and Indirect Indexing 167 11.12. Indexing Applications 169 11.13. Recordhandling Applications 172 11.14. File Maintenance 175 11.15. Subroutine Control 177 11.16. Conclusion 178 12. InputOutput Control 179 [by W. Buchholz] 12.1. A Generalized Approach to Connecting InputOutput and External Storage 179 12.2. InputOutput ×Instructions 180 12.3. Defining the Memory Area 181 12.4. Writing and Reading 182 12.5. Controlling and Locating 183 12.6. An Alternative Approach 184 12.7. Program Interruptions 184 12.8. Buffering 180 12.9. Interface 188 12.10. Operator Control of InputOutput Units 190 13. Multiprogramming 192 [by E. F. Codd, E. S. Lowry, E. McDonough, and C. A. Scalzi] 13.1. Introduction 192 13.2. Multiprogramming Requirements 193 13.3. 7030 Features that Assist Multiprogramming 195 13.4. Programmed Logic 197 13.5. Concluding Remarks 200 13.6. References 201 14. The Central Processing Unit 202 [by E. Bloch] 14.1. Concurrent System Operation 202 14.2. Concurrency within the Central Processing Unit 204 14.3. Data Flow 204 14.4. Arithmetic Unit 208 14.5. Checking 216 14.6. Component Count 216 14.7. Performance 217 14.8. Circuits 218 14.9. Packaging 223 15. The Lookahead Unit 228 [by R. S. Balance, J. Cocke, and H. G. Kolsky] 15.1. General Description 228 15.2. Timingsimulation Program 230 15.3. Description of the Lookahead Unit 238 15.4. Forwarding 240 15.5. Counter Sequences 241 15.6. Recovery after Interrupt 246 15.7. A Lookback at the Lookahead 247 16. The Exchange 248 [by W. Buchholz] 16.1. General Description 248 16.2. Starting a WRITE or READ Operation 250 16.3. Data Transfer during Writing 250 16.4. Data Transfer during Reading 251 16.5. Terminating a WRITE or READ Operation 252 16.6. Multiple Operations 252 16.7. CONTROL and LOCATE Operations 252 16.8. Interrogating the Control Word 253 16.9. Forced Termination 253 17. A Nonarithmetical System Extension 254 [by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene] 17.1. Nonarithmetical Processing 254 17.2. The Setup Mode 258 17.3. Bytesequence Formation 259 17.4. Pattern Selection 260 17.5. Transformation Facilities 261 17.6. Statistical Aids 263 17.7. The BYTEBYBYTE Instruction 263 17.8. Monitoring for Special Conditions 264 17.9. Instruction Set 265 17.10. Collating Operations 266 17.11. Table Lookup Operations 267 17.12. Example 267 Appendix A. Summary Data 273 A.1. List of the Larger IBM Storedprogram Computers 273 A.2. Instruction Formats 275 A.3. List of Registers and Special Addresses 276 A.4. Summary of Operations and Modifiers 277 A.5. Summary of Indicators 287 Appendix B. Programming Examples 292 Notation 292 B.1. Polynomial Evaluation 295 B.2. Cuberoot Extraction 296 B.3. Matrix Multiplication 298 B.4. Conversion of Decimal Numbers to a Floatingpoint Normalized Vector 299 B.5. Editing a Typed Message 301 B.6. Transposition of a Large Bit Matrix 303 Index 305acknhfbWerner BuchholzThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.Planning a computer system: {Project Stretch}
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a computer system: {Project Stretch}",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://edthelen.org/comphist/IBM7030PlanningMcJones.pdf",
acknowledgement = acknhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floatingpoint arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detailØ on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the ndigit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisymode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up  it
merely has a very high probability of showing up 
whereas builtin significance checks can be made
slightly pessimistic, so that actual significance loss
will not be greater than indicated. On the other hand,
little extra hardware and no extra storage are required
for the noisymode approach. Furthermore, significance
loss is relatively rare, so that running a problem
twice when Significance loss is suspected does not pose
a serious problem. What is serious is the possibility
of unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixedpoint arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixedpoint arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixedpoint arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixedpoint
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixedpoint operands do
give correct significance indications, the use of other
operations and of builtin scaling loops frequently
destÙroys entirely the leadingzeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. Highspeed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Indexarithmetic Unit 21 \\
3.10. Instruction Lookahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radixconversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Indexarithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. InputOutput Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
4.3. Data Hierarchies 39 \\
4.4. Classes of Operations 40 \\
5. Choosing a Number Base 42 \\
[by W. Buchholz] \\
5.1. Introduction 42 \\
5.2. Information Content 45 \\
5.3. Arithmetic Speed 49 \\
5.4. Numerical Data 50 \\
5.5. Nonnumerical Data 51 \\
5.6. Addresses 52 \\
5.7. Transformation 53 \\
5.8. Partitioning of Memory 54 \\
5.9. Program Interpretation 56 \\
5.10. Other Number Bases 58 \\
5.11. Conclusion 58 \\
6. Character Set 60 \\
[by R. W. Bemer and W. Buchholz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Taperecording Convention 71 \\
6.15. Cardpunching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variablefieldlength Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variablefieldlength Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical SiÚgns 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radixconversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floatingpoint Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixedpoint Arithmetic 92 \\
8.2. Floatingpoint Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floatingpoint Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Roundoff Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floatingpoint Arithmetic 103 \\
8.9. Structure of Floatingpoint Data 104 \\
Floatingpoint Features of the 7030 \\
8.10. Floatingpoint Instruction Format 106 \\
8.11. Floatingpoint Data Formats 106 \\
8.12. Singular Floatingpoint Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floatingpointarithmetic Operations 114 \\
8.17. Fixedpoint Arithmetic Using Unnormalized \\
Floatingpoint Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multipleprecision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Singleaddress Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Programinterrupt System 136 \\
10.6. Components of the Programinterrupt System 137
\\
10.7. Examples of Programinterrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Recordhandling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. InputOutput Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
InputOutput and External Storage 179 \\
12.2. InputOutput Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of InputOutput Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Lookahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timingsimulation Program 230 \\
15.3. Description of the Lookahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Lookback at the Lookahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Setup Mode 258 \\
17.3. Bytesequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTEBYBYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Lookup Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Storedprogram Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cuberoot Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floatingpoint Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
êãêuOZ !#/#1+Em;‚Yy/#1#techreportfparith.bibDescloux:1962:REFJ. DesclouxRemarks on errors in first order iterative processes with floatingpoint computersUniversity of Illinois Graduate College, Digital Computer LaboratoryUrbana, IL, USA71962Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTReport / University of Illinois, Digital Computer Laboratory; no. 113 Report (University of Illinois (UrbanaChampaign campus). Digital Computer Laboratory); no. 113.Electronic digital computers.; Numerical calculations.Supported by: National Science Foundation under grant G16489. ``March 22, 1962.''acknhfbJ. DesclouxRemarks on errors in first order iterative processes with floatingpoint computers
@TechReport{Descloux:1962:REF,
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}6",
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usually implemented on the computer by means of
floatingpoint and fixedpoint numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
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author = "A. A. Grau",
title = "On a floatingpoint number representation for use with
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journal = jCACM,
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number = "3",
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abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floatingpoint and fixedpoint numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
subset of the set of real numbers. In implementation a
real problem is posed by the fact that the set of
fixedpoint numbers is not a proper subset of the set
of floatingpoint numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
addition is implemented in the machine by one of {\em
two\/} machine operations, fixedpoint addition or
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journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
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year = "1962",
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subject = "Numerical analysis; Electronic digital computers",
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}†IlV #+M!#;K;M‡ùbookfparith.bibFlores:1963:LCAI. FloresThe Logic of Computer ArithmeticpubPHpubPH:adrxii + 4931963QA76.5 .F46Thu Sep 1 10:12:51 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:12:51 ???acknjI. FloresThe Logic of Computer Arithmetic
@Book{Flores:1963:LCA,
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}Š8kY #%57=K;5O‹Karticlefparith.bibEve:1963:SAIJ. EveStarting approximation for the iterative calculation of square rootsjCOMPJ62742761963CMPJA600104620 (print), 14602067 (electronic) OR 00104620 (print), 14602067 (electronic)00104620 OR 00104620Thu Sep 15 18:37:30 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:37:30 ???The Computer Journalacknjhttp://comjnl.oxfordjournals.org/J. EveStarting approximation for the iterative calculation of square roots
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting approximation for the iterative calculation
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abstract = "The 7090 at NYU has been modified to include a
``Significance Mode'' of operation which is intended to
facilitate the identification of significant bits in
the results of floatingpoint arithmetic operations.
The manner in which floatingpoint arithmetic is
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@Article{Hamza:1991:MBD,
author = "K. M. Hamza and M. A. H. AbdulKarim",
title = "Microprocessor Based Direct Square Root Extractor",
journal = "Modelling",
volume = "34",
number = "1",
pages = "4548",
month = "????",
year = "1991",
bibdate = "Thu Sep 1 10:15:42 1994",
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@Article{Hamming:1970:DN,
author = "R. W. Hamming",
title = "On the Distribution of Numbers",
journal = jBELLSYSTTECHJ,
volume = "49",
number = "8",
pages = "16091625",
month = oct,
year = "1970",
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bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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@Article{Hamming:1965:NLB,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "2",
pages = "260261",
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CODEN = "IEECA8",
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bibdate = "/‡Y3
@Article{Hammersley:1969:NAP,
author = "P. Hammersley",
title = "Note on {Algorithm 34}: Procedures for the Basic
Arithmetical Operations in MultiLength Working",
journal = jCOMPJ,
volume = "12",
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bibdate = "Fri Sep 29 08:51:33 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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@Article{Hammer:1965:BRBa,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
journal = jTECHNOMETRICS,
volume = "7",
number = "1",
pages = "8282",
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@Article{Hammel:1965:RLC,
author = "D. Hammel",
title = "{R6554} The Logic of Computer Arithmetic",
journal = jIEEETRANSELECCOMPUT,
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¢ˆW‚V#)S=!%E%;c/ES=‰Sæbookfparith.bibMaley:1964:MDCGerald A. Maley and Edward J. SkikoModern digital computerspubPHpubPH:adrxiv + 2161964QA76.5 .M192Thu Nov 18 10:04:00 MST 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.11.18 10:04:00 MSTPrenticeHall electrical engineering seriesbinary arithmeticElectronic digital computersacknhfbGerald A. Maley and Edward J. SkikoModern digital computers
@Book{Maley:1964:MDC,
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;A=)‹articlefparith.bibLynn:1964:REMM. Stuart LynnOn the RoundOff Error in the Method of Successive OverRelaxationjMATHCOMPUT18853649jan11964MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknhfbhttp://www.ams.org/mcom/M. Stuart LynnOn the RoundOff Error in the Method of Successive OverRelaxation
@Article{Lynn:1964:REM,
author = "M. Stuart Lynn",
title = "On the RoundOff Error in the Method of Successive
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journal = jMATHCOMPUT,
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W #++}=]7E‚;_+}=articlefparith.bibLamson:1964:DADRoger C. LamsonA Division Algorithm for a Digital Differential AnalyzerjIEEETRANSELECCOMPUTEC1315455feb21964IEECA8https://doi.org/10.1109/PGEC.1964.26383803677508 OR 03677508Thu Jul 14 06:56:57 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:56:57 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038079IEEE Transactions on Electronic ComputersacknhfbRoger C. LamsonA Division Algorithm for a Digital Differential Analyzer
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author = "Roger C. Lamson",
title = "A Division Algorithm for a Digital Differential
Analyzer",
journal = jIEEETRANSELECCOMPUT,
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™snY #1'gW57E‚5;ˆ1?cˆ1'g˜Iarticlefparith.bibGoldstein:1963:SADMax GoldsteinSignificance arithmetic on a digital computerjCACM63111117mar31963CACMA2https://doi.org/10.1145/366274.36633900010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:45 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:45 MSTThe 7090 at NYU has been modified to include a ``Significance Mode'' of operation which is intended to facilitate the identification of significant bits in the results of floatingpoint arithmetic operations. The manner in which floatingpoint arithmetic is handled in this mode is discussed. Several numerical experiments using this mode are described and comparisons are made with the ordinary ``normalized mode.'' Examples include power series evaluation, linear equations solution, determinant evaluation and matrix inversion.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79The 7090 at NYU has been modified to include a ``Significance Mode'' of operation which is intended to facilitate the identification of significant bits in the results of floatingpoint arithmetic operations. The manner in which floatingpoint arithmetic is handled in this mode is discussed. Several numerical experiments using this mode are described and comparisons are made with the ordinary ``normalized mode.'' Examples include power series evaluation, linear equations solution, determinant evaluation and matrix inversion.Max GoldsteinSignificance arithmetic on a digital computer
@Article{Goldstein:1963:SAD,
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title = "Significance arithmetic on a digital computer",
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abstract = "The 7090 at NYU has been modified to include a
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experiments using this mode are described and
comparisons are made with the ordinary ``normalized
mode.'' Examples include power series evaluation,
linear equations solution, determinant evaluation and
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acknowledgement = acknhfb,
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ï ïŒpY #93=]7E‚;_3earticlefparith.bibKrishnamurthy:1963:CMDE. V. KrishnamurthyOn Computer Multiplication and Division Using Binary LogarithmsjIEEETRANSELECCOMPUTEC123319320jun61963IEECA8https://doi.org/10.1109/PGEC.1963.26357203677508 OR 03677508Thu Jul 14 08:10:39 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:39 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037874IEEE Transactions on Electronic ComputersacknhfbE. V. KrishnamurthyOn Computer Multiplication and Division Using Binary Logarithms
@Article{Krishnamurthy:1963:CMD,
author = "E. V. Krishnamurthy",
title = "On Computer Multiplication and Division Using Binary
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}‰\oY #)+5=S;=+AŠ+articlefparith.bibKnuth:1963:LEEDonald E. KnuthLetter to the Editor: Evaluation of polynomials by computerjCACM625151feb21963CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)Tue Dec 26 16:31:38 1995http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.26 16:31:38 ???See cite Knuth:1962:EPC.acknhfbDonald E. KnuthSee \cite{Knuth:1962:EPC}.Letter to the {Editor}: {Evaluation} of polynomials by computer
@Article{Knuth:1963:LEE,
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title = "Letter to the {Editor}: {Evaluation} of polynomials by
computer",
journal = jCACM,
volume = "6",
number = "2",
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author = "H. Makino and H. Suzuki and H. Morinaka and Y. Nakase
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year = "1996",
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Square Roots",
journal = jIEEETRANSCOMPUT,
volume = "C20",
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pages = "16171618",
month = dec,
year = "1971",
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author = "J. C. Majithia and R. Kitai",
title = "An Iterative Array for Multiplication of Signed Binary
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volume = "C20",
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pages = "214216",
month = feb,
year = "1971",
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author = "J. C. Majithia",
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author = "J. C. Majithia and D. Levan",
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volume = "C21",
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ò ÚòdrY #+%=]7E‚U;ƒ__%‘iarticlefparith.bibLehmer:1963:RDOD. H. LehmerR6317 Division and Overflow Detection in Residue Number SystemsjIEEETRANSELECCOMPUTEC1213637feb21963IEECA8https://doi.org/10.1109/PGEC.1963.26349303677508 OR 03677508Thu Jul 14 08:10:36 MDT 2011http://ieeexplore.ieee.org/; http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:36 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemacknhfbD. H. Lehmer{R6317} Division and Overflow Detection in Residue Number Systems
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g gsY#1Y#'K57E‚#;#C%Y#Ž3 articlefparith.bibLindamood:1963:MCOGeorge E. Lindamood and George ShapiroMagnitude Comparison and Overflow Detection in Modular Arithmetic ComputersjSIAMREVIEW543423501963SIREADhttps://doi.org/10.1137/100509500361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 00361445Thu Mar 27 09:05:07 MDT 2014http://epubs.siam.org/toc/siread/5/4; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:05:07 MDTSIAM Reviewacknhfbhttp://epubs.siam.org/sirevOctober 1963George E. Lindamood and George ShapiroMagnitude Comparison and Overflow Detection in Modular Arithmetic Computers
@Article{Lindamood:1963:MCO,
author = "George E. Lindamood and George Shapiro",
title = "Magnitude Comparison and Overflow Detection in Modular
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
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abstract = "A particular set of unnormalized arithmetic operations
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acknowledgement = acknhfb,
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ÓÓœ)tZ#3Qw=17Eƒ);‡a_M!‡aQw›k articlefparith.bibMetropolis:1963:BOUN. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic SystemjIEEETRANSELECCOMPUTEC126896904dec121963IEECA8https://doi.org/10.1109/PGEC.1963.263592; https://doi.org/10.1109/PGEC.1963.26359303677508 OR 03677508Thu Jul 14 08:10:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037A particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.IEEE Transactions on Electronic ComputersCited in cite Sterbenz:1974:FPC.0124.07910acknhfbA particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.N. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic System
@Article{Metropolis:1963:BOU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Basic Operations in an Unnormalized Arithmetic
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ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multiprecision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = acknhfb,
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qœ¡²
q†)ŒS
@Book{Stone:1975:ICA,
editor = "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
and Samuel H. Fuller and others",
title = "Introduction to computer architecture",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
pages = "x + 565",
year = "1975",
ISBN = "0574184058",
ISBN13 = "9780574184054",
LCCN = "QA76.5 .I7; QA76.9.A73 I57; QA76.5 .I63; QA76.9.A73