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)+?indexsqlite_autoindex_strtab_1strtab’! ûöñìæàÚÔÎÈÂ¼¶°ª¤ž˜’art F. Oberman, e-mail: path =stuart.oberman@amd.com=@String{ack-sfo = "Stuart F. Oberman,
e-mail: \path=stuart.oberman@amd.com="}„ ƒ#…ack-rfbRonald F. Boisvert, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, Tel: +1 301 975 3812, e-mail: path =boisvert@cam.nist.gov=@String{ack-rfb = "Ronald F. Boisvert,
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National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA,
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Tera Computer Company,
2815 Eastlake East,
Seattle, WA 98102,
USA,
Tel: +1 206 325-0800,
e-mail: \path|preston@tera.com|"}‚-Oƒ
ack-njNorbert Juffa, 2445 Mission College Blvd. Santa Clara, CA 95054 USA email: path =norbert@iit.com=@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.
Santa Clara, CA 95054
USA
email: \path=norbert@iit.com="}†v…ˆcack-nhfbNelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: path |beebe@math.utah.edu|, path |beebe@acm.org|, path |beebe@computer.org| (Internet), URL: path |http://www.math.utah.edu/~beebe/|@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}ƒq‚W…ack-mfcMichael F. Cowlishaw, IBM UK (MP5), PO Box 31, Birmingham Road, Warwick, CV34 5JL, UK, e-mail: path |mfc@uk.ibm.com|, URL: path |http://www2.hursley.ibm.com/decimal|@String{ack-mfc = "Michael F. Cowlishaw,
IBM UK (MP5),
PO Box 31,
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Warwick, CV34 5JL,
UK,
e-mail: \path|mfc@uk.ibm.com|,
URL: \path|http://www2.hursley.ibm.com/decimal|"}„ƒ…ack-krKarin Remington, National Institute of Standards and Technology, Building 820, Room 365, Gaithersburg, MD 20899, USA, Tel: +1 301 975-5119, FAX: +1 301 990-4127, e-mail: path |karin@cam.nist.gov|@String{ack-kr = "Karin Remington,
National Institute of Standards and Technology,
Building 820, Room 365,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975-5119,
FAX: +1 301 990-4127,
e-mail: \path|karin@cam.nist.gov|"}ƒ‚„ack-jrJon Rokne, Department of Computer Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada@String{ack-jr = "Jon Rokne,
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Tera Computer Company,
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2445 Mission College Blvd.
Santa Clara, CA 95054
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University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
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\path|beebe@acm.org|,
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author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
remark = "Thanks for Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
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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 Unicode-compatible fonts to represent the additional digits needed by the system.Weights and measures; Numeration; base-16 arithmetic; hexadecimal arithmeticack-nhfbJohan Vilhelm Nystrom (1824--1885)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
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acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
subject = "Weights and measures; Numeration; base-16 arithmetic;
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remark = "Thanks for Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicode-compatible fonts to represent the additional
digits needed by the system.",
}
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K",
abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
logarithmic tables, and noticing how much faster the
first pages wear out than the last ones. The first
significant figure is oftener 1 than any other digit,
and the frequency diminishes up to 9.",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Mathematics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 40: ``The law of probability of the occurrence
of numbers is such that all mantissas of their
logarithms are equally probable.''",
}
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· ·m“MŽK§[[#-I3!W57C‚#;IIqarticlefparith.bibBeuchat:2008:AGMJ.-L. Beuchat and J.-M. MullerAutomatic Generation of Modular Multipliers for FPGA Applicationsj-IEEE-TRANS-COMPUT57121600--1613dec122008ITCOB4http://dx.doi.org/10.1109/TC.2008.1020018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)0018-9340 OR 00189340Mon Jul 4 12:17:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib2011.07.04 12:17:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4564441IEEE Transactions on Computersack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12J.-L. Beuchat and J.-M. MullerAutomatic Generation of Modular Multipliers for {FPGA} Applications
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keywords = "integer overflow detection; Java",
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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]187--22111apr41936Wed 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.Germanack-nhfbGerman patent application Z23624.K. ZuseReprinted in \cite[\S 4.1]{Randell:1982:ODC}.{Verfahren zur selbstt{\"a}tigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen}. ({German}) [{Procedure} for automatic execution of calculations by calculating machines]
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author = "K. Zuse",
title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
[{Procedure} for automatic execution of calculations by
calculating machines]",
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language = "German",
}‡iU #-)117=m;_W)g1ˆA#articlefparith.bibPhillips:1936:BCE. W. PhillipsBinary calculationj-J-INST-ACTUARIES67187--22119360020-2681 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 Actuariesack-nhfbE. W. PhillipsReprinted in \cite[\S 7.1]{Randell:1982:ODC}.Binary calculation
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o
o‹Y #+%%357E
;G%%Œarticlefparith.bibEscott:1937:QDNE. B. EscottQuestions, Discussions, and Notes: Rapid Method for Extracting a Square Rootj-AMER-MATH-MONTHLY4410644--646dec121937AMMYAE0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 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 Monthlyack-nhfbhttp://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 = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}rith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}
::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 twenty-one and published when he was twenty-two, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 59--61 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 62--68, ``A Factor Table Machine'', describe a machine that will print a table of factors and primes of all the integers from 1 to 100,000,000. Shannon notes on page 68: ``As to the practicality of such a device, it might be said that J. P. Kulik spent 20 years in constructing a table of primes up to 100,000,000 and when finished it was found to contain so many errors that it was not worth publishing. The machine described here could probably be made to handle 5 numbers per second so that the table would require only about 2 months to construct.''ack-nhfbApril 30, 1916--February 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 = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}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 law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
]XÀ]‡=Ž{
@Article{Anonymous:1977:CAF,
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volume = "C-26",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674892",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}˜‡"ŽG
@Article{Anonymous:1898:OFA,
author = "Anonymous",
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journal = j-SCI-AMER,
volume = "79",
number = "17",
pages = "265--266",
day = "22",
month = oct,
year = "1898",
CODEN = "SCAMAC",
DOI = "http://dx.doi.org/10.1038/scientificamerican10221898-265",
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bibdate = "Wed May 22 19:08:57 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v79/n17/pdf/scientificamerican10221898-265.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
‡Ž/
@Article{Anonymous:1893:IDb,
author = "Anonymous",
title = "The Instantaneous Divider",
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volume = "68",
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pages = "325--325",
day = "27",
month = may,
year = "1893",
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ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:04:00 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v68/n21/pdf/scientificamerican05271893-325a.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}‡&ŽO
@Article{Anonymous:1879:TRA,
author = "Anonymous",
title = "Three Rules for Abbreviating Multiplication",
journal = j-SCI-AMER,
volume = "41",
number = "12",
pages = "184--184",
day = "20",
month = sep,
year = "1879",
CODEN = "SCAMAC",
DOI = "http://dx.doi.org/10.1038/scientificamerican09201879-184",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}&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), 573--585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] containing an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography cite Hurlimann:2006:BLB cites 325 publications about Benford's Law.ack-nhfbhttp://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 law---hence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.Frank BenfordThe Law of Anomalous Numbers
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
qqÓ[ #-'E557=m;CŸ]WsŽEgŸe'EÌSarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous Numbersj-PROC-AMER-PHIL-SOC784551--572mar31938PAPCAA0003-049X (print), 2326-9243 (electronic) OR 0003049X (print), 23269243 (electronic)0003-049X 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=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-GIt has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. 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 Numberspub-OXFORDpub-OXFORD:adrxvi + 4031938QA241 .H28Fri Nov 30 06:49:15 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.30 06:49:15 ???ack-nhfbG. 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 = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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}hY #3'ƒ7-G'=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]Gauthier-VillarsFaculte des Sciences de ParisParis, France551--5721938Wed 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.Frenchack-nhfbL. CouffignalExtracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.Sur l'analyse m{\'e}canique. Application aux machines {\`a} calculer et aux calculs de la m{\'e}canique c{\'e}leste. ({French}) [{On} mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
} http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}!
ùù”!Y #-/sA7=]; ‡}/s–Uarticlefparith.bibShannon:1938:SARClaude E. ShannonA Symbolic Analysis of Relay and Switching Circuitsj-TRANS-AMER-INST-ELEC-ENG57713--723dec121938TAEEA50096-3860 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.''ack-nhfbhttp://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 = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
¼ ¼ŠW#X ##
)OE‚#;S]Œarticlefparith.bibK:1939:BRBdM. G. K.Book Review: booktitle Duodecimal Arithmetic, by George S. Terryj-J-R-STAT-SOC1022299--3001939http://dx.doi.org/10.2307/2980013Sat Jan 24 11:18:08 MST 2015http://www.jstor.org/stable/i349540; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib2015.01.24 11:18:08 MSThttp://www.jstor.org/stable/2980013Journal of the Royal Statistical Societyack-nhfbM. G. K.Book Review: {{\booktitle{Duodecimal Arithmetic}}, by George S. Terry}
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author = "M. G. K.",
title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "http://dx.doi.org/10.2307/2980013",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
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fjournal = "Journal of the Royal Statistical Society",
}g"Y#)Q57Eƒ;QoQarticlefparith.bibJager:1939:AADRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of Robert Jager (London, 1651)j-ISIS31125--31nov111939ISISA40021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)0021-1753 OR 00211753Tue Jul 30 21:26:49 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302217; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1930.bib2013.07.30 21:26:49 MDThttp://www.jstor.org/stable/226014Isisack-nhfbhttp://www.jstor.org/page/journal/isis/about.htmlRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
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author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
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volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
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ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
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URL = "http://www.jstor.org/stable/226014",
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title = "Analytical Calculation of the Maximum Error for a
Family of Truncated Multipliers Providing Minimum Mean
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author = "J. V. Garwick",
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journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
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author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
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pages = "87--88",
month = jun,
year = "1961",
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month = nov,
year = "1932",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
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}k
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, USA299--3001940Wed 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.ack-nhfbG. 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 = ack-nhfb,
}‰7%X #%5=m;‚#‚+5ˆ}miscfparith.bibBush:1940:AMV. BushArithmetical Machine299--3001940Wed 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.ack-nhfbVannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 1939--1940V. 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, 1939--1940",
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note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
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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, USA299--300aug81940Wed 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.ack-nhfbJ. 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 = ack-nhfb,
}"1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}'ne-of-a-kind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 1930--1966'', (found in http://discover.lib.umn.edu/): CWB as an attorney for the group retained by Honeywell in the Honeywell v. Sperry Rand ENIAC trial. The ABC had a 50-bit word.ack-nhfb1918--1963Clifford 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 = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}
%~
%‰9’s
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Journal of Systems Architecture",
pagecount = "15",
}¢ˆ(Q
@Article{Weinstein:1969:RNF,
author = "C. Weinstein",
title = "Roundoff noise in floating point fast {Fourier}
transform computation",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "17",
number = "3",
pages = "209--215",
month = sep,
year = "1969",
CODEN = "ITADAS",
ISSN = "0018-9278",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsoà‰B“
@Article{Weinstein:1969:CRN,
author = "C. Weinstein and A. V. Oppenheim",
title = "A comparison of roundoff noise in floating point and
fixed point digital filter realizations",
journal = j-PROC-IEEE,
volume = "57",
number = "6",
pages = "1181--1183",
month = jun,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
Þ‡Ž
@Article{Weinstein:1969:CCR,
author = "C. Weinstein and A. V. Oppenheim",
title = "Correction to {``A comparison of roundoff noise in
floating point and fixed point digital filter
realizations''}",
journal = j-PROC-IEEE,
volume = "57",
number = "8",
pages = "1466--1466",
month = aug,
year = "1969",
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ISSN = "0018-9219 (print), 1558-2256 (electronic)",
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bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
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fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}Þ
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@TechReport{Rajchman:1942:REP,
author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
title = "Report on Electronic Predictors for Anti-Aircraft Fire
Control",
institution = "Research Laboratories, R. C. A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
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year = "1942",
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@TechReport{Mauchly:1942:UHS,
author = "J. W. Mauchly",
title = "The use of high speed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
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note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
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@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
0
’0”_,Y#/IuQ57=m;
„ysW„yIu”?articlefparith.bibGoudsmit:1944:SFNS. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical Tablesj-NATURE1543921800--80123dec121944NATUAShttp://dx.doi.org/10.1038/154800a00028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 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 Lawack-nhfbhttp://www.nature.com/nature/archive/A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.S. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical Tables
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}Šk+Y #//357E
;G/‹marticlefparith.bibCrawford:1943:DNSW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of Cosinesj-AMER-MATH-MONTHLY503190--191mar31943AMMYAE0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 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 Monthlyack-nhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of Cosines
@Article{Crawford:1943:DNS,
author = "W. S. H. Crawford",
title = "Discussions and Notes: Square Roots from a Table of
Cosines",
journal = j-AMER-MATH-MONTHLY,
volume = "50",
number = "3",
pages = "190--191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
} "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
},
B ŒBŽG.W !#3-UA=‚ ;_‚u-gY‘utechreportfparith.bibvonNeumann:1945:FDRJohn von NeumannFirst Draft of a Report on the EDVACUniversity of Pennsylvania52--5330jun61945Mon 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, stored-program, general purpose, digital architecture upon which 99.99% of all computers today are based.ack-nhfbJohn von NeumannReprinted in \cite[\S 8.2]{Randell:1982:ODC}.First Draft of a Report on the {EDVAC}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}Œq-Y#)GQ57=m;
sWGŽ'articlefparith.bibFurry:1945:DNDW. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant Figuresj-NATURE15552--5313jan11945NATUAShttp://dx.doi.org/10.1038/155052a00028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 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 Lawack-nhfbhttp://www.nature.com/nature/archive/W. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant Figures
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "??",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}n \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}.
xix‡n1U #+!917=m;_=!g9ˆ[articlefparith.bibCesareo:1946:RIO. CesareoThe Relay Interpolatorj-BELL-LABS-RECORD23457--4601946BLRCAB0005-8564 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 Recordack-nhfbO. CesareoReprinted in \cite[\S 6.2]{Randell:1982:ODC}.The Relay Interpolator
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = j-BELL-LABS-RECORD,
volume = "23",
number = "??",
pages = "457--460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Bell Laboratories Record",
}«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 instrumentinst-INST-ADV-STUDYinst-INST-ADV-STUDY: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.~221--259]Swartzlander:1976:CDD, cite [ 8.3]Randell:1982:ODC, and cite [pp.~97--146]Aspray:1987:PJNDiscusses floating-point versus fixed-point computation, and concludes that floating-point is probably not justifiable. They wrote:par ``There appear to be two major purposes in a `floating' decimal point system both of which arise from the fact that the number of digits in a word is a constant fixed by design considerations for each particular machine. The first of these purposes is to retain in a sum or product as many significant digits as possible and the second of these is to free the human operator from the burden of estimating and inserting into a problem `scale factors' --- multipl8‰m/V#)Ee%E7=m;_EgiŠAarticlefparith.bibAiken:1946:ASCH. H. Aiken and G. M. HopperThe Automatic Sequence Controlled Calculatorj-ELECTR-ENG65384--391, 449--454, 522--5281946ELENAC0095-9197 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)ack-nhfbH. 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 = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
}p://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97--146]{Aspray:1987:PJN}",
acknowledgement = ack-nhfb,
remark = "Discusses floating-point versus fixed-point
computation, and concludes that floating-point is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors' --- multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}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.''ack-nhfbArthur W. Burks and Herman H. Goldstine and John von NeumannReport to the U.S. Army Ordnance Department. Reprinted in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S 8.3]{Randell:1982:ODC}, and \cite[pp.~97--146]{Aspray:1987:PJN}Preliminary discussion of the logical design of an electronic computing instrument
@TechReport{Burks:1946:PDL,
author = "Arthur W. Burks and Herman H. Goldstine and John von
Neumann",
title = "Preliminary discussion of the logical design of an
electronic computing instrument",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "42",
day = "28",
month = jun,
year = "1946",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97--146]{Aspray:1987:PJN}",
acknowledgement = ack-nhfb,
remark = "Discusses floating-point versus fixed-point
computation, and concludes that floating-point is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors' --- multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}
!Ã!‹3W#1S}K7E
;_o=SgŒarticlefparith.bibGoldstine:1946:ENIH. H. Goldstine and Adele GoldstineThe Electronic Numerical Integrator and Computer (ENIAC)j-MATH-TABLES-OTHER-AIDS-COMPUT21597--110jul71946MTTCAS0891-6837 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 Computationack-nhfbhttp://www.ams.org/mcom/H. H. Goldstine and Adele GoldstineReprinted in \cite[\S 7.7]{Randell:1982:ODC}.The {Electronic Numerical Integrator and Computer (ENIAC)}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "97--110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
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@TechReport{Dreyer:1946:REM,
author = "H.-J. Dreyer and A. Walther",
title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 1939--1945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
Hochschule",
address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
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author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument",
type = "Technical report",
number = "1",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
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}<
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keywords = "Computer arithmetic; Computer security; Floating-point
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author = "Y. L. Luke",
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bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
wrongisbn = "0-12-459940-6",
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@Book{Maley:1964:MDC,
author = "Gerald A. Maley and Edward J. Skiko",
title = "Modern digital computers",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 216",
year = "1964",
LCCN = "QA76.5 .M192",
bibdate = "Thu Nov 18 10:04:00 MST 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Prentice-Hall electrical engineering series",
acknowledgement = ack-nhfb,
keywords = "binary arithmetic",
subject = "Electronic digital computers",
}
ÐÐ”-HY #-+M-S57m…{Co…{+Q“Yarticlefparith.bibShirley:1951:BNBJohn W. ShirleyBinary Numeration before Leibnizj-AMER-J-PHYSICS198452--4541951AJPIAShttp://dx.doi.org/10.1119/1.19330420002-9505 (print), 1943-2909 (electronic) OR 00029505 (print), 19432909 (electronic)0002-9505 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 (1560--1621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.American Journal of Physicsack-nhfbhttp://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 (1560--1621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.John W. ShirleyBinary Numeration before {Leibniz}
@Article{Shirley:1951:BNB,
author = "John W. Shirley",
title = "Binary Numeration before {Leibniz}",
journal = j-AMER-J-PHYSICS,
volume = "19",
number = "8",
pages = "452--454",
year = "1951",
CODEN = "AJPIAS",
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URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (1560--1621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
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}pub-ACM,
address = pub-ACM:adr,
pages = "101--105",
year = "1952",
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bookpages = "vi + 114",
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
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}I
ˆfJU#)]Y/77=m;e]Y‰earticlefparith.bibDavis:1952:ARSK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken Digitsj-J-ACOUST-SOC-AM246637--642nov111952JASMAN0001-4966 OR 000149660001-4966 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 Americaack-mfcK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken Digits
@Article{Davis:1952:ARS,
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#_=m;‚'ƒ+inproceedingsfparith.bibAndrews:1952:RBLE. G. AndrewsJ. C. McPhersonProceedings of the AIEE-IRE '51: Papers and discussions presented at the December 10--12, 1951, joint AIEE-IRE computer conference, Philadelphia, PA: Review of electronic digital computersA review of the Bell Laboratories' digital computer developmentspub-ACMpub-ACM:adr101--1051952http://dx.doi.org/10.1145/1434770.1434787Fri Dec 03 09:17:58 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.12.03 09:17:58 ???Bell Laboratories Model 1--5 relay computers; complex fixed-point decimal arithmetic; complex floating-point decimal arithmeticack-nhfbvi + 114E. G. AndrewsProceedings of the AIEE-IRE '51: Papers and discussions presented at the December 10--12, 1951, joint AIEE-IRE computer conference, Philadelphia, PA: Review of electronic digital 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 AIEE-IRE '51: Papers and
discussions presented at the December 10--12, 1951,
joint AIEE-IRE computer conference, Philadelphia, PA:
Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
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address = pub-ACM:adr,
pages = "101--105",
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DOI = "http://dx.doi.org/10.1145/1434770.1434787",
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bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bookpages = "vi + 114",
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
decimal arithmetic",
}
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fjournal = "IEEE Transactions on Electronic Computers",
}:†hQ
@Article{Metze:1962:CBD,
author = "Gernot Metze",
title = "A Class of Binary Divisions Yielding Minimally
Represented Quotients",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "6",
pages = "761--764",
month = dec,
year = "1962",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460",
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fjournal = "IRE Transactions on Electronic Computers",
}Ý‰3’g
@Article{Metropolis:1980:SIN,
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@Article{Metropolis:1977:SAP,
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pages = "77--81",
year = "1977",
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ISSN = "0886-9561",
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MRclass = "65G05 (10A30 65C10)",
MRnumber = "MR0458846 (56 \#17046)",
MRreviewer = "Arten?‹–1
@Article{Metropolis:1973:SAC,
author = "N. Metropolis and Gian-Carlo Rota and S. Tanny",
title = "Significance arithmetic: the carrying algorithm",
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volume = "14",
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month = may,
year = "1973",
CODEN = "JCBTA7",
ISSN = "0097-3165",
ISSN-L = "0097-3165",
MRclass = "10A30 (02E10)",
MRnumber = "MR0321857 (48 \#222)",
MRreviewer = "R. Læ
*
g¦*ŠyMW'#-AQga/=m;_AYgkŠIinproceedingsfparith.bibSheldon:1952:ICPJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint AIEE--IRE Computer Confer ence. 10--12 December 1951The IBM card-programmed electronic calculatorAmerican Institute of Electrical EngineersNew York, NY, USA30--361952Wed Oct 13 11:28:45 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:28:45 ???Reprinted in cite [ 5.4]Randell:1982:ODC.ack-nhfbJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint {AIEE--IRE} Computer Confer ence. {10--12 December 1951}Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.The {IBM} card-programmed electronic calculator
@InProceedings{Sheldon:1952:ICP,
author = "J. W. Sheldon and L. Tatum",
booktitle = "Review of Electronic Digital Computers. Joint
{AIEE--IRE} Computer Confer ence. {10--12 December
1951}",
title = "The {IBM} card-programmed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "30--36",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}‰>LW#-EQQ=a;EQŠearticlefparith.bibMorrill:1952:SEMC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplierj-TRANS-IRE-PROF-GROUP-ELEC-COMPUTEC-152--59dec121952Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic Computersack-nhfbC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplier
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-1",
number = "??",
pages = "52--59",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = ack-nhfb,
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}‹KV #1-/!O77E‚#;SGc-/articlefparith.bibMichaelson:1952:BAR. L. MichaelsonBinary Arithmeticj-INC-STAT3135--40feb21952http://dx.doi.org/10.2307/29865911466-9404 OR 146694041466-9404 OR 14669404Thu Jan 22 18:10:18 MST 2015http://www.jstor.org/stable/i349863; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib2015.01.22 18:10:18 MSThttp://www.jstor.org/stable/2986591The Incorporated Statisticianack-nhfbhttp://www.jstor.org/journals/14669404.htmlR. L. MichaelsonBinary Arithmetic
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
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volume = "3",
number = "1",
pages = "35--40",
month = feb,
year = "1952",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2986591",
ISSN = "1466-9404",
ISSN-L = "1466-9404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib",
URL = "http://www.jstor.org/stable/2986591",
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fjournal = "The Incorporated Statistician",
journal-URL = "http://www.jstor.org/journals/14669404.html",
}
:â:™%OY #+%I57=m;'‰1e‰%M—Marticlefparith.bibBackus:1954:ISSJ. W. BackusThe IBM 701 Speedcoding Systemj-J-ACM114--6jan11954JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdfThe IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a three-address floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and built-in checking.Journal of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401The IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a three-address floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and built-in checking.J. W. BackusThe {IBM 701 Speedcoding} System
@Article{Backus:1954:ISS,
author = "J. W. Backus",
title = "The {IBM 701 Speedcoding} System",
journal = j-J-ACM,
volume = "1",
number = "1",
pages = "4--6",
month = jan,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
three-address floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
built-in checking.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
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}†NW #%+#=m;/†7bookfparith.bibIBM:1953:POTIBM CorporationPrinciples of Operation: Type 701 and Associated Equipmentpub-IBMpub-IBM:adr1031953Wed Sep 14 23:17:49 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.14 23:17:49 ???ack-nhfb{IBM Corporation}Principles of Operation: Type 701 and Associated Equipment
@Book{IBM:1953:POT,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
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publisher = pub-IBM,
address = pub-IBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
three-address floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
built-in checking.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}Ond coding manual --- Datatron
operation manual --- Central computer handbook ---
Paper tape system handbook --- Card converter Model 500
handbook --- Magnetic tape system handbook ---
Cardatron system handbook --- Model 560 DATAFILE
handbook --- Control console and consolette handbook
--- Floating point control unit handbook --- External
switching unit handbook --- Tape preparation unit
handbook.",
}P
W²WŒXQX#-?WQ=a;‚[?[ŽEarticlefparith.bibFreeman:1954:TSAH. Freeman and E. ParsonsTime-Sharing Analog Multiplier (TSAM)j-TRANS-IRE-PROF-GROUP-ELEC-COMPUTEC-3111--17mar31954Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic ComputersCited in US Patent 3,043,516 (10 July 1962): Time Summing Device for Division, Multiplication, Root Taking and Interpolation, by Harold W. Abbott and Vernon P. Mathis.ack-nhfbH. Freeman and E. ParsonsTime-Sharing Analog Multiplier ({TSAM})
@Article{Freeman:1954:TSA,
author = "H. Freeman and E. Parsons",
title = "Time-Sharing Analog Multiplier ({TSAM})",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-3",
number = "1",
pages = "11--17",
month = mar,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
remark = "Cited in US Patent 3,043,516 (10 July 1962): Time
Summing Device for Division, Multiplication, Root
Taking and Interpolation, by Harold W. Abbott and
Vernon P. Mathis.",
}ŽKPV #/Q1%/Em;-3†WU-1
manualfparith.bibBurroughs:1954:DHBurroughs Corporation. ElectroDataDatatron handbooksThe DivisionPasadena, CA, USA4--61954Sat 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.ack-nhfb{Burroughs Corporation. ElectroData}12 volumes in 1.Datatron handbooks
@Manual{Burroughs:1954:DH,
author = "{Burroughs Corporation. ElectroData}",
title = "Datatron handbooks",
organization = "The Division",
address = "Pasadena, CA, USA",
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1.",
acknowledgement = ack-nhfb,
keywords = "Datatron (Computer)",
remark = "Datatron programming and coding manual --- Datatron
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Paper tape system handbook --- Card converter Model 500
handbook --- Magnetic tape system handbook ---
Cardatron system handbook --- Model 560 DATAFILE
handbook --- Control console and consolette handbook
--- Floating point control unit handbook --- External
switching unit handbook --- Tape preparation unit
handbook.",
}
ÑGÑ‰;TV#)g[;7=a;]g[Š'articlefparith.bibMayer:1954:ODFM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback dividerj-IRE-TRANS-ELEC-COMPUTEC-3117--20mar31954IRELAO0367-9950 OR 03679950Sun Jul 17 09:52:58 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:52:58 ???IRE Transactions on Electronic Computersack-nhfbM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback divider
@Article{Mayer:1954:ODF,
author = "M. A. Mayer and B. M. Gordon and R. N. Nicola",
title = "An operational digital feedback divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
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}‰5SW#+AQQ=a;AQŠ]articlefparith.bibKovach:1954:AMUL. D. Kovach and W. ComleyAn Analog Multiplier Using Thyritej-TRANS-IRE-PROF-GROUP-ELEC-COMPUTEC-3242--45jun61954Sun Jul 17 09:57:13 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:57:13 ???Transactions of the I.R.E. Professional Group on Electronic Computersack-nhfbL. D. Kovach and W. ComleyAn Analog Multiplier Using Thyrite
@Article{Kovach:1954:AMU,
author = "L. D. Kovach and W. Comley",
title = "An Analog Multiplier Using Thyrite",
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CODEN = "????",
ISSN = "????",
bibdate = "Sun Jul 17 09:57:13 2011",
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number = "3",
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month = sep,
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ÓÃÓ¢`X #-)?57=m;Ž1OqeŽ)Gžgarticlefparith.bibPerkins:1956:EPCRobert PerkinsEASIAC, A Pseudo-Computerj-J-ACM3265--72apr41956JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Fri Nov 04 23:46:26 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 23:46:26 ???One of the primary functions of the MIDAC installation at the University of Michigan is the instru^ŠJ_W #//A;a7Ea;]/AŒ articlefparith.bibLilamand:1956:TDMM. Lejet LilamandA Time-Division Multiplierj-IRE-TRANS-ELEC-COMPUTEC-5126--34mar31956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.52197890367-9950 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 Computersack-nhfbM. Lejet LilamandA Time-Division Multiplier
@Article{Lilamand:1956:TDM,
author = "M. Lejet Lilamand",
title = "A Time-Division Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "1",
pages = "26--34",
month = mar,
year = "1956",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1956.5219789",
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fjournal = "IRE Transactions on Electronic Computers",
}‰m^W #3AQ+3E%;u1AQŠ}bookfparith.bibHildebrand:1956:INAFrancis Begnaud HildebrandIntroduction to numerical analysispub-MCGRAW-HILLpub-MCGRAW-HILL: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 analysisack-nhfbFrancis Begnaud HildebrandIntroduction to numerical analysis
@Book{Hildebrand:1956:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "511",
year = "1956",
LCCN = "QA300 .H5",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also second edition
\cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
subject = "Numerical analysis",
}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 man-months of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translation-interpretation
program in MIDAC.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
remark = "Early example of a decimal floating-point machine.",
}`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 man-months of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translation-interpretation program in MIDAC.Journal of the ACMdecimal floating-point arithmeticEarly example of a decimal floating-point machine.ack-nhfbhttp://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 man-months of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translation-interpretation program in MIDAC.Robert Perkins{EASIAC}, {A} Pseudo-Computer
@Article{Perkins:1956:EPC,
author = "Robert Perkins",
title = "{EASIAC}, {A} Pseudo-Computer",
journal = j-J-ACM,
volume = "3",
number = "2",
pages = "65--72",
month = apr,
year = "1956",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 23:46:26 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three man-months of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translation-interpretation
program in MIDAC.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
remark = "Early example of a decimal floating-point machine.",
}
F`FŒcY#+k;a7Ea;]k%articlefparith.bibSydnor:1956:AMSR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulatorj-IRE-TRANS-ELEC-COMPUTEC-5282--85jun61956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.52198040367-9950 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 Computersack-nhfbR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulator
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author = "R. L. Sydnor and T. R. O'Meara and J. Strathman",
title = "Analog Multipliers and Squarers Using a Multigrid
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number = "2",
pages = "82--85",
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CODEN = "IRELAO",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
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author = "Paolo Ercoli and Roberto Vacca",
title = "Errors Due to Overflow in Arithmetic Operations
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volume = "4",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "floating-point arithmetic; overflow",
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author = "A. Weinberger and J. L. Smith",
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ˆJŠ;gX #+%‚=m;s%‚Šwarticlefparith.bibHerzel:1957:SDDAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. (Italian) [On the frequency of initial digits of statistical numbers]Atti dell XV e XVII Riunione, Societa Italiana di Statistica??--??1957Sun Sep 18 12:00:07 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:00:07 ???Benford's Law; Law of Anomalous Numbers; Zipf's LawItalianack-nhfbAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]
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author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "Atti dell XV e XVII Riunione, Societa Italiana di
Statistica",
volume = "??",
number = "??",
pages = "??--??",
year = "1957",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}ŠufW #'%‚C=m;cs%c‚‹%articlefparith.bibGini:1957:SFDCorrado GiniSulla frequenza delle cifre iniziali dei numeri osservati. (Italian) [On the frequency of initial digits of observed numbers]Bull. Inst. Internat. Stat.3557--761957Sun Sep 18 11:54:25 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:54:25 ???29th session, 2nd delivery, Rio de Janerio.Benford's Law; Law of Anomalous Numbers; Zipf's LawItalianack-nhfbCorrado Gini29th session, 2nd delivery, Rio de Janerio.Sulla frequenza delle cifre iniziali dei numeri osservati. (Italian) [{On} the frequency of initial digits of observed numbers]
@Article{Gini:1957:SFD,
author = "Corrado Gini",
title = "Sulla frequenza delle cifre iniziali dei numeri
osservati. (Italian) [{On} the frequency of initial
digits of observed numbers]",
journal = "Bull. Inst. Internat. Stat.",
volume = "35",
number = "??",
pages = "57--76",
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note = "29th session, 2nd delivery, Rio de Janerio.",
URL = "",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
ðŠ]iW #//K;a7Ea;]/KŒarticlefparith.bibKalbfell:1957:EAMDavid C. KalbfellAn Electronic Analog Multiplierj-IRE-TRANS-ELEC-COMPUTEC-62100--103jun61957IRELAOhttp://dx.doi.org/10.1109/TEC.1957.52215790367-9950 OR 03679950Thu Jun 30 16:07:27 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:27 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579IRE Transactions on Electronic Computersack-nhfbDavid C. KalbfellAn Electronic Analog Multiplier
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author = "David C. Kalbfell",
title = "An Electronic Analog Multiplier",
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number = "2",
pages = "100--103",
month = jun,
year = "1957",
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DOI = "http://dx.doi.org/10.1109/TEC.1957.5221579",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
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author = "R. M. Howe and E. G. Gilbert",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
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fjournal = "IRE Transactions on Electronic Computers",
}
Uf"D
3‘P£!
@†^=
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and H. Igarashi and T. Toba and Y. Yamagami and Y.
Yano",
title = "A 6.7-{MFLOPS} Floating-Point Coprocessor with
Vector\slash Matrix Instructions",
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ºŠGkW #+O;a7Ea;]OŒarticlefparith.bibLehman:1957:HSDM. LehmanHigh-Speed Digital Multiplicationj-IRE-TRANS-ELEC-COMPUTEC-63204--205sep91957IRELAOhttp://dx.doi.org/10.1109/TEC.1957.52220250367-9950 OR 03679950Thu Jun 30 16:07:34 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:34 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025IRE Transactions on Electronic Computersack-nhfbM. LehmanHigh-Speed Digital Multiplication
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}‹yjZ #71/57=K;[13Œcarticlefparith.bibKogbetliantz:1957:CENE. G. KogbetliantzComputation of $ e^n $ for $ - infty < n < + infty $ Using an Electronic Computerj-IBM-JRD12110--115apr41957IBMJAE0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 00188646Tue Sep 06 18:04:49 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.06 18:04:49 ???IBM Journal of Research and Developmentack-njhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520E. G. KogbetliantzComputation of $ e^n $ for $ - \infty < n < + \infty $ Using an Electronic Computer
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author = "E. G. Kogbetliantz",
title = "Computation of $ e^n $ for $ - \infty < n < + \infty $
Using an Electronic Computer",
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month = apr,
year = "1957",
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ISSN-L = "0018-8646",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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{0{‹2mX !#)Cs+=m;‚cCŒ+techreportfparith.bibMetze:1957:SPOG. MetzeA Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow StorageReport81Digital Computer Laboratory, University of IllinoisUrbana, IL, USA771957Thu Nov 18 09:07:07 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:07:07 ???Flores' book cite [p. 485]Flores:1963:LCA cites this report, and says that its conclusion is that the disadvantages of one's complement arithmetic outweigh the advantages.ack-nhfbG. MetzeA Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow Storage
@TechReport{Metze:1957:SPO,
author = "G. Metze",
title = "A Study of Parallel One's Complement Arithmetic Units
with Separate Carry or Borrow Storage",
type = "Report",
number = "81",
institution = "Digital Computer Laboratory, University of Illinois",
address = "Urbana, IL, USA",
pages = "77",
year = "1957",
bibdate = "Thu Nov 18 09:07:07 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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remark = "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
report, and says that its conclusion is that the
disadvantages of one's complement arithmetic outweigh
the advantages.",
}‰MlV #'!mK7;K;o=!y‹articlefparith.bibLuke:1957:CLZY. L. LukeOn the Computation of $ log Z $ and $ arctan Z $j-MATH-TABLES-OTHER-AIDS-COMPUT1116--181957MTTCAS0891-6837 OR 08916837Thu Sep 1 10:16:09 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:16:09 ???Mathematical Tables and Other Aids to Computationack-njhttp://www.ams.org/mcom/Y. L. LukeOn the Computation of $ \log {Z} $ and $ \arctan {Z} $
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author = "Y. L. Luke",
title = "On the Computation of $ \log {Z} $ and $ \arctan {Z}
$",
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month = "????",
year = "1957",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}umber = "18,939d",
bibdate = "Tue Sep 11 15:35:33 MDT 2012",
bibsource = "http://ieeexplore.ieee.org/servlet/opac?punumber=5288520;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
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
non-negative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex data-processing machines.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. C. Gotlieb",
}n
lln\ #+%oU57Eƒ;‚†w['†w%o'
articlefparith.bibMurphy:1957:PIAR. W. MurphyA Positive-Integer Arithmetic for Data Processingj-IBM-JRD12158--170apr41957IBMJAEhttp://dx.doi.org/10.1147/rd.12.01580018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 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 non-negative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex data-processing machines.IBM Journal of Research and Developmentack-nhfbhttp://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 non-negative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex data-processing machines.R. W. MurphyA Positive-Integer Arithmetic for Data Processing
@Article{Murphy:1957:PIA,
author = "R. W. Murphy",
title = "A Positive-Integer Arithmetic for Data Processing",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "158--170",
month = apr,
year = "1957",
CODEN = "IBMJAE",
DOI = "http://dx.doi.org/10.1147/rd.12.0158",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
MRnumber = "18,939d",
bibdate = "Tue Sep 11 15:35:33 MDT 2012",
bibsource = "http://ieeexplore.ieee.org/servlet/opac?punumber=5288520;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
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
non-negative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex data-processing machines.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. C. Gotlieb",
}
<<‡]qU #)#E;7=m;]'#Eˆarticlefparith.bibWadel:1957:NBNL. B. WadelNegative base number systemsj-IRE-TRANS-ELEC-COMPUTEC-6123--??jun61957IRELAO0367-9950 OR 03679950Thu Nov 06 05:53:55 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:53:55 ???IRE Transactions on Electronic Computersnegative baseack-nhfbL. B. WadelNegative base number systems
@Article{Wadel:1957:NBN,
author = "L. B. Wadel",
title = "Negative base number systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "??",
pages = "123--??",
month = jun,
year = "1957",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Nov 06 05:53:55 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "negative base",
}ppZ !#++‚u/Em;‚E7‚+‚mtechreportfparith.bibTaylor:1957:CCAW. Bruce TaylorCOIN (Compile-Interpreter): an automatic programming, fixed and floating-point library of subroutines for the ERA 1103 computerOperations Research Office, Johns Hopkins UniversityBethesda, MD, USA431957Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTStaff paper / Johns Hopkins University, Operations Research Office; ORO-SP-32 Staff paper (Johns Hopkins University. Operations Research Office); ORO-SP-32.Military art and science --- Data processing.; Military research --- Data processing.Cover title. ``Operating under contract with the Department of the Army.'' ``Project COMPLAB.'' ``October 1957.'' ORO-SP-32ack-nhfbW. Bruce Taylor{COIN} (Compile-Interpreter): an automatic programming, fixed and floating-point library of subroutines for the {ERA} 1103 computer
@TechReport{Taylor:1957:CCA,
author = "W. Bruce Taylor",
title = "{COIN} (Compile-Interpreter): an automatic
programming, fixed and floating-point library of
subroutines for the {ERA} 1103 computer",
institution = "Operations Research Office, Johns Hopkins University",
address = "Bethesda, MD, USA",
pages = "43",
year = "1957",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Staff paper / Johns Hopkins University, Operations
Research Office; ORO-SP-32 Staff paper (Johns Hopkins
University. Operations Research Office); ORO-SP-32.",
acknowledgement = ack-nhfb,
keywords = "Military art and science --- Data processing.;
Military research --- Data processing.",
remark = "Cover title. ``Operating under contract with the
Department of the Army.'' ``Project COMPLAB.''
``October 1957.'' ORO-SP-32",
}‡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.5232--2361957Thu Nov 06 05:56:32 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:56:32 ???negative baseack-nhfbZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computer
@Article{Pawlak:1957:UEN,
author = "Z. Pawlak",
title = "Use of expansions with a negative basis in the
arithmometer of a digital computer",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "5",
number = "??",
pages = "232--236",
month = "????",
year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Staff paper / Johns Hopkins University, Operations
Research Office; ORO-SP-32 Staff paper (Johns Hopkins
University. Operations Research Office); ORO-SP-32.",
acknowledgement = ack-nhfb,
keywords = "Military art and science --- Data processing.;
Military research --- Data processing.",
remark = "Cover title. ``Operating under contract with the
Department of the Army.'' ``Project COMPLAB.''
``October 1957.'' ORO-SP-32",
}p
¾
Rœ¾ˆ
@Article{Taylor:1985:HFP,
author = "F. Taylor",
title = "A hybrid floating-point logarithmic number system
processor",
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volume = "32",
number = "1",
pages = "92--95",
month = jan,
year = "1985",
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ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",^ˆ
@Article{Taylor:1984:BFP,
author = "F. Taylor",
title = "Block floating-point distributed filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "3",
pages = "300--304",
month = mar,
year = "1984",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplo•‡4Ži
@Article{Taylor:1983:OFR,
author = "F. J. Taylor",
title = "An Overflow-Free Residue Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "5",
pages = "501--504",
month = may,
year = "1983",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1983.1676263",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "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=1676263",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
} ‡;Žw
@Article{Taylor:1982:VRA,
author = "F. J. Taylor",
title = "A {VLSI} Residue Arithmetic Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "6",
pages = "540--546",
month = jun,
year = "1982",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1982.1676036",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:12 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036",
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fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}š…o‹_
@Article{Taylor:1982:ARM,
author = "F. J. Taylor and C. H. Huang",
title = "An Autoscale Residue Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "4",
pages = "321--325",
month = apr,
year = "1982",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1982.1675999",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:30:01 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}™ic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://ieeexplore.ieee.org/servlet/opac?punumber=5288520;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50-megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50-megacycle
pulse-repetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phase-locked frequency divider which
provides a 3.125-megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a high-speed shift register, a
high-speed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50-megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variable-phase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of high-speed computing and measurements
applications.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}r used advantageously to provide features such as the variable-phase clock system used in the arithmetic unit.\par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of high-speed computing and measurements applications.R. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50-Megacycle 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 50-Megacycle Arithmetic Unit",
journal = j-IBM-JRD,
volume = "1",
number = "3",
pages = "257--278",
month = jul,
year = "1957",
CODEN = "IBMJAE",
DOI = "http://dx.doi.org/10.1147/rd.13.0257",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://ieeexplore.ieee.org/servlet/opac?punumber=5288520;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50-megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50-megacycle
pulse-repetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phase-locked frequency divider which
provides a 3.125-megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a high-speed shift register, a
high-speed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50-megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variable-phase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of high-speed computing and measurements
applications.",
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¼ˆ
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@Article{Besslich:1973:MDS,
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@Article{Bemer:1958:SMC,
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}vÚŠf•M
@Article{Beckmann:1993:FFTa,
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00—LY#3eY577+={;†3q!e†3eY—articlefparith.bibAshenhurst:1959:UFPRobert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point Arithmeticj-J-ACM63415--428jul71959JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 0004541168.00MR0105833 (21 \#4568)H. H. GoldstineFri Dec 08 13:06:24 1995http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.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 one-stage error propagation is developed for each operation; a suggested statistical model for long-run error propagation is also set forth.Journal of the Association for Computing Machinery0121.12102ack-nhfbhttp://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 one-stage error propagation is developed for each operation; a suggested statistical model for long-run 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 = j-J-ACM,
volume = "6",
number = "3",
pages = "415--428",
month = jul,
year = "1959",
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ISSN-L = "0004-5411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of one-stage
error propagation is developed for each operation; a
suggested statistical model for long-run error
propagation is also set forth.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
} bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}…
ð÷ðŒW #'-c57E‚;?c1cŽ!articlefparith.bibCarr:1959:EAFJohn W. Carr IIIError Analysis in Floating Point Arithmeticj-CACM2510--15may51959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:23 MDT 2004http://dblp.uni-trier.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 ACMack-nhfbhttp://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 = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}ŽY #//57Eo;?Oc/‘- articlefparith.bibBuchholz:1959:FFCWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)j-CACM2123--111959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Jan 22 06:28:45 MST 2001http://dblp.uni-trier.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 floating-point arithmeticack-nhfbhttp://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 = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
0ˆ*U #-'U;7=m;]O'Y‰?articlefparith.bibDaggett:1959:DBCD. H. DaggettDecimal-Binary Conversions in CORDICj-IRE-TRANS-ELEC-COMPUTEC-85335--339sep91959IRELAO0367-9950 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 floating-point arithmeticack-njD. H. DaggettDecimal-Binary Conversions in {CORDIC}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
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journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
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fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floating-point 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 Codingpub-WILEYpub-WILEY:adr10--151959TJ213 .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 2.1958--1961: 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 researchack-nhfbJohn 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 = pub-WILEY,
address = pub-WILEY:adr,
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = ack-nhfb,
bookpages = "????",
remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}
&ßð&Ž1œc
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author = "B. A. Jensen",
title = "Coding instructions for floating point trigonometric,
inverse trigonometric hyperbolic and exponential
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type = "Group report",
number = "30G-0009",
institution = "Massachusetts Institute of Technology, Lincoln
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abstract = "For centuries the decimal number system reigned
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until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
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oldlabel = "Knuth60",
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€€š|"[ #)+A57-Eƒ[;‚7„q?c„q+‚WAœarticlefparith.bibKnuth:1960:INSDonald E. KnuthAn Imaginary Number Systemj-CACM34245--247apr41960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.9923\#B554C. B. HaselgroveFri Nov 25 18:19:26 MST 2005http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet 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 ACMack-nhfbhttp://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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abstract = "For centuries the decimal number system reigned
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journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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author = "Dale D. Shea",
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volume = "7",
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author = "I. E. Perlin and J. R. Garrett",
title = "High Precision Calculation of $ \operatorname {Arcsin}
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{Arctan} x $ (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
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CODEN = "MCMPAF",
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bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
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¬
÷Z¬**Y #/)57E‚5;?Mc)articlefparith.bibSarafyan:1960:DCSDiran SarafyanDivisionless computation of square roots through continued squaringj-CACM35319--321may51960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.0022\#8639Fri Nov 25 18:19:26 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:26 MSTCommunications of the ACM$sqrt (x)$; elementary functionsack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Diran SarafyanDivisionless computation of square roots through continued squaring
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
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month = may,
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CODEN = "CACMA2",
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}…)U %#3//#=m;//…;Nincollectionfparith.bibReitwiesner:1960:BAG. W. ReitwiesnerBinary arithmeticAlt:1960:AC231--3081960Sat May 18 14:36:56 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:36:56 ???ack-nhfbG. W. ReitwiesnerBinary arithmetic
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author = "G. W. Reitwiesner",
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author = "Roland Silver",
title = "Letter to the {Editor}: Rounding in Floating-Point
Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
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"^ãô‰D“
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author = "Oliver Aberth",
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address = pub-ACADEMIC:adr,
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abstract = "Aberth addresses elementary issu —†ys
@Book{ANSI:1987:AIS,
author = "{ANSI\slash IEEE}",
title = "{ANSI\slash IEEE Std 854-1987: An American National
Standard: IEEE Standard for Radix-Independent
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publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "v + 14",
day = "5",
month = oct,
year = "1987",
ISBN = "0-7381-1167-8",
ISBN-13 = "978-0-7381-1167-4",
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note = "Revised 1994. INSPEC Accession Number: 3095617.",
price = "US\$44.00",
URL = "http://ieeexplore.ieee.org/iel1/2502/1121/00027840.pdf;
http://ieeexplore.ieee.org/xpl/standardstoc.jsp?isnumber=1121&isYear=1987",
acknowledgement = ack-nhfb,
}t‡B
@Article{wu:1987:FDS,
author = "I-Chen wu",
title = "A Fast {$1$-D} Serial-Parallel Systolic Multiplier",
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volume = "C-36",
number = "10",
pages = "1243--1247",
month = oct,
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CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1987.1676865",
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}î‰%’K
@Article{vonzurGathen:2004:FAG,
author = "J. Joachim von zur Gathen and Michael N{\"o}cker",
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volume = "315",
number = "2--3",
pages = "419--452",
day = "6",
month = may,
year = "2004",
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ISSN-L = "0304-3975",
bibdate = jš3
@Article{vonNeumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
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volume = "53",
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pages = "1021--1099",
month = nov,
year = "1947",
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MRclass = "65.0X",
MRnumber = "MR0024235 (= = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
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((T-Y #)#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'']j-CACM3286--86feb21960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:25 MST 2005http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:25 MSTSee cite Sarafyan:1959:NMC.Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79J. F. TraubSee \cite{Sarafyan:1959:NMC}.Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]
@Article{Traub:1960:CNM,
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year = "1960",
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abstract = "Three types of floating-point arithmetics with error
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division shift criteria are derived (for any base) for
Metropolis-style arithmetics. The limitations and most
suitable range of application for each arithmetic are
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acknowledgement = ack-nhfb,
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h,h‹@/W #1+e!577-=;7U+eŒmarticlefparith.bibWilkinson:1960:EAFJ. H. WilkinsonError Analysis of Floating-Point Computationj-NUM-MATH2319--340dec121960NUMMA70029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)0029-599X OR 0029599X65.00MR0116477 (22 \#7264)C. B. HaselgroveFri May 14 17:18:08 2010http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.05.14 17:18:08 ???Numerische Mathematikack-nhfbhttp://link.springer.com/journal/211J. H. WilkinsonError Analysis of Floating-Point Computation
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month = dec,
year = "1960",
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ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0116477 (22 \#7264)",
MRreviewer = "C. B. Haselgrove",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}“P.X #'#A57'=m;…)1Me-…)#A”
articlefparith.bibWadey:1960:FAW. G. WadeyFloating-Point Arithmeticsj-J-ACM72129--139apr41960JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 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 floating-point arithmetics with error control are discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-style arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.Journal of the ACMCited in cite Sterbenz:1974:FPC.ack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401C. B. HaselgroveThree types of floating-point arithmetics with error control are discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-style arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.W. G. WadeyFloating-Point Arithmetics
@Article{Wadey:1960:FA,
author = "W. G. Wadey",
title = "Floating-Point Arithmetics",
journal = j-J-ACM,
volume = "7",
number = "2",
pages = "129--139",
month = apr,
year = "1960",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00 (68.00)",
MRnumber = "22\#6090",
bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Three types of floating-point arithmetics with error
control are discussed and compared with conventional
floating-point arithmetic. General multiplication and
division shift criteria are derived (for any base) for
Metropolis-style arithmetics. The limitations and most
suitable range of application for each arithmetic are
discussed.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}nt), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
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xxpages = "220--221??",
}°
z+z‡-1U !#1==E[=m;M=ˆ techreportfparith.bibAnonymous:1961:MCMAnonymousModern Computing MethodsNotes on Applied Science16National Physical LaboratoryHer Majesty's Stationery Office, London220--2221961Fri 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.ack-nhfbAnonymousModern Computing Methods
@TechReport{Anonymous:1961:MCM,
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bibdate = "Fri Aug 20 10:05:25 2010",
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acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
xxpages = "220--221??",
}
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Ë ËŒ12Y #11
;a7E‚;]=
iarticlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSigned-Digit Number Representations for Fast Parallel Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-103389--400sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52192270367-9950 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 Computersack-nhfbAlgirdas Avi{\v{z}}ienisSigned-Digit Number Representations for Fast Parallel Arithmetic
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
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}T 2011",
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abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
design of the arithmetic units, residue-to-analog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
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fjournal = "IRE Transactions on Electronic Computers",
}³
MM/3Y #+5{;a7E‚;Š=]Š=5{›7articlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number Systemj-IRE-TRANS-ELEC-COMPUTEC-10163--70mar31961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52191540367-9950 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, analog-to-residue conversion, logical design of the arithmetic units, residue-to-analog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.IRE Transactions on Electronic Computersack-nhfbA system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analog-to-residue conversion, logical design of the arithmetic units, residue-to-analog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.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 = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "1",
pages = "63--70",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
design of the arithmetic units, residue-to-analog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
[[‰!4V #/)c57=m;?c)cŠarticlefparith.bibClarkson:1961:DMIW. K. ClarksonA Divisionless Method of Integer Conversionj-CACM47315--316jul71961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 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 ACMack-njhttp://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 = j-CACM,
volume = "4",
number = "7",
pages = "315--316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision addition-subtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}µ
''U5Y #%I[]57=ƒ;Š?cŠI[›Warticlefparith.bibCox:1961:NMPAlbert G. Cox and H. A. LutherA Note on Multiple Precision Arithmeticj-CACM48353--353aug81961CACMA2http://doi.acm.org/10.1145/366678.3666930001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Sat Dec 03 14:07:44 2005ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.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 addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a pm b = (a_0 pm b_0) + (a_1 pm b_1)t + cdots + (a_n pm b_n)t^n$. Here $ a_i pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.Communications of the ACMack-nhfbhttp://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 addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a \pm b = (a_0 \pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$. Here $ a_i \pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.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 = j-CACM,
volume = "4",
number = "8",
pages = "353--353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/366678.366693",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
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 addition-subtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
{ˆ[7W #-'!=m;+'‹
articlefparith.bibFreiman:1961:SACC. V. FreimanStatistical analysis of certain binary division algorithmsj-IRE-PROC49191--103jan11961Mon Sep 16 16:12:21 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.09.16 16:12:21 ???IRE Proceedingsack-sfoC. 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 = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}6Y #'%];a7E‚;]%]Žarticlefparith.bibCroy:1961:RTMJohn E. CroyRapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-104777--777dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52192860367-9950 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 Computersack-nhfbJohn E. CroyRapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmetic
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
r" ¢"³ÄÕ"†N
@Article{Ferguson:1991:SMC,
author = "Warren E. {Ferguson, Jr.}",
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month = jul,
year = "1991",
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DOI = "http://dx.doi.org/10.1109/6.83469",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Sep 01 16:17:34 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
keywords = "floating-point arithmetic",
remark = "Contains performance-comparison tables for Cyrix,
Intel, Motorola, and Weitek floating-point coprocessor
chips.",
} íc/
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author = "P. M. Fenwick",
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@Article{Ferrari:1969:CDM,
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journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
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pages = "960--960",
month = oct,
year = "1969",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/T-C.1969.222555",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L =ÄŽ7œo
@Article{Ferrari:1967:DMU,
author = "Domenico Ferrari",
title = "A Division Method Using a Parallel Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
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number = "2",
pages = "224--226",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1967.264580",
ISSN = "0367-7508",
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Garc{\'\i}a and Ester M. Garz{\'o}n",
title = "Floating point arithmetic teaching for computational
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@Article{Ferguson:1984:SFP,
author = "Kenneth M. Ferguson",
title = "{Savage} floating-point benchmark deficiencies of in
{16BST}",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}Hˆ<y
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author = "A. Fettweis",
title = "On the connection between multiplier word length
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volume = "19",
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bi‡ti
@Article{Ferro:1986:DTF,
author = "F. Ferro",
title = "{DSP} tackles floating-point arithmetic",
journal = j-COMP-DESIGN,
volume = "25",
number = "15",
pages = "53--56",
day = "15",
month = aug,
year = "1986",
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ISSN = "0010-4566",
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http://ww‰ibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}¸His work was supported by this contract, and led to the Ph.D..ack-nhfbThe 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 = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}
°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 Report61-483Electronic Technology Laboratory, The University of MichiganAnn Arbor, MI, USA91--103oct101961Thu 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=0006-3835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}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. 220--221]j-NORDISK-TIDSKR-INFORM-BEHAND13222--2221961BITTEL, NBITAB0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 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.floating-point accuracy; floating-point arithmeticack-nhfbhttp://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. 220--221]}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}T9Z #-)]I)U57C‚;
IqY)]‘{articlefparith.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point Computersj-NORDISK-TIDSKR-INFORM-BEHAND1287--88jun61961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF019392210006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.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=0006-3835&volume=1&issue=2&spage=87floating-point accuracy; floating-point arithmeticack-nhfbhttp://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 = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}.bib",
abstract = "Error checking codes based on residues have the
advantage over parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}»
Q5Q‹`