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Tera Computer Company,
2815 Eastlake East,
Seattle, WA 98102,
USA,
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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
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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),
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IBM UK (MP5),
PO Box 31,
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Warwick, CV34 5JL,
UK,
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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,
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Tera Computer Company,
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2445 Mission College Blvd.
Santa Clara, CA 95054
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email: \path=norbert@iit.com="}„0ˆc@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,
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}{xvþtüsúrøp÷nómòjðhïfîdìbë`é^è\æZåWãVáUàSßQÝPÛOÎMÌIÊHÈGÇEÅCÂAÀ@¿>½<»:¹8µ7´5²4±3¯2ª1¨/¦-£,¢*¡'ž%"›!™ —•“‘ŒŠ‰ˆ†
„ƒ}|yw~u|szrxounriqhnfmekcibgae_c\`Z]XZWWUTTQQOPMNJLHIGEFDCC@B=@;>8;7:593614.2,1*-'+#*!( '" ?«-}¦-3 L
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@InCollection{Carr:1959:PC,
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remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
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subject = "automation; mathematics; computers; operations
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}‡a‡Ž
@Article{Hastings:1977:FPH,
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author = "Harvey L. Garner",
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acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
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.",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
}
> ‡>ˆFW ##-+u=m;a+iu‡q
unpublishedfparith.bibBabbage:1837:MPCCharles BabbageOn the mathematical powers of the calculating engine161--173dec121837Wed Oct 13 11:09:59 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:09:59 ???Manuscript held by Museum of the History of Science, Oxford, UK. Reprinted in cite [ 2.1]Randell:1982:ODC.ack-nhfbCharles BabbageManuscript held by Museum of the History of Science, Oxford, UK. Reprinted in \cite[\S 2.1]{Randell:1982:ODC}.On the mathematical powers of the calculating engine
@Unpublished{Babbage:1837:MPC,
author = "Charles Babbage",
title = "On the mathematical powers of the calculating engine",
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fjournal = "Philosophical transactions of the Royal Society of
London",
remark = "Early work on signed-digit arithmetic, reported by
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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
and coins, proposed to be called the tonal system, with
sixteen to the base",
publisher = "J. B. Lippincott and Co.",
address = "Philadelphia, PA, USA",
pages = "106",
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LCCN = "QC96 .N95",
bibdate = "Sat Oct 29 10:28:27 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
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.",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
}
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keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
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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“MŽG§d[#-I3!S57C‚#;IImarticlefparith.bibBeuchat:2008:AGMJ.-L. Beuchat and J.-M. MullerAutomatic Generation of Modular Multipliers for FPGA Applicationsj-IEEE-TRANS-COMPUT57121600--1613dec122008ITCOB4https://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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author = "J.-L. Beuchat and J.-M. Muller",
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keywords = "integer overflow detection; Java",
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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
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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.",
}
eZÄ"e‡;Žw
@Article{Anonymous:1977:CAF,
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bibdate = "Mon Jul 11 21:56:55 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674892",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}˜‡ ŽC
@Article{Anonymous:1898:OFA,
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volume = "79",
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day = "22",
month = oct,
year = "1898",
CODEN = "SCAMAC",
DOI = "https://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",
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volume = "68",
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month = may,
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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",
}‡$ŽK
@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 = "https://doi.org/10.1038/scientificamerican09201879-184",
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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",
acknowledgement = ack-nhfb,
}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.''",
}
À ÀŠS#X ##
)KE‚#;S]‹articlefparith.bibK:1939:BRBdM. G. K.Book Review: booktitle Duodecimal Arithmetic, by George S. Terryj-J-R-STAT-SOC1022299--3001939https://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}
@Article{K:1939:BRBd,
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 = "https://doi.org/10.2307/2980013",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
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
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
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ISSN = "0021-1753 (print), 1545-6994 (electronic)",
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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http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
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}
ú
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author = "G. Gerwig and H. Wetter and E. M. Schwarz and J. Haess
and C. A. Krygowski and B. M. Fleischer and M.
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@Article{Gerrity:1982:CRR,
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title = "Computer Representation of Real Numbers",
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pages = "709--714",
month = aug,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676076",
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@Article{German:1999:ISI,
author = "Steven M. German",
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Arithmetic Hardware",
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URL = "http://www.wkap.nl/jrnltoc.htm/0925-9856;
http://www.wkap.nl/oasis.htm/194805",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
}æ†
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@Article{George:1975:ARR,
author = "James E. George",
title = "Algorithms to Reveal the Representation of Characters,
Integers, and Floating-Point Numbers",
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number = "3",
pages = "210--216",
month = sep,
year = "1975",
CODEN = "ACMSCU",
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ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "ACM Transactions on Mathematical Software",
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}†D
@Article{Gentleman:1974:MAR,
author = "M. W. Gentleman and S. B. Marovich",
title = "More on Algorithms that Reveal Properties of Floating
Point Arithmetic Units",
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month = apr,
year = "1971",
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DOI = "https://doi.org/10.1145/1093425.1093426",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSA
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",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
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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.",
}
P
8Š›P‰t“i
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author = "B. Vinnakota",
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author = "B. Vinnakota",
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author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
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institution = "Research Laboratories, R. C. A. Manufacturing Company,
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author = "J. W. Mauchly",
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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",
}
4
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@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 = "https://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",
},
F FŽG.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}.",
}Œm-Y#)GM57=m;
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@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 = "https://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
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author = "O. Cesareo",
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volume = "23",
number = "??",
pages = "457--460",
year = "1946",
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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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author = "H.-J. Dreyer and A. Walther",
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[{The} {Ipm} Calculator. {The} development of
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type = "{Bericht}",
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author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
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type = "Technical report",
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Mathematics",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
}<
™‰y=V#/GE57=m;_WGgEŠIarticlefparith.bibWilliams:1948:EDCF. C. Williams and T. KilburnElectronic digital computersj-NATURE162487??--??1948NATUAS0028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 OR 00280836Wed Oct 13 12:00:02 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:02 ???Reprinted in cite [ 8.4]Randell:1982:ODC.Natureack-nhfbhttp://www.nature.com/nature/archive/F. C. Williams and T. KilburnReprinted in \cite[\S 8.4]{Randell:1982:ODC}.Electronic digital computers
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = j-NATURE,
volume = "162",
number = "487",
pages = "??--??",
year = "1948",
CODEN = "NATUAS",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Oct 13 12:00:02 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
}’dW #-S{=m;SˆIarticlefparith.bibHartree:1949:NSRDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical IntegrationJournal of Research of the National Bureau of Standards4262--??1949Wed Feb 14 19:07:37 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:07:37 ???ack-nhfbDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical Integration
@Article{Hartree:1949:NSR,
author = "Douglas R. (Douglas Rayner) Hartree",
title = "Note On Systematic Roundoff Errors in Numerical
Integration",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "42",
number = "??",
pages = "62--??",
month = "????",
year = "1949",
bibdate = "Wed Feb 14 19:07:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
Çö ‰SCW '#+'7;Q'=m;_';g?‰Uinproceedingsfparith.bibWorsley:1950:EDB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, 22--25 June 1949The EDSAC demonstrationUniversity Mathematical LaboratoryCambridge, UK12--16jan11950Wed Oct 13 11:39:09 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:39:09 ???Reprinted in cite [ 8.6]Randell:1982:ODC.ack-nhfbB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, {22--25 June 1949}Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.The {EDSAC} demonstration
@InProceedings{Worsley:1950:ED,
author = "B. H. Worsley",
booktitle = "Report of a Conference on High Speed Automatic
Calculating Machines, {22--25 June 1949}",
title = "The {EDSAC} demonstration",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "12--16",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 11:39:09 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
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}‰NBW'#'C7Q'=m;_C;g#‰Oinproceedingsfparith.bibWilkes:1950:EM. V. Wilkes and W. RenwickReport of a Conference on High Speed Automatic Calculating Machines, 22--25 June 1949The EDSACUniversity Mathematical LaboratoryCambridge, UK9--11jan11950Wed Oct 13 12:00:41 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:41 ???Reprinted in cite [ 8.5]Randell:1982:ODC.ack-nhfbM. V. Wilkes and W. Renwick{Report of a Conference on High Speed Automatic Calculating Machines, 22--25 June 1949}Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.The {EDSAC}
@InProceedings{Wilkes:1950:E,
author = "M. V. Wilkes and W. Renwick",
booktitle = "{Report of a Conference on High Speed Automatic
Calculating Machines, 22--25 June 1949}",
title = "The {EDSAC}",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "9--11",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 12:00:41 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}Œ6AW #-1E+3!E%;„I5EŽÐbookfparith.bibStifler:1950:HSCW. W. Stifler, Jr.High-speed computing devicespub-MCGRAW-HILLpub-MCGRAW-HILL:adrxiii + 4511950QA75 .E5Fri Aug 20 10:18:44 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:18:44 MDTSupervised by Charles Brown Tompkins and C. H. Wakelin, Engineering Research Associates. The contents of this volume were first assembled in the form of a report to the Office of Naval Research, prepared under a provision of contract N6-ONR-240, Task 1. Cited in cite Sterbenz:1974:FPC.computersack-nhfbW. W. {Stifler, Jr.}High-speed computing devices
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "High-speed computing devices",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiii + 451",
year = "1950",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6-ONR-240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}
,¶‹,\FZ #'i?7=m;9'„Ci’1
articlefparith.bibGill:1951:PSSS. GillA process for the step-by-step integration of differential equations in an automatic digital computing machinej-PROC-CAMBRIDGE-PHIL-SOC4796--1081951PCPSA40008-1981 OR 00081981Tue Aug 28 05:54:12 2001http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.08.28 05:54:12 ???Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciencesaccurate floating-point summation; floating-point arithmetic; rounding errorsHigham cite Higham:1993:AFP comments ``In 1951 Gill [8] noticed that the rounding error in the sum of two numbers could be estimated by subtracting one of the numbers from the sum, and he made use of this estimate in a Runge--Kutta code in a program library for the EDSAC computer.''ack-nhfbS. GillA process for the step-by-step integration of differential equations in an automatic digital computing machine
@Article{Gill:1951:PSS,
author = "S. Gill",
title = "A process for the step-by-step integration of
differential equations in an automatic digital
computing machine",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "47",
pages = "96--108",
year = "1951",
CODEN = "PCPSA4",
ISSN = "0008-1981",
bibdate = "Tue Aug 28 05:54:12 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a Runge--Kutta code in a program library for the
EDSAC computer.''",
}†(EU %#)#K5=m;g#O†Wincollectionfparith.bibBrown:1951:HRRG. W. BrownHistory of RAND's random digitsHouseholder:1951:MCM31--321951Sun Sep 18 12:02:43 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:02:43 ???http://www.rand.org/pubs/papers/2008/P113.pdfack-nhfbG. W. BrownHistory of {RAND}'s random digits
@InCollection{Brown:1951:HRR,
author = "G. W. Brown",
title = "History of {RAND}'s random digits",
crossref = "Householder:1951:MCM",
pages = "31--32",
year = "1951",
bibdate = "Sun Sep 18 12:02:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.rand.org/pubs/papers/2008/P113.pdf",
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}ˆGDU #)#]C77;m;y#]‰{articlefparith.bibBooth:1951:SBMA. D. BoothA signed binary multiplication techniquej-QUART-J-MECH-APPLIED-MATH42236--2401951QJMMAV0033-5614 OR 003356140033-5614 OR 00335614Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied Mathematicsack-sfoA. D. BoothA signed binary multiplication technique
@Article{Booth:1951:SBM,
author = "A. D. Booth",
title = "A signed binary multiplication technique",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "4",
number = "2",
pages = "236--240",
month = "????",
year = "1951",
CODEN = "QJMMAV",
ISSN = "0033-5614",
ISSN-L = "0033-5614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
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Ð.x½… ŠA
@Book{Hennessy:1990:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture\emdash {A} Quantitative
Approach",
title = "Computer Architecture\emdash {A} Quantitative
Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMAN…g‹O
@Book{Henrici:1964:ENA,
author = "Peter Henrici",
title = "Elements of numerical analysis",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 328",
year = "1964",
LCCN = "QA297 .H4",
bibdate = "Fri Aug 20 09:17:19 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Based on the author's lecture notes for a course
entitled {\em Numerical Mathematical Analysis\/} at the
University of California, Los Angeles. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}‡Ž3
@Book{Hennessy:2002:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture\emdash {A} Quantitative
Approach",
title = "Computer Architecture\emdash {A} Quantitative
Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
edition = "Third",
pages = "xxi + 883 + A-87 + B-42 + C-1 + D-1 + E-1 + F-1 + G-1
+ H-1 + I-1 + R-22 + I-44",
year = "2002",
ISBN = "1-55860-596-7",
ISBN-13 = "978-1-55860-596-1",
LCCN = "????",
bibdate = "Fri May 31 15:46:29 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$89.95",
URL = "http://www.mkp.com/books_catalog/catalog.asp?ISBN=1-55860-596-7;
http://www.mkp.com/CA3",
acknowledgement = ack-nhfb,
}ê†Œ3
@Book{Hennessy:1996:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture\emdash {A} Quantitative
Approach",
title = "Computer Architecture\emdash {A} Quantitative
Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
edition = "Second",
pages = "xxiii + 760 + A-77 + B-47 + C-26 + D-26 + E-13 + R-16
+ I-14",
year = "1996",
ISBN = "1-55860-329-8",
ISBN-13 = "978-1-55860-329-5",
LCCN = "QA76.9.A73P377 1995",
bibdate = "Mon May 20 10:01:59 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$69.95",
acknowledgement = ack-nhfb,
}£… ŠA
@Book{Hennessy:1990:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture\emdash {A} Quantitative
Approach",
title = "Computer Architecture\emdash {A} Quantitative
Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xxviii + 594",
year = "1990",
ISBN = "1-55860-069-8",
ISBN-13 = "978-1-55860-069-0",
LCCN = "QA76.9.A73 P377 1990",
bibdate = "Mon Jan 31 08:47:46 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}X„.ˆ]
@Book{Heinrich:1993:MRM,
author = "Joe Heinrich",
title = "{MIPS R4000} Microprocessor User's Manual",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "xxvi + 438 + A182 + B62 + C6 + D4 + E4",
year = "1993",
ISBN = "0-13-105925-4",
ISBN-13 = "978-0-13-105925-2",
LCCN = "QA76.8.M523H45 1993",
bibdate = "Wed Aug 10 11:02:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$34.00",
acknowledgement = ack-nhfb,
}e•ï•¥
¸ iÃ}
ú„@‰
@Article{Anuta:1996:MMC,
author = "M. A. Anuta and Daniel W. Lozier and P. R. Turner",
title = "The {MasPar MP-1} as a Computer Arithmetic
Laboratory",
journal = j-J-RES-NATL-BUR-STAND,
volume = "101",
number = "2",
pages = "165--174",
month = mar # "\slash " # apr,
year = "1996",
CODEN = "JRNBAG",
ISSN = "0091-0635",
bibdate = "Fri Jul 09 07:18:42 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/få†
Œ
@Article{Andrews:1981:EFM,
author = "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
Taylor",
title = "Evaluation of Functions on Microcomputers: $ \exp (x)
$",
journal = j-COMPUT-MATH-APPL,
volume = "7",
number = "6",
pages = "503--508",
year = "1981",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:40:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
xxmonth = "(none)",
}åG‡>Ž
@Article{Anonymous:1875:AOM,
author = "Anonymous",
title = "The Arithmetical Operations of Multiplication and
Division",
journal = j-SCI-AMER,
volume = "32",
number = "3",
pages = "41--42",
day = "16",
month = jan,
year = "1875",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican01161875-41",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:29:24 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/v32/n3/pdf/scientificamerican01161875-41.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
M„I‰
@Article{Anonymous:1993:FSB,
author = "Anonymous",
title = "The ``fastest system on the block'' label must be
qualified with new multiplatform, floating-point
benchmarks",
journal = j-PC-WEEK,
volume = "10",
number = "22",
pages = "85--??",
month = jun,
year = "1993",
ISSN = "0740-1604",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "PC Week",
}1í„O‰
@Article{Anonymous:1992:FPc,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "11",
number = "10",
pages = "101--??",
month = oct,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "0733-3536",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A Helping Hand for FEA.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
Š$‡o_
@Article{Anonymous:1982:ARBf,
author = "Anonymous",
title = "Article Review: {{\booktitle{Ada model arithmetic:
costs and benefits}}: Wallis, P. J. L. \booktitle{IEE
Proc.-E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
pp 75--80}",
journal = j-MICROPROC-MICROSYS,
volume = "6",
number = "9",
pages = "497--498",
month = nov,
year = "1982",
CODEN = "MIMID57b/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a Runge--Kutta code in a program library for the
EDSAC computer.''",
}F
ÄÄŽ9GX#1]o1573%;m;Qym]YsŽ}articlefparith.bibGoldstine:1951:NIMHerman H. Goldstine and John von NeumannNumerical Inverting of Matrices of High Order. IIj-PROC-AM-MATH-SOC2188--2021951PAMYAR0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)0002-9939 OR 0002993965.0XMR0041539 (12,861b)F. J. MurrayThu Nov 8 14:49:46 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:46 ???See cite vonNeumann:1947:NIM for Part I. Reprinted in cite [Paper~15, pp.~558--572]Taub:1963:JNCa.http://www.jstor.org/view/00029939/di970628/97p0185x/0Proceedings of the American Mathematical Society043.12301ack-nhfbHerman H. Goldstine and John von NeumannSee \cite{vonNeumann:1947:NIM} for Part I. Reprinted in \cite[Paper~15, pp.~558--572]{Taub:1963:JNCa}.Numerical Inverting of Matrices of High Order. {II}
@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = j-PROC-AM-MATH-SOC,
volume = "2",
pages = "188--202",
year = "1951",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper~15, pp.~558--572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
}ith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (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",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}H
A RÁëJ‡'ŽO
@Book{Mar:1992:DSP,
editor = "Amy Mar",
title = "Digital signal processing applications using the
{ADSP}-2100 family",
publisher = pub-PH,
address = pub-PH:adr,
pages = "????",
year = "1992",
ISBN = "0-13-219726-X (vol. 1), 0-13-178567-2 (vol. 2)",
ISBN-13 = "978-0-13-219726-7 (vol. 1), 978-0-13-178567-0 (vol.
2)",
LCCN = "TK5102.9 .D53 1992",
bibdate = "Sat Jan 15 05:58:58 MST 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Vol. 2: edited by Jere Babst. System requirements for
computer disks: IBM-compatible PC; DOS 3.0 or higher;
high-density disk drive.",
subject = "Signal processing; Digital techniques;
Microprocessors",
}
Ü…Š
@Book{McCracken:1964:NMF,
author = "Daniel D. McCracken and William S. Dorn",
title = "Numerical methods and {FORTRAN} programming, with
applications in engineering and science",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 457",
year = "1964",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical analysis --- Data processing.; {Fortran}
(Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}ˆ5
@Book{McCalla:1967:INM,
author = "Thomas Richard McCalla",
title = "Introduction to Numerical Methods and {Fortran}
Programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 359",
month = jan,
year = "1967",
ISBN = "0-471-58125-9",
ISBN-13 = "978-0-471-58125-3",
LCCN = "QA297 .M25",
bibdate = "Sat Sep 27 17:58:26 MDT 1997",
bibsource = "http://www.aŒÓ
@Book{Mood:1963:ITS,
author = "Alexander McFarlane Mood and Franklin A. Graybill",
title = "Introduction to the theory of statistics",
publisher = pub-MCGRAW-HILL,
address = pŠ”
@Book{Markstein:2000:IEF,
author = "Peter Markstein",
title = "{IA-64} and elementary functions: speed and
precision",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xix + 298",
year = "2000",
ISBN = "0-13-018348-2",
ISBN-13 = "978-0-13-018348-4",
LCCN = "QA76.9.A73 M365 2000",
bibdate = "Fri Jan 5 08:00:52 MST 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparitÔƒf‡M
@Book{Mead:1980:IVS,
author = "Carver Mead and Lynn Conway",
title = "Introduction to {VLSI} systems",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xvi + 396",
year = "1980",
ISBN = "0-201-04358-0",
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LCCN = "TK7874 .M371",
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@Book{McMcusersmanual:1987:MMF,
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ISBN = "0-13-566936-7 (pbk.)",
ISBN-13 = "978-0-13-566936-5 (pbk.)",
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acknowledgement = ack-nhfb,
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ÔÔ”)HY #-+M-O57m…{Co…{+Q“Uarticlefparith.bibShirley:1951:BNBJohn W. ShirleyBinary Numeration before Leibnizj-AMER-J-PHYSICS198452--4541951AJPIAShttps://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",
DOI = "https://doi.org/10.1119/1.1933042",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (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,
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keywords = "Bell Laboratories Model 1--5 relay computers; complex
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±±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
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@InProceedings{Andrews:1952:RBL,
author = "E. G. Andrews",
editor = "J. C. McPherson",
booktitle = "Proceedings of the AIEE-IRE '51: Papers and
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acknowledgement = ack-nhfb,
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}~„I‰
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@InProceedings{Sheldon:1952:ICP,
author = "J. W. Sheldon and L. Tatum",
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{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}.",
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}‰>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,
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title = "A Stabilized Electronic Multiplier",
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volume = "EC-1",
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}‹KV #1-/!K77E‚#;SGc-/articlefparith.bibMichaelson:1952:BAR. L. MichaelsonBinary Arithmeticj-INC-STAT3135--40feb21952https://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
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DOI = "https://doi.org/10.2307/2986591",
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bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
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: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",
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bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/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,
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title = "Principles of Operation: Type 701 and Associated
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publisher = pub-IBM,
address = pub-IBM:adr,
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bibdate = "Wed Sep 14 23:17:49 1994",
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abstract = "The IBM 701 Speedcoding System is a set of
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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",
}Od 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
ZµZŒXQX#-?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;
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acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
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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.",
}ŽHPV #/O1%/Em;-3†WS-1manualfparith.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",
year = "1954",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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note = "12 volumes in 1.",
acknowledgement = ack-nhfb,
keywords = "Datatron (Computer)",
remark = "Datatron programming and coding manual --- Datatron
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Cardatron system handbook --- Model 560 DATAFILE
handbook --- Control console and consolette handbook
--- Floating point control unit handbook --- External
switching unit handbook --- Tape preparation unit
handbook.",
}
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@Article{Mayer:1954:ODF,
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@Article{Kovach:1954:AMU,
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pages = "50--52",
month = jan,
year = "1999",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11Yxx",
MRnumber = "1 674 202",
bibdate = "Tue Jun 22 10:29:34 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}øš;´w
@Article{Jamieson:1989:SNR,
author = "M. J. Jamieson",
title = "Short Notes: Rapidly Converging Iterative Formulae for
Finding Square Roots and their Computational
Efficiencies",
journal = j-COMP-J,
volume = "32",
number = "1",
pages = "93--94",
month = feb,
year = "1989",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/32.1.93",
ISSN = "0010
µ
×Ç×¢`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^ŠF_W #//A;]7Ea;]/AŒ articlefparith.bibLilamand:1956:TDMM. Lejet LilamandA Time-Division Multiplierj-IRE-TRANS-ELEC-COMPUTEC-5126--34mar31956IRELAOhttps://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 = "https://doi.org/10.1109/TEC.1956.5219789",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:18 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‰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.",
}
J`JŒcY#+k;]7Ea;]k!articlefparith.bibSydnor:1956:AMSR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulatorj-IRE-TRANS-ELEC-COMPUTEC-5282--85jun61956IRELAOhttps://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
@Article{Sydnor:1956:AMS,
author = "R. L. Sydnor and T. R. O'Meara and J. Strathman",
title = "Analog Multipliers and Squarers Using a Multigrid
Modulator",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "2",
pages = "82--85",
month = jun,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219804",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:21 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‡8bV#)W;=m;MW;‡{
articlefparith.bibStegun:1956:PCIrene A. Stegun and Milton AbramowitzPitfalls in computationJournal of the Society for Industrial and Applied Mathematics4207--2191956Tue Aug 28 06:16:28 2001http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.08.28 06:16:28 ???Cited in cite Sterbenz:1974:FPC.ack-nhfbIrene A. Stegun and Milton AbramowitzPitfalls in computation
@Article{Stegun:1956:PC,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Pitfalls in computation",
journal = "Journal of the Society for Industrial and Applied
Mathematics",
volume = "4",
pages = "207--219",
year = "1956",
bibdate = "Tue Aug 28 06:16:28 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}‡baU #1+[;7=m;]+[ˆ_ articlefparith.bibRobertson:1956:NCDJ. E. RobertsonA new class of digital division methodsj-IRE-TRANS-ELEC-COMPUTEC-565--73jun61956IRELAO0367-9950 OR 03679950Fri Nov 09 19:14:45 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 19:14:45 ???IRE Transactions on Electronic Computersack-nhfbJ. E. RobertsonA new class of digital division methods
@Article{Robertson:1956:NCD,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:14:45 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}gital Equipment Corp., Hudson, MA, USACMOS integrated circuits; Digital arithmetic; Microprocessor chips; Pipeline processingA 135K transistor, uniformly pipelined 50-MHz CMOS 64-bit floating-point arithmetic processor chip is described. The execution unit is capable of sustaining pipelined performance of one 32-bit or 64-bit result every 20 ns for all operations except double-precision multiply (40 ns) and divide. The chip employs an exponent difference prediction scheme and a unified leading-one and sticky-bit computation logic for the addition and subtraction operations. A hardware multiplier using a radix-8 modified Booth algorithm and a divider using a radix-2 SRT algorithm are employed.Bradley J. Benschneider and William J. Bowhill and Elizabeth M. Cooper and Moshe N. Gavrielov and Paul E. Gronowski and Vijay K. Maheshwari and Victor Peng and Jeffrey D. Pickholtz and Sridhar SamudralaA pipelined {50-MHz} {CMOS} 64-bit floating-point arithmetic processor
@Article{Benschneider:1989:PMC,
author = "Bradley J. Benschneider and William J. Bowhill and
Elizabeth M. Cooper and Moshe N. Gavrielov and Paul E.
Gronowski and Vijay K. Maheshwari and Victor Peng and
Jeffrey D. Pickholtz and Sridhar Samudrala",
title = "A pipelined {50-MHz} {CMOS} 64-bit floating-point
arithmetic processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1317--1323",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 135K transistor, uniformly pipelined 50-MHz CMOS
64-bit floating-point arithmetic processor chip is
described. The execution unit is capable of sustaining
pipelined performance of one 32-bit or 64-bit result
every 20 ns for all operations except double-precision
multiply (40 ns) and divide. The chip employs an
exponent difference prediction scheme and a unified
leading-one and sticky-bit computation logic for the
addition and subtraction operations. A hardware
multiplier using a radix-8 modified Booth algorithm and
a divider using a radix-2 SRT algorithm are employed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Digital Equipment Corp., Hudson, MA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "20 Ns; 40 Ns; 50 MHz; 64 Bit; Addition; CMOS; Divider;
Execution unit; Exponent difference prediction scheme;
Floating-point arithmetic processor; Hardware
multiplier; Microprocessor; Processor chip; Radix-2 SRT
algorithm; Radix-8 modified Booth algorithm; Sticky-bit
computation logic; Subtraction; Unified leading-one;
Uniformly pipelined",
numericalindex = "Word length 6.4E+01 bit; Frequency 5.0E+07 Hz; Time
2.0E-08 s; Time 4.0E-08 s",
summary = "A 135K transistor, uniformly pipelined 50-MHz CMOS
64-bit floating-point arithmetic processor chip is
described. The execution unit is capable of sustaining
pipelined performance of one 32-bit or 64-bit result
every 20 ns for all operations except \ldots{}",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
Z³ZŒVeX#+IO57=m;M1SeIQSarticlefparith.bibErcoli:1957:EDOPaolo Ercoli and Roberto VaccaErrors Due to Overflow in Arithmetic Operations Particularly as Regards FINAC Electronic Computerj-J-ACM44450--455oct101957JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Thu Dec 08 09:28:48 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.12.08 09:28:48 ???See letter cite Ercoli:1960:LEE.Journal of the ACMfloating-point arithmetic; overflowack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Paolo Ercoli and Roberto VaccaSee letter \cite{Ercoli:1960:LEE}.Errors Due to Overflow in Arithmetic Operations Particularly as Regards {FINAC} Electronic Computer
@Article{Ercoli:1957:EDO,
author = "Paolo Ercoli and Roberto Vacca",
title = "Errors Due to Overflow in Arithmetic Operations
Particularly as Regards {FINAC} Electronic Computer",
journal = j-J-ACM,
volume = "4",
number = "4",
pages = "450--455",
month = oct,
year = "1957",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Dec 08 09:28:48 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Ercoli:1960:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "floating-point arithmetic; overflow",
}ˆJdU#3Gw;7=m;]Gw‰; articlefparith.bibWeinberger:1956:OMAA. Weinberger and J. L. SmithA One-Microsecond Adder Using One-Megacycle Circuitryj-IRE-TRANS-ELEC-COMPUTEC-565--73jun61956IRELAO0367-9950 OR 03679950Fri Nov 09 19:38:57 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 19:38:57 ???IRE Transactions on Electronic Computersack-nhfbA. Weinberger and J. L. SmithA One-Microsecond Adder Using One-Megacycle Circuitry
@Article{Weinberger:1956:OMA,
author = "A. Weinberger and J. L. Smith",
title = "A One-Microsecond Adder Using One-Megacycle
Circuitry",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:38:57 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
J
ˆJŠ;gX #+%‚=m;s%‚Šwarticlefparith.bibHerzel:1957:SDDAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. (Italian) [On the frequency of initial digits of statistical numbers]Atti dell XV e XVII Riunione, Societa Italiana di Statistica??--??1957Sun Sep 18 12:00:07 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:00:07 ???Benford's Law; Law of Anomalous Numbers; Zipf's LawItalianack-nhfbAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]
@Article{Herzel:1957:SDD,
author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "Atti dell XV e XVII Riunione, Societa Italiana di
Statistica",
volume = "??",
number = "??",
pages = "??--??",
year = "1957",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = 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",
year = "1957",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "29th session, 2nd delivery, Rio de Janerio.",
URL = "",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
˜ ô˜ŠYiW #//K;]7Ea;]/KŒarticlefparith.bibKalbfell:1957:EAMDavid C. KalbfellAn Electronic Analog Multiplierj-IRE-TRANS-ELEC-COMPUTEC-62100--103jun61957IRELAOhttps://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
@Article{Kalbfell:1957:EAM,
author = "David C. Kalbfell",
title = "An Electronic Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "2",
pages = "100--103",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "https://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",
}Œ hY#'E%;]7Ea;]E%articlefparith.bibHowe:1957:TRAR. M. Howe and E. G. GilbertTrigonometric Resolution in Analog Computers by Means of Multiplier Elementsj-IRE-TRANS-ELEC-COMPUTEC-6286--92jun61957IRELAOhttps://doi.org/10.1109/TEC.1957.52215760367-9950 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=5221576IRE Transactions on Electronic Computersack-nhfbR. M. Howe and E. G. GilbertTrigonometric Resolution in Analog Computers by Means of Multiplier Elements
@Article{Howe:1957:TRA,
author = "R. M. Howe and E. G. Gilbert",
title = "Trigonometric Resolution in Analog Computers by Means
of Multiplier Elements",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "2",
pages = "86--92",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221576",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
8IV¥†I- A
@Article{Narayanaswami:1994:AE,
author = "Chandrasekhar Narayanaswami and William Luken",
title = "Approximating $ x^n $ efficiently",
journal = j-INFO-PROC-LETT,
volume = "50",
number = "4",
pages = "205--210",
day = "25",
month = may,
year = "1994",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "65D20 (41-04 65B
mE
@Article{Nelsen:1987:PSR,
author = "Roger B. Nelsen and James E. Schultz",
title = "T‡/Ž_
@Article{Nannarelli:2014:GEI,
author = "Alberto Nannarelli and Peter-Michael Seidel and Ping
Tak Peter Tang",
title = "{Guest Editors}' Introduction: Special Section on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "1852--1853",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2331711",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}‡)ŽS
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@Article{Lehman:1957:HSD,
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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",
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report, and says that its conclusion is that the
disadvantages of one's complement arithmetic outweigh
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
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abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
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
pp
n\ #+%oQ57Eƒ;‚†w['†w%o#
articlefparith.bibMurphy:1957:PIAR. W. MurphyA Positive-Integer Arithmetic for Data Processingj-IBM-JRD12158--170apr41957IBMJAEhttps://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",
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ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
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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",
}
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title = "Negative base number systems",
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volume = "EC-6",
number = "??",
pages = "123--??",
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}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",
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keywords = "negative base",
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series = "Staff paper / Johns Hopkins University, Operations
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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
¸
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({German}) [{Fast} multiplication of large numbers]",
journal = j-COMPUTING,
volume = "7",
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@Article{Schmookler:1971:HSD,
author = "Martin S. Schmookler and Arnold Weinberger",
title = "High speed decimal addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "8",
pages = "862--867",
month = aug,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223362",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
be)",
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",
}rbe 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 = "https://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.",
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",
}
bb½r^#+eQ57Eƒ;‚™S[™Ye¶Uarticlefparith.bibWalker:1957:EMAR. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50-Megacycle Arithmetic Unitj-IBM-JRD13257--278jul71957IBMJAEhttps://doi.org/10.1147/rd.13.02570018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 00188646Tue Sep 11 15:35:35 MDT 2012http://ieeexplore.ieee.org/servlet/opac?punumber=5288520; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; http://www.research.ibm.com/journal/2012.09.11 15:35:35 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687; http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdfAn experimental 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.IBM Journal of Research and Developmentack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520An 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 m
…#Š uW #)+e57=K;?c+e‹
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author = "John W. {Carr III}",
editor = "Eugene M. Grabbe and Simon Ramo and Dean E.
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booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pub-WILEY,
address = pub-WILEY:adr,
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year = "1959",
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note = "Chapter 2.",
acknowledgement = ack-nhfb,
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",
}
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title = "Coding instructions for floating point trigonometric,
inverse trigonometric hyperbolic and exponential
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type = "Group report",
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for manipulating complex numbers on machines.",
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abstract = "For centuries the decimal number system reigned
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title = "Conversion between floating point representations",
journal = j-CACM,
volume = "3",
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "352.68.00",
MRnumber = "22\#8714",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
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}§
e e‰'V #)o57;m;?co‰warticlefparith.bibPerry:1960:CBFC. PerryConversion between floating point representationsj-CACM3270--2741960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782352.68.0022\#8714Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79C. PerryConversion between floating point representations
@Article{Perry:1960:CBF,
author = "C. Perry",
title = "Conversion between floating point representations",
journal = j-CACM,
volume = "3",
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "352.68.00",
MRnumber = "22\#8714",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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}x&Y#+I‚;'57Ek;A=I‚QŽGarticlefparith.bibPerlin:1960:HPCI. E. Perlin and J. R. GarrettHigh Precision Calculation of $ operatorname Arcsin x $, $ operatorname Arccos x $, and $ operatorname Arctan x $ (in Technical Notes and Short Papers)j-MATH-COMPUT1471270--274jul71960MCMPAF0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)0025-5718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationack-njhttp://www.ams.org/mcom/I. E. Perlin and J. R. GarrettHigh Precision Calculation of $ \operatorname {Arcsin} x $, $ \operatorname {Arccos} x $, and $ \operatorname {Arctan} x $ (in {Technical Notes and Short Papers})
@Article{Perlin:1960:HPC,
author = "I. E. Perlin and J. R. Garrett",
title = "High Precision Calculation of $ \operatorname {Arcsin}
x $, $ \operatorname {Arccos} x $, and $ \operatorname
{Arctan} x $ (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "71",
pages = "270--274",
month = jul,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
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bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
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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",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
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acknowledgement = ack-nhfb,
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ZMreviewer = "M. Lotkin",
}…)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
@InCollection{Reitwiesner:1960:BA,
author = "G. W. Reitwiesner",
title = "Binary arithmetic",
crossref = "Alt:1960:AC",
pages = "231--308",
year = "1960",
bibdate = "Sat May 18 14:36:56 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}Š(W#'AG57;K;?cAG‹articlefparith.bibPope:1960:MPAD. A. Pope and M. L. SteinMultiple Precision Arithmeticj-CACM312652--654dec121960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 1 10:15:08 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:08 ???Communications of the ACMack-njhttp://portal.acm.org/browse_dl.cfm?idx=J79D. A. Pope and M. L. SteinMultiple Precision Arithmetic
@Article{Pope:1960:MPA,
author = "D. A. Pope and M. L. Stein",
title = "Multiple Precision Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "652--654",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
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}
Š ½Š†/,U #/#I#=m;;#I‡articlefparith.bibSklansky:1960:CSAJ. SklanskyConditional Sum Addition Logicj-TRANS-IREEC-92226--230jun61960Fri Nov 09 19:17:08 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 19:17:08 ???Transactions of the IREack-nhfbJ. SklanskyConditional Sum Addition Logic
@Article{Sklansky:1960:CSA,
author = "J. Sklansky",
title = "Conditional Sum Addition Logic",
journal = j-TRANS-IRE,
volume = "EC-9",
number = "2",
pages = "226--230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the IRE",
}Œ?+Y #+'57E‚5;?ac'karticlefparith.bibSilver:1960:LERRoland SilverLetter to the Editor: Rounding in Floating-Point Arithmeticj-CACM312A9--A9dec121960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:29 MSTCommunications of the ACMfloating-point arithmetic; rounding errorsack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Roland SilverLetter to the {Editor}: Rounding in Floating-Point Arithmetic
@Article{Silver:1960:LER,
author = "Roland Silver",
title = "Letter to the {Editor}: Rounding in Floating-Point
Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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acknowledgement = ack-nhfb,
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¬
G
L]Š¬›È„ˆ†I
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "662--670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = Š ”
@Article{Williams:1996:TMF,
author = "K. B. Williams",
title = "Testing Math Functions: {When} requirements are tight,
we must carefully examine all potential sources of
error. {Make} sure your math library isn't the weak
link in the chain",
journal = j-CCCUJ,
volume = "14",
number = "12",
pages = "49--54, 58--65",
month = dec,
year = "1996",
CODEN = "CCJˆI‘
@Article{Williamson:1985:NAB,
author = "D. Williamson and S. Sridharan and P. McCrea",
title = "A new approach for block floating-point arithmetic in
recursive filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "7",
pages = "719--722",
month = jul,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-40k…Q‹#
@Article{Williams:1995:SBA,
author = "T. Williams and N. Patkar and G. Shen",
title = "{SPARC64}: a 64-b 64-active-instruction
out-of-order-execution {MCM} processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "30",
number = "11",
pages = "1215--1226",
month = nov,
year = "1995",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
ˆh‘Q
@Article{Williams:1993:FM,
author = "Al Williams",
title = "32-bit floating-point math",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "70, 72, 74, 76, 80",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 08:57:56 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
http://www.math.utah.edu/pub/tex/bib/fpà…y‹s
@Article{Williams:1993:BFM,
author = "Al Williams",
title = "Bit Floating-Point Math",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "70--??",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This approach to floating-point math uses 32-bit
instructions. Although Al uses the 80386 as an example,
these techniques can be applied to other 32-bit
processors as well.",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}Ô…7Šo
@Article{Williams:1991:ZOS,
author = "Ted E. Williams and Mark A. Horowitz",
title = "A zero-overhead self-timed 160-ns 54-b {CMOS}
divider",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "26",
number = "11",
pages = "1651--1661",
month = nov,
year = "1991",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
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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,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
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journal = j-CACM,
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month = feb,
year = "1960",
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note = "See \cite{Sarafyan:1959:NMC}.",
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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",
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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
@Article{Wilkinson:1960:EAF,
author = "J. H. Wilkinson",
title = "Error Analysis of Floating-Point Computation",
journal = j-NUM-MATH,
volume = "2",
pages = "319--340",
month = dec,
year = "1960",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0116477 (22 \#7264)",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}“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",
}), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
xxpages = "220--221??",
}°
~/~‡-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,
author = "Anonymous",
title = "Modern Computing Methods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}‘M0Z#)C#I)Q57C‚;cKqYCg-’warticlefparith.bibAmble:1961:AFPO. Amble and Jan V. GarwickOn the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp. 87--88]j-NORDISK-TIDSKR-INFORM-BEHAND13220--222sep91961BITTEL, NBITABhttps://doi.org/10.1007/BF019334340006-3835 (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=3; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee cite Garwick:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220floating-point accuracy; floating-point arithmeticack-nhfbhttp://link.springer.com/journal/10543O. Amble and Jan V. GarwickSee \cite{Garwick:1961:AFP,Garwick:1961:RAF}.On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 87--88]}
@Article{Amble:1961:AFP,
author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 87--88]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
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earticlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSigned-Digit Number Representations for Fast Parallel Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-103389--400sep91961IRELAOhttps://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,
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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
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QQ+3Y #+5{;]7E‚;Š=]Š=5{›3articlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number Systemj-IRE-TRANS-ELEC-COMPUTEC-10163--70mar31961IRELAOhttps://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
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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.",
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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
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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
--O5Y #%I[W57=ƒ;Š?cŠI[›Qarticlefparith.bibCox:1961:NMPAlbert G. Cox and H. A. LutherA Note on Multiple Precision Arithmeticj-CACM48353--353aug81961CACMA2https://doi.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 = "https://doi.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.",
}Œ}6Y #'%];]7E‚;]%]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--777dec121961IRELAOhttps://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 = "https://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",
}
ÿÿî"
3ÌÝg‰+’W
@Article{Grehan:1988:FPCa,
author = "Rick Grehan",
title = "Floating-Point Without a Coprocessor",
journal = j-BYTE,
volume = "13",
number = …R‹%
@Article{Groeger:1989:DRG,
author = "Detlef Gr{\"o}ger",
title = "{Zur Division mit Rest auf Gleitkommarechnern.
(German)} [On division with remainder on floating point
co‰B“
@Article{Gregory:1977:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base conversion in residue number systems",
journal = j-BIT,
volume = "17",
number = "3",
pages = "286--302",
month = sep,
year = "1977",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932149",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclas-ˆ-[
@Article{Gregory:1979:EFC,
author = "Robert Todd Gregory",
title = "Error-free computation with finite number systems",
journal = j-SIGNUM,
volume = "14",
number = "3",
pages = "9--16",
month = sep,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "http://portal.ac ‰'’O
@Article{Griffin:1991:REA,
author = "C. Griffin and P. Rao and F. Taylor",
title = "Roundoff error analysis of the discrete {Wigner}
distribution using fixed-point arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "9",
pages = "2096--2098",
month = sep,
year = "1991",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "105k„e‰K
@Article{Grehan:1989:FPR,
author = "R. Grehan",
title = "Floating-Point Revisited",
journal = j-BYTE,
volume = "14",
number = "4",
pages = "311--318",
month = apr,
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}¶‰{“w
@Article{Grehan:1988:FPCb,
author = "R. Grehan",
title = "Floating-Point Without a Coprocessor, Part 2",
journal = j-BYTE,
volume = "13",
number = "10",
pages = "293--297 (or 293--298??)",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "ftp://garbo.u Ô‰+’W
@Article{Grehan:1988:FPCa,
author = "Rick Grehan",
title = "Floating-Point Without a Coprocessor",
journal = j-BYTE,
volume = "13",
number = "9",
pages = "313--319",
month = sep,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database Ò‹–?
@Article{Grehan:1988:BBL,
author = "R. Grehan and T. Thompson",
title = "{Borland} beefs up its languages",
journal = j-BYTE,
volume = "13",
number = "10",
pages = "151--154",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "http://www.math.utah.edu/p Ïibdate = "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",
}P9Z #-)]I)Q57C‚;
IqY)]‘warticlefparith.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point Computersj-NORDISK-TIDSKR-INFORM-BEHAND1287--88jun61961BITTEL, NBITABhttps://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 = "https://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",
}b",
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",
}»
[;[‹\\1’&¤M
@InCollection{Demmel:2002:CAF,
author = "J. Demmel and Plamen Koev and Ben Diament",
title = "The Complexity of Accurate Floating Point
Computation",
crossref = "Li:2002:PIC",
volume = "III (1--3)",
year = "2002",
MRclass = "65G30 (65Y20)",
MRnumber = "MR1957571 (2004b:65060)",
bibdate = "Mon Apr 25 06:44:54 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ht*
m
@InCollection{Goldberg:1996:CA,
author = …r‹e
@InCollection{Gavrilova:2003:ESC,
author = "M. L. Gavrilova",
booktitle = "Computational science and its applications---ICCSA
2003. Part III",
title = "An explicit solu„ˆ9
@InCollection{Demmel:2004:AEA,
author = "James Demmel and Plamen Koev",
title = "Accurate and efficient algorithms for floating point
computation",
crossref = "Hilledt:2004:AME",
pages = "73--88",
year = "2004",
MRclass = "65Gxx (65Fxx)",
MRnumber = "MR2296263",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}Ü‚v…m
@InCollection{Garner:1965:NSA,
author = "H. L. Garner",
title = "Number systems and arithmetic",
crossref = "Alt:1965:AC",
volume = "6",
pages = "131--194",
year = "1965",
bibdate = "Sat May 18 14:18:19 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}$Š[•7
@InCollection{Crowell:1987:FPA,
author = "Charles Crowell",
title = "Floating-point arithmetic with the {TMS32020}",
crossref = "Lin:1987:DSP",
pages = "245--268",
year = "1987",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$30.67",
acknowledgement = ack-nhfb,
bibno = "42623
Œ ˜
@InCollection{Corliss:1984:AGT,
author = "George F. Corliss and Louis B. Rall",
title = "Automatic generation of {Taylor} series in
{Pascal-SC}: {Basic} operations and applications to
differential equations",
crossref = "Anonymous:1984:TFA",
pages = "177--209",
year = "1984",
bibdate = "Fri Dec 8 13:09:09 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Mˆ7
@InCollection{Cody:1988:FPS,
author = "W. J. Cody",
title = "Floating-point standards --- theory and practice",
crossref = "Moore:1988:RCR",
pages = "99--107",
year = "1988",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Argonne National Laboratory, Argonne, I Àƒ#†G
@InCollection{Cody:1971:SEF,
author = "W. J. Cody",
title = "Software for the Elementary Functions",
crossref = "Rice:1971:MS",
pages = "171--186",
year = "1971",
bibdate = "Thu Sep 15 18:56:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}&ƒ8†q
@InCollection{Clark:1971:SCP,
author = "N. W. Clark and W. J. Cody and H. Kuki",
title = "Self-Contained Power Routines",
crossref = "Rice:1971:MS",
pages = "399--415",
year = "1971",
bibdate = "Thu Sep 15 18:56:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}$
#
ò#KvW#)E{#57E';;E{‘articlefparith.bibStern:1963:CSRT. E. Stern and R. M. LernerA circuit for the square root of the sum of the squaresj-PROC-IEEE514593--596apr41963IEEPAD0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)0018-9219 OR 00189219Sat Jul 16 15:28:13 MDT 2005http://ieeexplore.ieee.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.07.16 15:28:13 MDTProceedings of the IEEEack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5T. E. Stern and R. M. LernerA circuit for the square root of the sum of the squares
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}Š
uV#'o]+3)E%;mM;o]‹bookfparith.bibMood:1963:ITSAlexander McFarlane Mood and Franklin A. GraybillIntroduction to the theory of statisticspub-MCGRAW-HILLpub-MCGRAW-HILL:adrSecond4431963HA29 .M75 1963Fri Aug 20 10:02:03 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:02:03 MDTMcGraw-Hill series in probability and statisticsCited in cite Sterbenz:1974:FPC.Mathematical statisticsack-nhfbAlexander McFarlane Mood and Franklin A. GraybillIntroduction to the theory of statistics
@Book{Mood:1963:ITS,
author = "Alexander McFarlane Mood and Franklin A. Graybill",
title = "Introduction to the theory of statistics",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
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LCCN = "HA29 .M75 1963",
bibdate = "Fri Aug 20 10:02:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/