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National Institute of Standards and Technology,
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Seattle, WA 98102,
USA,
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email: \path=norbert@iit.com="}vcacknhfbNelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 841120090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, email: path beebe@math.utah.edu, path beebe@acm.org, path beebe@computer.org (Internet), URL: path http://www.math.utah.edu/~beebe/@String{acknhfb = "Nelson H. F. Beebe,
University of Utah,
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Salt Lake City, UT 841120090, USA,
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FAX: +1 801 581 4148,
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\pathbeebe@acm.org,
\pathbeebe@computer.org (Internet),
URL: \pathhttp://www.math.utah.edu/~beebe/"}qWackmfcMichael F. Cowlishaw, IBM UK (MP5), PO Box 31, Birmingham Road, Warwick, CV34 5JL, UK, email: path mfc@uk.ibm.com, URL: path http://www2.hursley.ibm.com/decimal@String{ackmfc = "Michael F. Cowlishaw,
IBM UK (MP5),
PO Box 31,
Birmingham Road,
Warwick, CV34 5JL,
UK,
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URL: \pathhttp://www2.hursley.ibm.com/decimal"}ackkrKarin Remington, National Institute of Standards and Technology, Building 820, Room 365, Gaithersburg, MD 20899, USA, Tel: +1 301 9755119, FAX: +1 301 9904127, email: path karin@cam.nist.gov@String{ackkr = "Karin Remington,
National Institute of Standards and Technology,
Building 820, Room 365,
Gaithersburg, MD 20899, USA,
Tel: +1 301 9755119,
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email: \pathkarin@cam.nist.gov"}ackjrJon Rokne, Department of Computer Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada@String{ackjr = "Jon Rokne,
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2500 University Drive N.W.,
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Tera Computer Company,
2815 Eastlake East,
Seattle, WA 98102,
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Santa Clara, CA 95054
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University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 841120090, USA,
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FAX: +1 801 581 4148,
email: \pathbeebe@math.utah.edu,
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@InProceedings{Greenley:1995:UNG,
author = "D. Greenley and J. Bauman and D. Chang and Dennis Chen
and R. Eltejaein and P. Ferolito and P. Fu and Robert
EU+
@Article{Zhou:1988:NBS,
author = "B. B. Zhou",
title = "A new bitserial systolic multiplier over {$ \mathrm
{GF}(2^m) $}",
journal = jIEEETRANSCOMPUT,
volume = "37",
number = "6",
pages = "749751",
month = jun,
year = "1988",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.2216",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2216",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}j [7
@Article{Rao:1970:BEC,
author = "T. R. N. Rao",
title = "Biresidue ErrorCorrecting Codes for Computer
Arithmetic",
journal = jIEEETRANSCOMPUT,
volume = "C19",
number = "5",
pages = "398402",
month = may,
year = "1970",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1970.222937",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Wed Jul 13 08:01:32 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}J
@Article{Montalvo:1998:NST,
author = "L. A. Montalvo and K. K. Parhi and A. Guyot",
title = "New {SvobodaTung} division",
journal = jIEEETRANSCOMPUT,
volume = "47",
number = "9",
pages = "10141020",
month = sep,
year = "1998",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.713319",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Wed Jul 6 09:35:56 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/ieeetr[7
@Article{Rao:1970:BEC,
author = "T. R. N. Rao",
title = "Biresidue ErrorCorrecting Codes for Computer
Arithmetic",
journal = jIEEETRANSCOMPUT,
volume = "C19",
number = "5",
pages = "398402",
month = may,
year = "1970",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1970.222937",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Wed Jul 13 08:01:32 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}ce = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = acknhfb,
authordates = "Johan Vilhelm Nystr{\"o}m (18241885)",
subject = "Weights and measures; Numeration; base16 arithmetic;
hexadecimal arithmetic",
remark = "Thanks for Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicodecompatible fonts to represent the additional
digits needed by the system.",
}
: :FW ##+u=m;a+iuq
unpublishedfparith.bibBabbage:1837:MPCCharles BabbageOn the mathematical powers of the calculating engine161173dec121837Wed Oct 13 11:09:59 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:09:59 ???Manuscript held by Museum of the History of Science, Oxford, UK. Reprinted in cite [ 2.1]Randell:1982:ODC.acknhfbCharles BabbageManuscript held by Museum of the History of Science, Oxford, UK. Reprinted in \cite[\S 2.1]{Randell:1982:ODC}.On the mathematical powers of the calculating engine
@Unpublished{Babbage:1837:MPC,
author = "Charles Babbage",
title = "On the mathematical powers of the calculating engine",
month = dec,
year = "1837",
bibdate = "Wed Oct 13 11:09:59 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript held by Museum of the History of Science,
Oxford, UK. Reprinted in \cite[\S
2.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
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volume = "C26",
number = "5",
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@Article{Aggarwal:1979:REM,
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bibdate = "Thu Nov 06 06:16:38 2014",
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U #/;?9/=m;;?Obookfparith.bibKarpinski:1925:HALouis Charles KarpinskiThe History of ArithmeticRand McNally & CompanyNew York, NY, USAxi + 2001925Fri Nov 28 18:09:05 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:09:05 ???ackmfcLouis Charles KarpinskiThe History of Arithmetic
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}TW #)1e57E;Qo1iarticlefparith.bibSmith:1924:FPADavid Eugene SmithThe First Printed Arithmetic (Treviso, 1478)jISIS633113311924ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:57:26 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211087; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1920.bib2013.07.30 21:57:26 MDThttp://www.jstor.org/stable/224315Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlDavid Eugene SmithThe First Printed Arithmetic ({Treviso}, 1478)
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@Article{Agrawal:1983:ICA,
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month = nov,
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@Article{Agrawal:1979:HSA,
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;GI9articlefparith.bibJ:1930:RPRbR. A. J.Recent Publications: Reviews: em Standard Table of Square Roots, by L. M. MilneThomsonjAMERMATHMONTHLY376314314jun61930AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:35:55 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:35:55 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlR. A. J.Recent Publications: Reviews: {{\em Standard Table of Square Roots}}, by {L. M. MilneThomson}
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@Article{Laughlin:1930:LND,
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title = "LargeNumber Division by Calculating Machine",
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would simplify information systems. His master's
thesis, written when he as twentyone and published
when he was twentytwo, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 5961 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 6268,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}
::CW '#7s/_1=m;=
=O7=s%mastersthesisfparith.bibShannon:1937:SARClaude Elwood ShannonA Symbolic Analysis of Relay and Switching CircuitsMaster of ScienceDepartment of Electrical Engineering, MITCambridge, MA, USA7210aug81937Thu Nov 18 10:35:20 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 10:35:20 ???Not submitted until 1940http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdfSmiley cite [p. 91]Smiley:2010:MWI claims: ``He [Shannon] also had the insight, like Atanasoff, that the binary arithmetic that relay switches represented would simplify information systems. His master's thesis, written when he as twentyone and published when he was twentytwo, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 5961 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 6268, ``A Factor Table Machine'', describe a machine that will print a table of factors and primes of all the integers from 1 to 100,000,000. Shannon notes on page 68: ``As to the practicality of such a device, it might be said that J. P. Kulik spent 20 years in constructing a table of primes up to 100,000,000 and when finished it was found to contain so many errors that it was not worth publishing. The machine described here could probably be made to handle 5 numbers per second so that the table would require only about 2 months to construct.''acknhfbApril 30, 1916February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
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address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
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bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = acknhfb,
authordates = "April 30, 1916February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twentyone and published
when he was twentytwo, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 5961 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 6268,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}umbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution lawhence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multidigit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
UD
@Article{Akishita:2001:FSS,
author = "Toru Akishita",
title = "Fast Simultaneous Scalar Multiplication on Elliptic
Curve with {Montgomery} Form",
journal = jLECTNOTESCOMPSCI,
volume = "2259",
pages = "255??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "03029743 (print), 16113349 (electronic)",
ISSNL = "03029743",
bibdate = "Sat Feb 2 13:07:44 MST 2002",
bibsource = "http://link.springerny.com/link/service/series/0558/tocs/t2259.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springerny.com/link/service/series/0558/bibs/2259/22590255.htm;
http://link.springerny.com/link/service/series/0558/papers/2259/22590255.pdf",
acknowledgement = acknhfb,
fjournal = "Lecture Notes in Computer Science",
} 35
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number = "2",
pages = "99109",
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month = feb,
year = "1998",
CODEN = "????",
ISSN qc
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pages = "????",
month = "????",
year = "2012",
CODEN = "NUALEG",
DOI = "http://dx.doi.org/10.1007/s110750119496z",
ISSN = "10171398 (print), 15729265 (electronic)",
ISSNL = "10171398",
bibdati
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author = "Mayez AlMouhamed and Lubomir Bic",
title = "Effects of Loop Fusion and Statement Migration on the
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month = nov,
year = "1995",
CODEN = "JPDCER",
DOI = "http://dx.doi.org/10.1006/jpdc.1995.1144",
ISSN =T
@Article{Alam:1993:RTO,
author = "M. S. Alam and M. A. Karim",
title = O
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author = "H. A. AlTwaijry and M. J. Flynn",
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@Article{Akleylek:2012:MRR,
author = "Sedat Akleylek and Ferruh Ozbudak",
title = "Modified Redundant Representation for Designing
Arithmetic Circuits with Small Complexity",
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month = mar,
year = "2012",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2011.29",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Fri Feb 3 07:35:03 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}K
@Article{Akbarpour:2010:VSI,
author = "Behzad Akbarpour and Amr T. AbdelHamid and
Sofi{\`e}ne Tahar and John Harrison",
title = "Verifying a Synthesized Implementation of {IEEE754}
FloatingPoint Exponential Function using {HOL}",
journal = jCOMPJ,
volume = "53",
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month = may,
year = "2010",
CODEN = "CMPJA6",
DOI = "http:///&e Law of Anomalous Numbers is thus a general probability law of widespread application.Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledgeBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom cite Logan:1978:FDP: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 573585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] containing an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography cite Hurlimann:2006:BLB cites 325 publications about Benford's Law.acknhfbhttp://www.jstor.org/journal/procamerphilsociIt has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution lawhence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multidigit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.Frank BenfordThe Law of Anomalous Numbers
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = jPROCAMERPHILSOC,
volume = "78",
number = "4",
pages = "551572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003049X (print), 23269243 (electronic)",
ISSNL = "0003049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution lawhence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multidigit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
qq[ #'E557=m;C]WsEge'ESarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous NumbersjPROCAMERPHILSOC784551572mar31938PAPCAA0003049X (print), 23269243 (electronic) OR 0003049X (print), 23269243 (electronic)0003049X OR 0003049XThu Feb 15 16:28:28 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 16:28:28 ???http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2GIt has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution lawhence the name ``Anomalous Numbers.''par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.par The equation also gives the frequency of digits in the second, third + place of a multidigit number, and it is shown that the same law applies to reciprocals.par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. Th%
Y Y9 W#)]!)!=m;]Ibookfparith.bibHardy:1938:ITNG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of NumberspubOXFORDpubOXFORD:adrxvi + 4031938QA241 .H28Fri Nov 30 06:49:15 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.30 06:49:15 ???acknhfbG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numbers
@Book{Hardy:1938:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pubOXFORD,
address = pubOXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
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}hY #3'7G'=m;''/_ phdthesisfparith.bibCouffignal:1938:AMAL. CouffignalSur l'analyse mecanique. Application aux machines a calculer et aux calculs de la mecanique celeste. (French) [On mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]GauthierVillarsFaculte des Sciences de ParisParis, France5515721938Wed Oct 13 11:17:22 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:17:22 ???Extracts reprinted in cite [ 2.7]Randell:1982:ODC. Translated by Mr. R. Basu.FrenchacknhfbL. CouffignalExtracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.Sur l'analyse m{\'e}canique. Application aux machines {\`a} calculer et aux calculs de la m{\'e}canique c{\'e}leste. ({French}) [{On} mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
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address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = acknhfb,
language = "French",
} http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = acknhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
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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
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!Y #/sA7=]; }/sUarticlefparith.bibShannon:1938:SARClaude E. ShannonA Symbolic Analysis of Relay and Switching CircuitsjTRANSAMERINSTELECENG57713723dec121938TAEEA500963860 OR 00963860Sat Nov 20 08:54:12 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www2.research.att.com/~njas/doc/shannonbio.html2010.11.20 08:54:12 ???Transactions of the American Institute of Electrical EngineersThis is Shannon's first published paper (his Master's thesis). In 1940, it received the Alfred Noble Prize of the combined engineering societies of the United States, an award given each year to a person not over thirty for a paper published in one of the journals of the participating societies. H. H. Goldstine cite Goldstine:1972:CPN called this work ``one of the most important master's theses ever written ... a landmark in that it helped to change digital circuit design from an art to a science.''acknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714Claude E. ShannonA Symbolic Analysis of Relay and Switching Circuits
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
journal = jTRANSAMERINSTELECENG,
volume = "57",
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bibdate = "Sat Nov 20 08:54:12 2010",
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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.''",
}
W#X ##
)OE#;S]articlefparith.bibK:1939:BRBdM. G. K.Book Review: booktitle Duodecimal Arithmetic, by George S. TerryjJRSTATSOC10222993001939http://dx.doi.org/10.2307/2980013Sat Jan 24 11:18:08 MST 2015http://www.jstor.org/stable/i349540; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrssa1930.bib2015.01.24 11:18:08 MSThttp://www.jstor.org/stable/2980013Journal of the Royal Statistical SocietyacknhfbM. G. K.Book Review: {{\booktitle{Duodecimal Arithmetic}}, by George S. Terry}
@Article{K:1939:BRBd,
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title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
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bibsource = "http://www.jstor.org/stable/i349540;
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acknowledgement = acknhfb,
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}g"Y#)Q57E;QoQarticlefparith.bibJager:1939:AADRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of Robert Jager (London, 1651)jISIS3112531nov111939ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:26:49 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302217; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1930.bib2013.07.30 21:26:49 MDThttp://www.jstor.org/stable/226014Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = jISIS,
volume = "31",
number = "1",
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}
/^=
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author = "Martin F{\"u}rer",
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journal = jSIAMJCOMPUT,
volume = "39",
number = "3",
pages = "9791005",
month = "????",
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DOI = "",
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ISSNL = "00975397",
bibdate = "Tue May 18 08:22:12 MDT 2010",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "SIAM Journal on Computing",
journalURL = "http://epubs.siam.org/sicomp",
}
O
@Article{Fulton:1982:BJB,
author = "T. A. Fulton and L. N. Dunkleberger",
title = "{B.S.T.J.} Briefs: a {Josephson} Parallel Multiplier",
journal = jBELLSYSTTECHJ,
volume = "61",
number = "5",
pages = "931933",
month = may # "" # jun,
year = "1982",
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ISSN = "00058580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "The Bell System Technical Journal",
journalURL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)15387305/issues/",
}nqc
@Article{Fujiyama:1989:FD,
author = "T. Fujiyama and Y. Shimazu and T. Tokuda and S.
Tsujimichi",
title = "A 24bit floatingpoint {DSP}",
journal = "Mitsubishi Denki Giho",
volume = "63",
number = "12",
pages = "5962",
month = "????",
year = "1989",
ISSN = "03692302",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib"
y!
@Article{Fujii:1992:FPC,
author = "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
T. Demura and G. Ootomo",
title = "A floatingpoint cell library and a {100Mflops} image
signal processor",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "27",
number = "7",
pages = "10801088",
month = jul,
year = "1992",
CODEN = "IJSCBC",
ISSN = "00189200 (print),
qc
@Article{Fujii:1992:FCL,
author = "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
T. Demura and G. Ootomo",
title = "A FloatingPoint Cell Library and a {100MFLOPS} Image
Signal Processor",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "27",
number = "7",
pages = "10801088",
month = jul,
year = "1992",
CODEN = "IJSCBC",
ISSN = "00189200 (print), 1558173X (electronic)",
ISSNL = "00189200",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "IEEE Journal of SolidState Circuits",
}
fVfx'V '#)7#1'=m;!7kmastersthesisfparith.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;_'gtechreportfparith.bibStibitz:1940:CG. R. StibitzComputerUnpublished memorandumBell Telephone LaboratoriesNew York, NY, USA2993001940Wed Oct 13 11:30:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:30:38 ???Reprinted in cite [ 6.1]Randell:1982:ODC.acknhfbG. R. StibitzReprinted in \cite[\S 6.1]{Randell:1982:ODC}.Computer
@TechReport{Stibitz:1940:C,
author = "G. R. Stibitz",
title = "Computer",
type = "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}7%X #%5=m;#+5}miscfparith.bibBush:1940:AMV. BushArithmetical Machine2993001940Wed Oct 13 11:37:32 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:37:32 ???Reprinted in cite [ 7.3]Randell:1982:ODC. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.acknhfbVannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 19391940V. BushReprinted in \cite[\S 7.3]{Randell:1982:ODC}. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.Arithmetical Machine
@Misc{Bush:1940:AM,
author = "V. Bush",
title = "Arithmetical Machine",
howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 19391940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = acknhfb,
}s$W !#1+/91'=m;_+g/qtechreportfparith.bibAtanasoff:1940:CMSJ. V. AtanasoffComputing machine for the solution of large systems of linear algebraic equationsUnpublished memorandumIowa State CollegeAmes, IA, USA299300aug81940Wed Oct 13 11:36:11 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:36:11 ???Reprinted in cite [ 7.2]Randell:1982:ODC.acknhfbJ. V. AtanasoffReprinted in \cite[\S 7.2]{Randell:1982:ODC}.Computing machine for the solution of large systems of linear algebraic equations
@TechReport{Atanasoff:1940:CMS,
author = "J. V. Atanasoff",
title = "Computing machine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}"19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of WisconsinMadison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the AtanasoffBerry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 19671973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the AtanasoffBerry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50bit word.",
}'neofakind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 19301966'', (found in http://discover.lib.umn.edu/): CWB as an attorney for the group retained by Honeywell in the Honeywell v. Sperry Rand ENIAC trial. The ABC had a 50bit word.acknhfb19181963Clifford Edward BerryDesign of electrical data recording and reading mechanism
@MastersThesis{Berry:1941:DED,
author = "Clifford Edward Berry",
title = "Design of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
authordates = "19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of WisconsinMadison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the AtanasoffBerry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 19671973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the AtanasoffBerry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50bit word.",
}
9=(9
.]
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MRnumber Lg
@Article{Thompson:1987:IEF,
author = "P. Thompson",
title = "Implementing an El
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author = "P. Thompson",
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}Մ={
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: W:d*X!#/k +m_kg Qtechreportfparith.bibRajchman:1942:REPJ. A. Rajchman and G. A. Morton and A. W. VanceReport on Electronic Predictors for AntiAircraft Fire ControlResearch Laboratories, R. C. A. Manufacturing Company, Inc.Camden, NJ, USA112115apr41942http://www.math.utah.edu/pub/tex/bib/fparith.bibReprinted in cite [ 7.4]Randell:1982:ODC.acknhfbJ. A. Rajchman and G. A. Morton and A. W. VanceReprinted in \cite[\S 7.4]{Randell:1982:ODC}.Report on Electronic Predictors for AntiAircraft Fire Control
@TechReport{Rajchman:1942:REP,
author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
title = "Report on Electronic Predictors for AntiAircraft Fire
Control",
institution = "Research Laboratories, R. C. A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
month = apr,
year = "1942",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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@TechReport{Mauchly:1942:UHS,
author = "J. W. Mauchly",
title = "The use of high speed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
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@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = jJAMSTATASSOC,
volume = "37",
number = "217",
pages = "112115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "01621459 (print), 1537274X (electronic)",
ISSNL = "01621459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = acknhfb,
fjournal = "Journal of the American Statistical Association",
journalURL = "http://www.tandfonline.com/loi/uasa20",
}
0
0_,Y#/IuQ57=m;
ysWyIu?articlefparith.bibGoudsmit:1944:SFNS. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical TablesjNATURE154392180080123dec121944NATUAShttp://dx.doi.org/10.1038/154800a000280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Sun Sep 18 11:57:19 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:57:19 ???http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdfA rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.NatureBenford's Law; Law of Anomalous Numbers; Zipf's Lawacknhfbhttp://www.nature.com/nature/archive/A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.S. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical Tables
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = jNATURE,
volume = "154",
number = "3921",
pages = "800801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "00280836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}k+Y #//357E
;G/marticlefparith.bibCrawford:1943:DNSW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of CosinesjAMERMATHMONTHLY503190191mar31943AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:36:57 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:36:57 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of Cosines
@Article{Crawford:1943:DNS,
author = "W. S. H. Crawford",
title = "Discussions and Notes: Square Roots from a Table of
Cosines",
journal = jAMERMATHMONTHLY,
volume = "50",
number = "3",
pages = "190191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
} "00280836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
},
B BG.W !#3UA= ;_ugYutechreportfparith.bibvonNeumann:1945:FDRJohn von NeumannFirst Draft of a Report on the EDVACUniversity of Pennsylvania525330jun61945Mon Jun 06 19:17:03 2005ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.06 19:17:03 ???Reprinted in cite [ 8.2]Randell:1982:ODC.This is the report that got von Neumann's name associated with the serial, storedprogram, general purpose, digital architecture upon which 99.99% of all computers today are based.acknhfbJohn von NeumannReprinted in \cite[\S 8.2]{Randell:1982:ODC}.First Draft of a Report on the {EDVAC}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, storedprogram, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W670ORD4926. Reprinted in
\cite[pp.~177246]{Stern:1981:EUA},
\cite[pp.~399413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}qY#)GQ57=m;
sWG'articlefparith.bibFurry:1945:DNDW. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant FiguresjNATURE155525313jan11945NATUAShttp://dx.doi.org/10.1038/155052a000280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Sun Sep 18 11:51:37 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:51:37 ???http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdfNatureBenford's Law; Law of Anomalous Numbers; Zipf's Lawacknhfbhttp://www.nature.com/nature/archive/W. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant Figures
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = jNATURE,
volume = "155",
number = "??",
pages = "5253",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "00280836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}n \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, storedprogram, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W670ORD4926. Reprinted in
\cite[pp.~177246]{Stern:1981:EUA},
\cite[pp.~399413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}.
xixn1U #+!917=m;_=!g9[articlefparith.bibCesareo:1946:RIO. CesareoThe Relay InterpolatorjBELLLABSRECORD234574601946BLRCAB00058564 OR 00058564Wed Oct 13 11:31:47 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:31:47 ???Reprinted in cite [ 6.2]Randell:1982:ODC.Bell Laboratories RecordacknhfbO. CesareoReprinted in \cite[\S 6.2]{Randell:1982:ODC}.The Relay Interpolator
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = jBELLLABSRECORD,
volume = "23",
number = "??",
pages = "457460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "00058564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Bell Laboratories Record",
}0]!#)13;=q;YUi1]techreportfparith.bibBurks:1946:PDLArthur W. Burks and Herman H. Goldstine and John von NeumannPreliminary discussion of the logical design of an electronic computing instrumentinstINSTADVSTUDYinstINSTADVSTUDY:adr4228jun61946Wed Oct 13 08:17:48 2004ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.10.13 08:17:48 ???Report to the U.S. Army Ordnance Department. Reprinted in cite [pp.~221259]Swartzlander:1976:CDD, cite [ 8.3]Randell:1982:ODC, and cite [pp.~97146]Aspray:1987:PJNDiscusses floatingpoint versus fixedpoint computation, and concludes that floatingpoint is probably not justifiable. They wrote:par ``There appear to be two major purposes in a `floating' decimal point system both of which arise from the fact that the number of digits in a word is a constant fixed by design considerations for each particular machine. The first of these purposes is to retain in a sum or product as many significant digits as possible and the second of these is to free the human operator from the burden of estimating and inserting into a problem `scale factors'  multipl8m/V#)Ee%E7=m;_EgiAarticlefparith.bibAiken:1946:ASCH. H. Aiken and G. M. HopperThe Automatic Sequence Controlled CalculatorjELECTRENG65384391, 449454, 5225281946ELENAC00959197 OR 00959197Wed Oct 13 11:26:29 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:26:29 ???Reprinted in cite [ 5.2]Randell:1982:ODC.Electrical Engineering (American Institute of Electrical Engineers)acknhfbH. H. Aiken and G. M. HopperReprinted in \cite[\S 5.2]{Randell:1982:ODC}.The {Automatic Sequence Controlled Calculator}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = jELECTRENG,
volume = "65",
number = "??",
pages = "384391, 449454, 522528",
year = "1946",
CODEN = "ELENAC",
ISSN = "00959197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
}p://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors'  multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}0icative constants which serve to keep numbers within the limits of the machine.par There is, of course, no denying the fact that human time is consumed in arranging for the introduction of suitable scale factors. We only argue that the time so consumed is a very small percentage of the total time we will spend in preparing an interesting problem for our machine. The first advantage of the floating point is, we feel, somewhat illusory. In order to have such a floating point, one must waste memory capacity which could otherwise be used for carrying more digits per word. It would therefore seem to us not at all clear whether the modest advantages of a floating binary point offset the loss of memory capacity and the increased complexity of the arithmetic and control circuits.''acknhfbArthur W. Burks and Herman H. Goldstine and John von NeumannReport to the U.S. Army Ordnance Department. Reprinted in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S 8.3]{Randell:1982:ODC}, and \cite[pp.~97146]{Aspray:1987:PJN}Preliminary discussion of the logical design of an electronic computing instrument
@TechReport{Burks:1946:PDL,
author = "Arthur W. Burks and Herman H. Goldstine and John von
Neumann",
title = "Preliminary discussion of the logical design of an
electronic computing instrument",
institution = instINSTADVSTUDY,
address = instINSTADVSTUDY:adr,
pages = "42",
day = "28",
month = jun,
year = "1946",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors'  multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}
!!3W#1S}K7E
;_o=Sgarticlefparith.bibGoldstine:1946:ENIH. H. Goldstine and Adele GoldstineThe Electronic Numerical Integrator and Computer (ENIAC)jMATHTABLESOTHERAIDSCOMPUT21597110jul71946MTTCAS08916837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 7.7]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationacknhfbhttp://www.ams.org/mcom/H. H. Goldstine and Adele GoldstineReprinted in \cite[\S 7.7]{Randell:1982:ODC}.The {Electronic Numerical Integrator and Computer (ENIAC)}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "2",
number = "15",
pages = "97110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "08916837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
}:2Y!#+C;=m;'C/#techreportfparith.bibDreyer:1946:REMH.J. Dreyer and A. WaltherDer Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945. (German) [The Ipm Calculator. The development of mathematical instruments in Germany 19391945]BerichtA3Institut fur Praktische Mathematik, Technische HochschuleDarmstadt, West Germany45746019aug81946Wed Oct 13 11:20:15 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:20:15 ???Reprinted in cite [ 3.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. JonesGermanacknhfbH.J. Dreyer and A. WaltherReprinted in \cite[\S 3.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones{Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945}. ({German}) [{The} {Ipm} Calculator. {The} development of mathematical instruments in {Germany} 19391945]
@TechReport{Dreyer:1946:REM,
author = "H.J. Dreyer and A. Walther",
title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 19391945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
Hochschule",
address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = acknhfb,
language = "German",
}
\5U #'917=m;_=g9Karticlefparith.bibJuley:1947:BCJ. JuleyThe Ballistic ComputerjBELLLABSRECORD24591947BLRCAB00058564 OR 00058564Wed Oct 13 11:32:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:32:38 ???Reprinted in cite [ 6.3]Randell:1982:ODC.Bell Laboratories RecordacknhfbJ. JuleyReprinted in \cite[\S 6.3]{Randell:1982:ODC}.The Ballistic Computer
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author = "J. Juley",
title = "The Ballistic Computer",
journal = jBELLLABSRECORD,
volume = "24",
number = "??",
pages = "59",
year = "1947",
CODEN = "BLRCAB",
ISSN = "00058564",
bibdate = "Wed Oct 13 11:32:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
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fjournal = "Bell Laboratories Record",
}4Y!#1]3;=m;;]Ctechreportfparith.bibGoldstine:1947:PCPHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrumentTechnical report1instINSTADVSTUDYinstINSTADVSTUDY:adr691apr41947Wed Jun 01 17:41:33 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 17:41:33 ???Report prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in cite [80151]Taub:1963:JNCa. Knuth cite [p.~278]Knuth:1997:SA cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.acknhfbHerman H. Goldstine and John von NeumannReport prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in \cite[80151]{Taub:1963:JNCa}. Knuth \cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.Planning and coding of problems for an electronic computing instrument
@TechReport{Goldstine:1947:PCP,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument",
type = "Technical report",
number = "1",
institution = instINSTADVSTUDY,
address = instINSTADVSTUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W36034OKD7481. Reprinted in
\cite[80151]{Taub:1963:JNCa}. Knuth
\cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this
report as the first published treatment of
doubleprecision arithmetic on digital computers.",
acknowledgement = acknhfb,
}
l lD7W #/)[57E;Qo)_
articlefparith.bibRicheson:1947:FAPA. W. RichesonThe First Arithmetic Printed in EnglishjISIS37124756may51947ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:27:09 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302230; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1940.bib2013.07.30 21:27:09 MDThttp://www.jstor.org/stable/226161Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlA. W. RichesonThe First Arithmetic Printed in {English}
@Article{Richeson:1947:FAP,
author = "A. W. Richeson",
title = "The First Arithmetic Printed in {English}",
journal = jISIS,
volume = "37",
number = "12",
pages = "4756",
month = may,
year = "1947",
CODEN = "ISISA4",
ISSN = "00211753 (print), 15456994 (electronic)",
ISSNL = "00211753",
bibdate = "Tue Jul 30 21:27:09 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302230;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1940.bib",
URL = "http://www.jstor.org/stable/226161",
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fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}J6Y '#'Ck=1=m;''G;o?inproceedingsfparith.bibMauchly:1947:PPEJ. W. MauchlyProceedings of a Symposium on Large Scale Digital Calculating Machinery, 710 January 1947Preparation of problems for EDVACtype machinesHarvard University PressCambridge, MA, USA591947Wed Oct 13 11:55:58 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:55:58 ???Reprinted in em Annals of the Computation Laboratory of Harvard University, bf 16, 203207 (1948). Reprinted in cite [ 8.2]Randell:1982:ODC.acknhfbJ. W. Mauchly{Proceedings of a Symposium on Large Scale Digital Calculating Machinery, 710 January 1947}Reprinted in {\em Annals of the Computation Laboratory of Harvard University}, {\bf 16}, 203207 (1948). Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.Preparation of problems for {EDVAC}type machines
@InProceedings{Mauchly:1947:PPE,
author = "J. W. Mauchly",
booktitle = "{Proceedings of a Symposium on Large Scale Digital
Calculating Machinery, 710 January 1947}",
title = "Preparation of problems for {EDVAC}type machines",
publisher = "Harvard University Press",
address = "Cambridge, MA, USA",
year = "1947",
bibdate = "Wed Oct 13 11:55:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in {\em Annals of the Computation Laboratory
of Harvard University}, {\bf 16}, 203207 (1948).
Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}
d
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journal = "arXiv.org",
volume = "??",
number = "??",
pages = "145",
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month = jan,
year = "2012",
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ISSN = "????",
ISSNL = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
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in \cite[v.~5, pp.~479557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
acknowledgement = acknhfb # " and " # ackjg,
fjournal = "Bulletin of the American Mathematical Society",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of doubleprecision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~10351038, the authors show that when
the sum of $m$ products of two $s$digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}8
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@Article{vonNeumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
title = "Numerical Inverting of Matrices of High Order",
journal = jBULLAMS,
volume = "53",
number = "11",
pages = "10211099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "00029904 (print), 1936881X (electronic)",
ISSNL = "00029904",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[v.~5, pp.~479557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
acknowledgement = acknhfb # " and " # ackjg,
fjournal = "Bulletin of the American Mathematical Society",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of doubleprecision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~10351038, the authors show that when
the sum of $m$ products of two $s$digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}
/
ar/\9
@Article{Balasubramaniam:2007:ECS,
author = "P. Balasubramaniam and E. Karthikeyan",
title = "Elliptic curve scalar multiplication algorithm using
complementary recoding",
journal = jAPPLMATHCOMP,
volume = "190",
number = "1",
pages = "5156",
day = "1",
month = jul,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "00963003 (print), 18735649 (electronic)",
ISSNL = "00963003",
bibdate = "Sat Jul 12 09:03:06 MDT 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = acknhfb,
fjournal = "Applied Mathematics and Computation",
journalURL = "http://www.sciencedirect.com/science/journal/00963003",
}+jU
@Article{Bakhrakh:1993:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floatingpoint arithmetic
operations",
journal = jPROGCOMPSOFT,
volume = "18",
number = "6",
pages = "255258",
year = "1993",
CODEN = "PCSODA",
ISSN
jU
@Article{Bakhrakh:1992:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floatingpoint arithmetic
operations. ({Russian})",
journal = jPROGRAMMIROVANIE,
volume = "6",
pages = "1317",
year = "1992",
CODEN = "PROGD3",
ISSN = "01323474, 03617688",
MRclass = "65G05",
MRnumber = "1 227 941",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation appears in
\cite{Bakhrakh:1993:NIF}.",
acknowledgement = acknhfb,
fjournal = "Programmirovanie",
language = "Russian",
}

@Article{Baker:1997:LEP,
author = "Louis Baker",
title = "Letter to the {Editor}: {Pentium II} Math Bug",
journal = jDDJ,
volume = "22",
number = "10",
pages = "1010",
month = oct,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044789X",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Comments on the Ariane 5 missile failure mentioned in
\cite{Collins:1997:IPI}.",
acknowledgement = acknhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Baker:1993:SLR,
author = "Henry G. {Baker, Jr.}",
title = "Safe and leakproof resource management using {Ada83}
limited types",
journal = jSIGADALETTERS,
volume = "13",
number = "5",
pages = "3242",
month = sep # "\slash " # oct,
year = "1993",
CODEN = "AALEE5",
ISSN = "10943641 (print), 15579476 (electronic)",
ISSNL = "10943641",
bibdate = "Sat
;
@Article{Baker:1992:LCE,
author = "H. G. Baker",
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number = "11",
pages = "1516",
month = nov,
year = "1992",
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ISSN = "03621340 (print), 15232867 (print), 15581160
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fjournal = "ACM SIGPLAN Notices",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
{
k
kB;V !#)'S7)1=Q;'S3techreportfparith.bibTukey:1948:NSRJohn W. TukeyA note on the squareroot iterationSRG Memorandum report10instPRINCETONinstPRINCETON:adr181948Tue May 15 08:00:09 2012http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2012.05.15 08:00:09 ???acknhfbJohn W. TukeyA note on the squareroot iteration
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author = "John W. Tukey",
title = "A note on the squareroot iteration",
type = "SRG Memorandum report",
number = "10",
institution = instPRINCETON,
address = instPRINCETON:adr,
pages = "18",
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http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}:U #)%?'7=m;_9%g? articlefparith.bibEckert:1948:ECW. J. EckertElectrons and computationjSCIMONTHLY675315323nov111948SCMOAA00963771 OR 00963771Wed Oct 13 11:27:40 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:27:40 ???Reprinted in cite [ 5.3]Randell:1982:ODC.The Scientific MonthlyacknhfbW. J. EckertReprinted in \cite[\S 5.3]{Randell:1982:ODC}.Electrons and computation
@Article{Eckert:1948:EC,
author = "W. J. Eckert",
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volume = "67",
number = "5",
pages = "315323",
month = nov,
year = "1948",
CODEN = "SCMOAA",
ISSN = "00963771",
bibdate = "Wed Oct 13 11:27:40 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "The Scientific Monthly",
}B9V #'%uK7E
;_o=%g}U
articlefparith.bibAlt:1948:BTLaFranz L. AltA Bell Telephone Laboratories' Computing MachineIjMATHTABLESOTHERAIDSCOMPUT321113jan11948MTTCAS08916837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 6.4]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationacknhfbhttp://www.ams.org/mcom/Franz L. AltReprinted in \cite[\S 6.4]{Randell:1982:ODC}.A {Bell Telephone Laboratories}' Computing Machine{I}
@Article{Alt:1948:BTLa,
author = "Franz L. Alt",
title = "A {Bell Telephone Laboratories}' Computing
Machine{I}",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "3",
number = "21",
pages = "113",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "08916837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
} 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/a/turingalanmathison.bib;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Turing:1992:PM} with summary and
notes (including corrections)",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
ZMnumber = "0033.28501",
acknowledgement = acknhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
}<
y=V#/GE57=m;_WGgEIarticlefparith.bibWilliams:1948:EDCF. C. Williams and T. KilburnElectronic digital computersjNATURE162487????1948NATUAS00280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Wed Oct 13 12:00:02 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:02 ???Reprinted in cite [ 8.4]Randell:1982:ODC.Natureacknhfbhttp://www.nature.com/nature/archive/F. C. Williams and T. KilburnReprinted in \cite[\S 8.4]{Randell:1982:ODC}.Electronic digital computers
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = jNATURE,
volume = "162",
number = "487",
pages = "????",
year = "1948",
CODEN = "NATUAS",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "00280836",
bibdate = "Wed Oct 13 12:00:02 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
}dW #S{=m;SIarticlefparith.bibHartree:1949:NSRDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical IntegrationJournal of Research of the National Bureau of Standards4262??1949Wed Feb 14 19:07:37 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:07:37 ???acknhfbDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical Integration
@Article{Hartree:1949:NSR,
author = "Douglas R. (Douglas Rayner) Hartree",
title = "Note On Systematic Roundoff Errors in Numerical
Integration",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "42",
number = "??",
pages = "62??",
month = "????",
year = "1949",
bibdate = "Wed Feb 14 19:07:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}
SCW '#+'7;Q'=m;_';g?Uinproceedingsfparith.bibWorsley:1950:EDB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949The EDSAC demonstrationUniversity Mathematical LaboratoryCambridge, UK1216jan11950Wed Oct 13 11:39:09 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:39:09 ???Reprinted in cite [ 8.6]Randell:1982:ODC.acknhfbB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, {2225 June 1949}Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.The {EDSAC} demonstration
@InProceedings{Worsley:1950:ED,
author = "B. H. Worsley",
booktitle = "Report of a Conference on High Speed Automatic
Calculating Machines, {2225 June 1949}",
title = "The {EDSAC} demonstration",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "1216",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 11:39:09 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
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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, 2225 June 1949The EDSACUniversity Mathematical LaboratoryCambridge, UK911jan11950Wed Oct 13 12:00:41 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:41 ???Reprinted in cite [ 8.5]Randell:1982:ODC.acknhfbM. V. Wilkes and W. Renwick{Report of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949}Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.The {EDSAC}
@InProceedings{Wilkes:1950:E,
author = "M. V. Wilkes and W. Renwick",
booktitle = "{Report of a Conference on High Speed Automatic
Calculating Machines, 2225 June 1949}",
title = "The {EDSAC}",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "911",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 12:00:41 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}6AW #1E+3!E%;I5Ebookfparith.bibStifler:1950:HSCW. W. Stifler, Jr.Highspeed computing devicespubMCGRAWHILLpubMCGRAWHILL:adrxiii + 4511950QA75 .E5Fri Aug 20 10:18:44 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:18:44 MDTSupervised by Charles Brown Tompkins and C. H. Wakelin, Engineering Research Associates. The contents of this volume were first assembled in the form of a report to the Office of Naval Research, prepared under a provision of contract N6ONR240, Task 1. Cited in cite Sterbenz:1974:FPC.computersacknhfbW. W. {Stifler, Jr.}Highspeed computing devices
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "Highspeed computing devices",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "xiii + 451",
year = "1950",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6ONR240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}
,,\FZ #'i?7=m;9'Ci1
articlefparith.bibGill:1951:PSSS. GillA process for the stepbystep integration of differential equations in an automatic digital computing machinejPROCCAMBRIDGEPHILSOC47961081951PCPSA400081981 OR 00081981Tue Aug 28 05:54:12 2001http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.08.28 05:54:12 ???Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciencesaccurate floatingpoint summation; floatingpoint arithmetic; rounding errorsHigham cite Higham:1993:AFP comments ``In 1951 Gill [8] noticed that the rounding error in the sum of two numbers could be estimated by subtracting one of the numbers from the sum, and he made use of this estimate in a RungeKutta code in a program library for the EDSAC computer.''acknhfbS. GillA process for the stepbystep integration of differential equations in an automatic digital computing machine
@Article{Gill:1951:PSS,
author = "S. Gill",
title = "A process for the stepbystep integration of
differential equations in an automatic digital
computing machine",
journal = jPROCCAMBRIDGEPHILSOC,
volume = "47",
pages = "96108",
year = "1951",
CODEN = "PCPSA4",
ISSN = "00081981",
bibdate = "Tue Aug 28 05:54:12 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
keywords = "accurate floatingpoint summation; floatingpoint
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a RungeKutta code in a program library for the
EDSAC computer.''",
}(EU %#)#K5=m;g#OWincollectionfparith.bibBrown:1951:HRRG. W. BrownHistory of RAND's random digitsHouseholder:1951:MCM31321951Sun Sep 18 12:02:43 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:02:43 ???http://www.rand.org/pubs/papers/2008/P113.pdfacknhfbG. W. BrownHistory of {RAND}'s random digits
@InCollection{Brown:1951:HRR,
author = "G. W. Brown",
title = "History of {RAND}'s random digits",
crossref = "Householder:1951:MCM",
pages = "3132",
year = "1951",
bibdate = "Sun Sep 18 12:02:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.rand.org/pubs/papers/2008/P113.pdf",
acknowledgement = acknhfb,
}GDU #)#]C77;m;y#]{articlefparith.bibBooth:1951:SBMA. D. BoothA signed binary multiplication techniquejQUARTJMECHAPPLIEDMATH422362401951QJMMAV00335614 OR 0033561400335614 OR 00335614Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied MathematicsacksfoA. D. BoothA signed binary multiplication technique
@Article{Booth:1951:SBM,
author = "A. D. Booth",
title = "A signed binary multiplication technique",
journal = jQUARTJMECHAPPLIEDMATH,
volume = "4",
number = "2",
pages = "236240",
month = "????",
year = "1951",
CODEN = "QJMMAV",
ISSN = "00335614",
ISSNL = "00335614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
}
HiV
@Book{Motorola:1985:MFP,
author = "Motorola",
title = "{MC68881} FloatingPoint Coprocessor User's Manual",
publisher = pubMOTOROLA,
address = pubMOTOROLA:adr,
edition = "Second",
year = "1985",
1c
@Book{Miller:2009:RNR,
editor = "Frederic P. Miller and Agnes F. Vandome and John
McBrewster",
title = "Roman Numerals: Roman numeral analysis, Roman
arithmetic, Roman abacus, {Kharosthi}, {Unicode}
numerals, {Etruscan} numerals, Positional notation,
Arabic numerals, Districts of {Turku}",
publisher = "Alphascript Publishing",
address = "17 Rue Meldrum, Beau Bassin, 171301 Mauritius",
pages = "88 (est.)",
year = "2009",
ISBN = "6130064802",
ISBN13 = "9786130064808",
LCCN = "????",
bibdate = "Wed Oct 28 09:06:59 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$50",
acknowledgement = acknhfb,
}+M?
@Book{Morgan:1992:NM,
author = "Don Morgan",
title = R%
@Book{Moore:1988:RCR,
editor = "Ramon E. Moore",
booktitle = "Reliability in computing: the role of interval methods
in scientific computing",
title = "Reliability in computing: the role of interval methods
in scientific computing",
volume = "19",
publisher = pubACADEMIC,
address = pubACADEMIC:adr,
pages = "428",
year = "1988",
ISBN = "0125056303",
ISBN13 = "9780125056304",
LCCN = "????",
bibdate = "Sat Nov 29 11:20:25 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Perspectives in Computing",
acknowledgement = acknhfb,
}1c
@Book{Menninger:1992:NWN,
author = "Karl Menninger",
title = "Number Words and Number Symbols: a Cultural History of
Numbers",
publisher = pubDOVER,
address = pubDOVER:adr,
pages = "xiii + 480",
year = "1992",
ISBN = "0486270963",
ISBN13 = "9780486270968",
LCCN = "QA141.2 .M4513 1992",
bibdate = "Fri Nov 28 18:29:23 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
}
Ƀ8q
@Book{Moore:1966:IA,
author = "Ramon E. Moore",
title = "Interval analysis",
publisher = pubPH,
address = pubPH:adr,
pages = "xi + 145",
year = "1966",
LCCN = "QA297 .M63",
bibdate = "Sat Feb 14 08:15:54 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}c@
@Book{Mood:1963:ITS,
author = "Alexander McFarlane Mood and Franklin A. Graybill",
title = "Introduction to the theory of statistics",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
edition = "Second",
pages = "443",
year = "1963",
LCCN = "HA29 .M75 1963",
bibdate = "Fri Aug 20 10:02:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGrawHill series in probability and statistics",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
}fM
@Book{Mead:1980:IVS,
author = "Carver Mead and Lynn Conway",
title = "Introduction to {VLSI} systems",
publisher = pubAW,
address = pubAW:adr,
pages = "xvi + 396",
year = "1980",
ISBN = "0201043580",
ISBN13 = "9780201043587",
LCCN = "TK7874 .M371",
bibdate = "Mon Sep 16 16:25:00 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}&
qc
@Article{Anonymous:1982:ARBf,
author = "Anonymous",
title = "Article Review: {{\booktitle{Ada model arithmetic:
costs and benefits}}: Wallis, P. J. L. \booktitle{IEE
Proc.E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
pp 7580}",
journal = jMICROPROCMICROSYS,
volume = "6",
number = "9",
pages = "497498",
month = nov,
year = "1982",
CODEN = "MIMID5$&O
@Article{Anonymous:1879:TRA,
author = "Anonymous",
title = "Three Rules for Abbreviating Multiplication",
journal = jSCIAMER,
volume = "41",
number = "12",
pages = "184184",
day = "20",
month = sep,
year = "1879",
CODEN = "SCAMAC",
DOI = "http://dx.doi.org/10.1038/scientificamerican09201879184",
ISSN = "00368733 (print), 19467087 (electronic)",
ISSNL = "00368733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879184.pdf",
acknowledgement = acknhfb,
fjournal = "Scientific American",
journalURL = "http://www.nature.com/scientificamerican",
}τV
@Article{Anonymous:1992:FPa,
author = "Anonymous",
title = "Floating Point",
journal = jCOMPUTAIDEDENG,
volume = "11",
number = "8",
pages = "58??",
month = aug,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "07333536",
ISSNL = "07333536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "OpenGL: The NeWs of 3D Graphics?",
acknowledgement = acknhfb,
fjournal = "Computeraided engineering: CAE",
}
tJ
@Article{Anonymous:1996:IBT,
author = "Anonymous",
title = "Inquiry Board Traces {Ariane 5} Failure to Overflow
Error",
journal = jSIAMNEWS,
volume = "29",
number = "8",
pages = "1, 12, 13",
month = oct,
year = "1996",
ISSN = "00361437",
bibdate = "Sat Apr 28 18:48:53 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.si!C
@Article{Andrews:1982:MMS,
author = "M. Andrews",
title = "Mathematical Microprocessor Software: a $ \sqrt (x) $
Comparison",
journal = jIEEEMICRO,
volume = "2",
number = "3",
pages = "6379",
month = may,
year = "1982",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1982.290970",
ISSN = "02721732 (print), 19374143 (electronic)",
ISSNL = "02721732",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEEE Micro",
journalURL = "http://www.computer.org/csdl/mags/mi/index.html",
}R1qc
@Article{An:1988:CRE,
author = "S. H. An and K. Yao",
title = "Convergent and roundoff error properties of reflection
coefficients in adaptive spatial recursive least
squares lattice algorithm",
journal = jIEEETRANSCIRCUITSSYST,
volume = "35",
number = "2",
pages = "241246",
month = feb,
year = "1988",
CODEN = "ICSYBT",
ISSN = "00984094 (print), 1558127 b/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
keywords = "accurate floatingpoint summation; floatingpoint
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a RungeKutta code in a program library for the
EDSAC computer.''",
}F
9GX#1]o1573%;m;Qym]Ys}articlefparith.bibGoldstine:1951:NIMHerman H. Goldstine and John von NeumannNumerical Inverting of Matrices of High Order. IIjPROCAMMATHSOC21882021951PAMYAR00029939 (print), 10886826 (electronic) OR 00029939 (print), 10886826 (electronic)00029939 OR 0002993965.0XMR0041539 (12,861b)F. J. MurrayThu Nov 8 14:49:46 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:46 ???See cite vonNeumann:1947:NIM for Part I. Reprinted in cite [Paper~15, pp.~558572]Taub:1963:JNCa.http://www.jstor.org/view/00029939/di970628/97p0185x/0Proceedings of the American Mathematical Society043.12301acknhfbHerman H. Goldstine and John von NeumannSee \cite{vonNeumann:1947:NIM} for Part I. Reprinted in \cite[Paper~15, pp.~558572]{Taub:1963:JNCa}.Numerical Inverting of Matrices of High Order. {II}
@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = jPROCAMMATHSOC,
volume = "2",
pages = "188202",
year = "1951",
CODEN = "PAMYAR",
ISSN = "00029939 (print), 10886826 (electronic)",
ISSNL = "00029939",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper~15, pp.~558572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
acknowledgement = acknhfb,
fjournal = "Proceedings of the American Mathematical Society",
}arith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (15601621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = acknhfb,
fjournal = "American Journal of Physics",
journalURL = "http://scitation.aip.org/content/aapt/journal/ajp",
}H
s" bsxq
@InProceedings{Gross:1985:FPA,
author = "Thomas Gross",
title = "FloatingPoint Arithmetic on a ReducedInstructionSet
Processor",
crossref = "Hwang:1985:PSC",
pages = "8692",
year = "1985",
bibdate = "Thu Sep 01 12:02:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmeticɆ
@InProceedings{Grnarov:1983:LMN,
author = "A. L. Grnarov and M. D. Ercegovac",
title = "Online multiplicative normalization",
crossref = "IEEE:1983:PSC",
pages = "151155",
year = "1983",
bibdate = "Tue Nov 13 15:44:54 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith6/papers/ARITH6_Grnarov_Ercegovac.pdf",
abstract = "In this article we describe a derivation and an
algorithm for online multiplicative normalization of
fractions. The algorithm is a variation of the
continued product normalization algorithm and it is
used for online evaluation of elementary functions.",
acknowledgement = acknhfb,
keywords = "ARITH6; elementary functions; online arithmetic",
}ȉ%K
@InProceedings{Griffin:1989:RNS,
author = "M. F. Griffin and F. J. Taylor",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, ICASSP89, 2326 May 1989",
title = "A residue number system reduced instruction set
computer ({RISC}) concept",
volume = "4",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "25812584",
year = "1989",
CODEN = "?
{w
@InProceedings{Griffin:1989:ESR,
author = "M. Griffin and M. Sousa and F. Taylor",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, ICASSP89, 2326 May 1989",
title = "Efficient scaling in the residue number system",
volume = "2",
publisher = pubIEEE,
address = pubIEEE:adr,
pages = "10751078",
year = "1989",
CODEN = "????",
DOI = "http://dx.doi
_?
@InProceedings{Gridley:1985:IPS,
author = "Curt Gridley",
title = "Improving the Performance of Scientific Applications
on a Supermicro Using a Custom Floating Point Processor
and An Optimizing Compiler",
crossref = "USENIX:1985:SCP",
pages = "597610",
year = "1985",
bibdate = "Tue Feb 20 15:42:13 MST 1996",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
affiliation = "Massachusetts Computer Corp.",
}re
@InProceedings{Gregory:1981:RAR,
author = "R. T. Gregory",
title = "Residue Arithmetic with Rational Operands",
crossref = "IEEE:1981:PSC",
pages = "144145",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith5/papers/ARITH5_Gregory.pdf",
abstract = "A method is described for doing residue arithmÊaC
@InProceedings{Gregory:1975:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base Conversion in Residue Number Systems",
crossref = "IEEE:1975:SCA",
pages = "117125",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith3/papers/ARITH3_Gregory.pdf",
abstract = "We are concerned in q
HY #+MS57m{Co{+QYarticlefparith.bibShirley:1951:BNBJohn W. ShirleyBinary Numeration before LeibnizjAMERJPHYSICS1984524541951AJPIAShttp://dx.doi.org/10.1119/1.193304200029505 (print), 19432909 (electronic) OR 00029505 (print), 19432909 (electronic)00029505 OR 00029505http://www.math.utah.edu/pub/tex/bib/fparith.bibhttp://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042Though it is frequently stated that binary numeration was first formally proposed by Leibniz as an illustration of his dualistic philosophy, the mathematical papers of Thomas Hariot (15601621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.American Journal of Physicsacknhfbhttp://scitation.aip.org/content/aapt/journal/ajpThough it is frequently stated that binary numeration was first formally proposed by Leibniz as an illustration of his dualistic philosophy, the mathematical papers of Thomas Hariot (15601621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.John W. ShirleyBinary Numeration before {Leibniz}
@Article{Shirley:1951:BNB,
author = "John W. Shirley",
title = "Binary Numeration before {Leibniz}",
journal = jAMERJPHYSICS,
volume = "19",
number = "8",
pages = "452454",
year = "1951",
CODEN = "AJPIAS",
DOI = "http://dx.doi.org/10.1119/1.1933042",
ISSN = "00029505 (print), 19432909 (electronic)",
ISSNL = "00029505",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (15601621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = acknhfb,
fjournal = "American Journal of Physics",
journalURL = "http://scitation.aip.org/content/aapt/journal/ajp",
}pubACM,
address = pubACM:adr,
pages = "101105",
year = "1952",
DOI = "http://dx.doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
bookpages = "vi + 114",
keywords = "Bell Laboratories Model 15 relay computers; complex
fixedpoint decimal arithmetic; complex floatingpoint
decimal arithmetic",
}I
fJU#)]Y/77=m;e]Yearticlefparith.bibDavis:1952:ARSK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken DigitsjJACOUSTSOCAM246637642nov111952JASMAN00014966 OR 0001496600014966 OR 00014966Fri Nov 28 16:38:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 16:38:51 ???Journal of the Acoustical Society of AmericaackmfcK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken Digits
@Article{Davis:1952:ARS,
author = "K. Davis and R. Biddulph and S. Balashek",
title = "Automatic Recognition of Spoken Digits",
journal = jJACOUSTSOCAM,
volume = "24",
number = "6",
pages = "637642",
month = nov,
year = "1952",
CODEN = "JASMAN",
ISSN = "00014966",
ISSNL = "00014966",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ackmfc # " and " # acknhfb,
fjournal = "Journal of the Acoustical Society of America",
}gIZ '#'+
#_=m;'+inproceedingsfparith.bibAndrews:1952:RBLE. G. AndrewsJ. C. McPhersonProceedings of the AIEEIRE '51: Papers and discussions presented at the December 1012, 1951, joint AIEEIRE computer conference, Philadelphia, PA: Review of electronic digital computersA review of the Bell Laboratories' digital computer developmentspubACMpubACM:adr1011051952http://dx.doi.org/10.1145/1434770.1434787Fri Dec 03 09:17:58 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.12.03 09:17:58 ???Bell Laboratories Model 15 relay computers; complex fixedpoint decimal arithmetic; complex floatingpoint decimal arithmeticacknhfbvi + 114E. G. AndrewsProceedings of the AIEEIRE '51: Papers and discussions presented at the December 1012, 1951, joint AIEEIRE computer conference, Philadelphia, PA: Review of electronic digital computersJ. C. McPhersonA review of the {Bell Laboratories}' digital computer developments
@InProceedings{Andrews:1952:RBL,
author = "E. G. Andrews",
editor = "J. C. McPherson",
booktitle = "Proceedings of the AIEEIRE '51: Papers and
discussions presented at the December 1012, 1951,
joint AIEEIRE computer conference, Philadelphia, PA:
Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
publisher = pubACM,
address = pubACM:adr,
pages = "101105",
year = "1952",
DOI = "http://dx.doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
bookpages = "vi + 114",
keywords = "Bell Laboratories Model 15 relay computers; complex
fixedpoint decimal arithmetic; complex floatingpoint
decimal arithmetic",
}
l= (9J[l1c
@Article{Metropolis:1980:SIN,
author = "N. Metropolis",
title = "Summation of imprecise numbers",
journal = jCOMPMATHAPPL,
volume = "6",
number = "3",
pages = "297299",
year = "1980",
CODEN = "CMAPDK",
DOI = "http://dx.doi.org/10.1016/08981221(80)900371",
ISSN = "08981221 (print), 18737668 (electronic)",
ISSNL = "08981221",
MRclass = "65U05",
MRnumber = "MR6040j
@Article{Metropolis:1977:SAP,
author = "N. Metropolis and Stephen M. Tanny",
title = "Significance arithmetic: the probability of carrying",
journal = jCOMPMATHAPPL,
volume = "3",
number = "1",
pages = "7781",
year = "1977",
CODEN = "CMAPDK",
ISSN = "08869561",
ISSNL = "08981221",
MRclass = "65G05 (10A30 65C10)",
MRnumber = "MR0458846 (56 \#17046)",
MRreviewer = "Artenio<1
@Article{Metropolis:1973:SAC,
author = "N. Metropolis and GianCarlo Rota and S. Tanny",
title = "Significance arithmetic: the carrying algorithm",
journal = jJCOMBTHEORYA,
volume = "14",
pages = "386421",
month = may,
year = "1973",
CODEN = "JCBTA7",
ISSN = "00973165",
ISSNL = "00973165",
MRclass = "10A30 (02E10)",
MRnumber = "MR0321857 (48 \#222)",
MRreviewer = "R. LfM
@Article{Metropolis:1973:ABC,
author = "Nicholas C. Metropolis",
title = "Analyzed Binary Computing",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "6",
pages = "573576",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009109",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Wed M'
@Article{Metropolis:1968:ANA,
author = "N. Metropolis",
title = "Algorithms in unnormalized arithmetic: Polynomial
evaluation and matrix decomposition",
journal = "Colloques internationaux, Centre National de la
Recherche Scientifique, Paris",
volume = "165",
pages = "293303",
year = "1968",
bibdate = "Wed Nov 14 19:04:40 2007",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0207.15804",
acknowledgement = acknhfb,
classmath = "*65H05 (Single nonlinear equations (numerical
methods)) 65F05 (Direct methods for linear systems)",
}A
@Article{Metropolis:1965:RCU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Radix Conversion in an Unnormalized Arithmetic
System",
journal = jMATHCOMPUT,
volume = "19",
number = "91",
pages = "435441",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
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ZMnumber = "0146.14607",
acknowledgement = acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}9
*
g*yMW'#AQga/=m;_AYgkIinproceedingsfparith.bibSheldon:1952:ICPJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint AIEEIRE Computer Confer ence. 1012 December 1951The IBM cardprogrammed electronic calculatorAmerican Institute of Electrical EngineersNew York, NY, USA30361952Wed Oct 13 11:28:45 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:28:45 ???Reprinted in cite [ 5.4]Randell:1982:ODC.acknhfbJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint {AIEEIRE} Computer Confer ence. {1012 December 1951}Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.The {IBM} cardprogrammed electronic calculator
@InProceedings{Sheldon:1952:ICP,
author = "J. W. Sheldon and L. Tatum",
booktitle = "Review of Electronic Digital Computers. Joint
{AIEEIRE} Computer Confer ence. {1012 December
1951}",
title = "The {IBM} cardprogrammed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "3036",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}>LW#EQQ=a;EQearticlefparith.bibMorrill:1952:SEMC. D. Morrill and R. V. BaumA Stabilized Electronic MultiplierjTRANSIREPROFGROUPELECCOMPUTEC15259dec121952Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic ComputersacknhfbC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplier
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC1",
number = "??",
pages = "5259",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = acknhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}KV #1/!O77E#;SGc/articlefparith.bibMichaelson:1952:BAR. L. MichaelsonBinary ArithmeticjINCSTAT313540feb21952http://dx.doi.org/10.2307/298659114669404 OR 1466940414669404 OR 14669404Thu Jan 22 18:10:18 MST 2015http://www.jstor.org/stable/i349863; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrssd1950.bib2015.01.22 18:10:18 MSThttp://www.jstor.org/stable/2986591The Incorporated Statisticianacknhfbhttp://www.jstor.org/journals/14669404.htmlR. L. MichaelsonBinary Arithmetic
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = jINCSTAT,
volume = "3",
number = "1",
pages = "3540",
month = feb,
year = "1952",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2986591",
ISSN = "14669404",
ISSNL = "14669404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrssd1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = acknhfb,
fjournal = "The Incorporated Statistician",
journalURL = "http://www.jstor.org/journals/14669404.html",
}
::%OY #+%I57=m;'1e%MMarticlefparith.bibBackus:1954:ISSJ. W. BackusThe IBM 701 Speedcoding SystemjJACM1146jan11954JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4backus.pdfThe IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a threeaddress floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and builtin checking.Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401The IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a threeaddress floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and builtin checking.J. W. BackusThe {IBM 701 Speedcoding} System
@Article{Backus:1954:ISS,
author = "J. W. Backus",
title = "The {IBM 701 Speedcoding} System",
journal = jJACM,
volume = "1",
number = "1",
pages = "46",
month = jan,
year = "1954",
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ISSN = "00045411 (print), 1557735X (electronic)",
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bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
threeaddress floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
builtin checking.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}NW #%+#=m;/7bookfparith.bibIBM:1953:POTIBM CorporationPrinciples of Operation: Type 701 and Associated EquipmentpubIBMpubIBM:adr1031953Wed Sep 14 23:17:49 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.14 23:17:49 ???acknhfb{IBM Corporation}Principles of Operation: Type 701 and Associated Equipment
@Book{IBM:1953:POT,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
Equipment",
publisher = pubIBM,
address = pubIBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
threeaddress floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
builtin checking.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}Ond coding manual  Datatron
operation manual  Central computer handbook 
Paper tape system handbook  Card converter Model 500
handbook  Magnetic tape system handbook 
Cardatron system handbook  Model 560 DATAFILE
handbook  Control console and consolette handbook
 Floating point control unit handbook  External
switching unit handbook  Tape preparation unit
handbook.",
}P
WWXQX#?WQ=a;[?[Earticlefparith.bibFreeman:1954:TSAH. Freeman and E. ParsonsTimeSharing Analog Multiplier (TSAM)jTRANSIREPROFGROUPELECCOMPUTEC311117mar31954Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic ComputersCited in US Patent 3,043,516 (10 July 1962): Time Summing Device for Division, Multiplication, Root Taking and Interpolation, by Harold W. Abbott and Vernon P. Mathis.acknhfbH. Freeman and E. ParsonsTimeSharing Analog Multiplier ({TSAM})
@Article{Freeman:1954:TSA,
author = "H. Freeman and E. Parsons",
title = "TimeSharing Analog Multiplier ({TSAM})",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC3",
number = "1",
pages = "1117",
month = mar,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = acknhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
remark = "Cited in US Patent 3,043,516 (10 July 1962): Time
Summing Device for Division, Multiplication, Root
Taking and Interpolation, by Harold W. Abbott and
Vernon P. Mathis.",
}KPV #/Q1%/Em;3WU1
manualfparith.bibBurroughs:1954:DHBurroughs Corporation. ElectroDataDatatron handbooksThe DivisionPasadena, CA, USA461954Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MST12 volumes in 1.Datatron (Computer)Datatron programming and coding manual  Datatron operation manual  Central computer handbook  Paper tape system handbook  Card converter Model 500 handbook  Magnetic tape system handbook  Cardatron system handbook  Model 560 DATAFILE handbook  Control console and consolette handbook  Floating point control unit handbook  External switching unit handbook  Tape preparation unit handbook.acknhfb{Burroughs Corporation. ElectroData}12 volumes in 1.Datatron handbooks
@Manual{Burroughs:1954:DH,
author = "{Burroughs Corporation. ElectroData}",
title = "Datatron handbooks",
organization = "The Division",
address = "Pasadena, CA, USA",
year = "1954",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1.",
acknowledgement = acknhfb,
keywords = "Datatron (Computer)",
remark = "Datatron programming and coding manual  Datatron
operation manual  Central computer handbook 
Paper tape system handbook  Card converter Model 500
handbook  Magnetic tape system handbook 
Cardatron system handbook  Model 560 DATAFILE
handbook  Control console and consolette handbook
 Floating point control unit handbook  External
switching unit handbook  Tape preparation unit
handbook.",
}
G;TV#)g[;7=a;]g['articlefparith.bibMayer:1954:ODFM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback dividerjIRETRANSELECCOMPUTEC311720mar31954IRELAO03679950 OR 03679950Sun Jul 17 09:52:58 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:52:58 ???IRE Transactions on Electronic ComputersacknhfbM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback divider
@Article{Mayer:1954:ODF,
author = "M. A. Mayer and B. M. Gordon and R. N. Nicola",
title = "An operational digital feedback divider",
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volume = "EC3",
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pages = "1720",
month = mar,
year = "1954",
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fjournal = "IRE Transactions on Electronic Computers",
}5SW#+AQQ=a;AQ]articlefparith.bibKovach:1954:AMUL. D. Kovach and W. ComleyAn Analog Multiplier Using ThyritejTRANSIREPROFGROUPELECCOMPUTEC324245jun61954Sun Jul 17 09:57:13 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:57:13 ???Transactions of the I.R.E. Professional Group on Electronic ComputersacknhfbL. D. Kovach and W. ComleyAn Analog Multiplier Using Thyrite
@Article{Kovach:1954:AMU,
author = "L. D. Kovach and W. Comley",
title = "An Analog Multiplier Using Thyrite",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC3",
number = "2",
pages = "4245",
month = jun,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Jul 17 09:57:13 2011",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
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}6RX #'y5E
;y9
articlefparith.bibGorn:1954:AACSaul GornThe Automatic Analysis and Control of Computing ErrorsjJSIAM226981jun61954JSIMAV03684245 (print), 1095712X (electronic) OR 03684245 (print), 1095712X (electronic)Thu Oct 15 18:16:06 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.15 18:16:06 MDTJournal of the Society for Industrial and Applied MathematicsacknhfbSaul GornThe Automatic Analysis and Control of Computing Errors
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author = "Saul Gorn",
title = "The Automatic Analysis and Control of Computing
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journal = jJSIAM,
volume = "2",
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pages = "6981",
month = jun,
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CODEN = "JSIMAV",
ISSN = "03684245 (print), 1095712X (electronic)",
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Mathematics",
}
6MM
gO
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}>
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@Article{Stevenson:1981:ITP,
author = "David Stevenson",
title = "{IEEE Task 754}: a Proposed Standard for Binary
FloatingPoint Arithmetic: Draft 8.0",
journal = jCOMPUTER,
volume = "14",
number = "3",
pages = "5162",
month = mar,
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month = sep,
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month = feb,
year = "1984",
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author = "W. J. (Wallace John) Eckert and Rebecca Bradley
Jones",
title = "Faster, faster; a simple description of a giant
electronic calculator and the problems it solves",
publisher = pubIBM,
address = pubIBM:adr,
pages = "160",
year = "1955",
LCCN = "QA76 .E25",
bibdate = "Fri Aug 20 08:57:56 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
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xxpublisher = pubMCGRAWHILL,
}VV#/IM%57=m;IMIM{articlefparith.bibCrockett:1955:GMMJ. B. Crockett and H. ChernoffGradient Methods of MaximizationjPACJMATH533501955PJMAAI00308730 (print), 19455844 (electronic) OR 00308730 (print), 19455844 (electronic)00308730 OR 00308730Fri Aug 20 08:54:24 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 08:54:24 ???Pacific Journal of MathematicsCited in cite Sterbenz:1974:FPC.acknhfbJ. B. Crockett and H. ChernoffGradient Methods of Maximization
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author = "J. B. Crockett and H. Chernoff",
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number = "??",
pages = "3350",
year = "1955",
CODEN = "PJMAAI",
ISSN = "00308730 (print), 19455844 (electronic)",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}5UX #%57=m;1Oe%=articlefparith.bibMoshman:1954:GPRJack MoshmanThe Generation of PseudoRandom Numbers on a Decimal CalculatorjJACM128891apr41954JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???Journal of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Jack MoshmanThe Generation of PseudoRandom Numbers on a Decimal Calculator
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author = "Jack Moshman",
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Calculator",
journal = jJACM,
volume = "1",
number = "2",
pages = "8891",
month = apr,
year = "1954",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
}
nnfZX #1W57=m;1e1Warticlefparith.bibParsons:1955:SDCFrances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic OperationsjJACM23205207jul71955JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Wed Nov 09 01:00:34 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.09 01:00:34 ???Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Frances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic Operations
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author = "Frances L. Parsons",
title = "A Simple DeskCalculator Method for Checking Binary
Results of Digital Computer Arithmetic Operations",
journal = jJACM,
volume = "2",
number = "3",
pages = "205207",
month = jul,
year = "1955",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Wed Nov 09 01:00:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}dYV #/)=)7;K;9)=articlefparith.bibLenaerts:1955:ASRE. H. LenaertsAutomatic Square RootingjELECTRONENG27287289jul71955ELEGAP00134902 OR 00134902Thu Sep 1 10:15:41 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:41 ???Electronic EngineeringacknjE. H. LenaertsAutomatic Square Rooting
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pages = "287289",
month = jul,
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bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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author = "Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and
James P. {Wong, Jr.}",
title = "Approximations for Digital Computers",
publisher = pubPRINCETON,
address = pubPRINCETON:adr,
pages = "viii + 201",
year = "1955",
LCCN = "QA76 .H33",
bibdate = "Mon Sep 30 14:51:50 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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}
:
9
@Article{Gorn:1954:AAC,
author = "Saul Gorn",
title = "The Automatic Analysis and Control of Computin&M
@Article{Goldstein:1963:SAD,
author = "Max Goldstein",
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(Q
@Article{Goldstine:1996:ENI,
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@Article{Gomez:1985:PFA,
author = "Gustavo Rodr{\'\i}guez G{\'o}mez and David {Carrasco
Villareal}",
title = "Problems in floatingpoint arithmetic, and a method
for obtaining internal characteristics of digital
computers. ({Spanish})",
journal = "Miscel{\'a}nea Mat.",
volume = "15",
pages = "1525",
year = "1985",
MRclass = "65G05",
MRnumber = "86h:65060",
bibdate = "Fri Dec 8 08:24:13 1995",
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language = "Spanish",
}=}
@Article{Goldstine:1951:NIM,
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}G
@Article{Goldstine:1946:ENI,
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title = "Arithmetic Operations in Digital Computers",
publisher = "D. Van Nostrand",
address = "New York, NY, USA",
pages = "iv + 397",
year = "1955",
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`X #)?57=m;1Oqe)Ggarticlefparith.bibPerkins:1956:EPCRobert PerkinsEASIAC, A PseudoComputerjJACM326572apr41956JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 23:46:26 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 23:46:26 ???One of the primary functions of the MIDAC installation at the University of Michigan is the instru^J_W #//A;a7Ea;]/A articlefparith.bibLilamand:1956:TDMM. Lejet LilamandA TimeDivision MultiplierjIRETRANSELECCOMPUTEC512634mar31956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.521978903679950 OR 03679950Thu Jun 30 15:46:18 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:18 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789IRE Transactions on Electronic ComputersacknhfbM. Lejet LilamandA TimeDivision Multiplier
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subject = "Numerical analysis",
}ib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
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keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}`ction of beginners in the various aspects of digital machine use including programming and coding. ldots In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. ldots To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Journal of the ACMdecimal floatingpoint arithmeticEarly example of a decimal floatingpoint machine.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401One of the primary functions of the MIDAC installation at the University of Michigan is the instruction of beginners in the various aspects of digital machine use including programming and coding. \ldots{} In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. \ldots{} To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Robert Perkins{EASIAC}, {A} PseudoComputer
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author = "Robert Perkins",
title = "{EASIAC}, {A} PseudoComputer",
journal = jJACM,
volume = "3",
number = "2",
pages = "6572",
month = apr,
year = "1956",
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ISSNL = "00045411",
bibdate = "Fri Nov 04 23:46:26 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}
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bibdate = "Tue Sep 13 09:05:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "ACM SIGNUM Newsletter",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
} ?
@Article{Du:1973:CSS,
author = "MinWen Du and C. Dennis Weiss",
title = "Circuit Structure and Switching Function
Verification",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "6",
pages = "618625",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009116",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH2",
}
00LY#3eY577+={;3q!e3eYarticlefparith.bibAshenhurst:1959:UFPRobert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point ArithmeticjJACM63415428jul71959JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541168.00MR0105833 (21 \#4568)H. H. GoldstineFri Dec 08 13:06:24 1995http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:06:24 ???Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Journal of the Association for Computing Machinery0121.12102acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Robert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point Arithmetic
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = jJACM,
volume = "6",
number = "3",
pages = "415428",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of onestage
error propagation is developed for each operation; a
suggested statistical model for longrun error
propagation is also set forth.",
acknowledgement = acknhfb,
fjournal = "Journal of the Association for Computing Machinery",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
} bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
W #'c57E;?c1c!articlefparith.bibCarr:1959:EAFJohn W. Carr IIIError Analysis in Floating Point ArithmeticjCACM251015may51959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:23 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:23 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79John W. {Carr III}Error Analysis in Floating Point Arithmetic
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = jCACM,
volume = "2",
number = "5",
pages = "1015",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a;
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acknowledgement = acknhfb,
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}Y #//57Eo;?Oc/ articlefparith.bibBuchholz:1959:FFCWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)jCACM2123111959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Mon Jan 22 06:28:45 MST 2001http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 06:28:45 MSTCommunications of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Wilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
title = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = jCACM,
volume = "2",
number = "12",
pages = "311",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
0*U #'U;7=m;]O'Y?articlefparith.bibDaggett:1959:DBCD. H. DaggettDecimalBinary Conversions in CORDICjIRETRANSELECCOMPUTEC85335339sep91959IRELAO03679950 OR 03679950Thu Sep 08 08:14:00 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:00 ???IRE Transactions on Electronic Computersdecimal floatingpoint arithmeticacknjD. H. DaggettDecimalBinary Conversions in {CORDIC}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
title = "DecimalBinary Conversions in {CORDIC}",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "5",
pages = "335339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floatingpoint arithmetic",
}LW %#%ym9'!=%;!;{1my!9[incollectionfparith.bibCarr:1959:PCJohn W. Carr IIIEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeHandbook of Automation, Computation, and ControlProgramming and CodingpubWILEYpubWILEY:adr10151959TJ213 .G72Fri Aug 20 08:41:16 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 08:41:16 ???Chapter 2.19581961: Volume 1. Control fundamentals. Volume 2. Computers and data processing. Volume 3. Systems and components. Cited in cite Sterbenz:1974:FPC.automation; mathematics; computers; operations researchacknhfbJohn W. {Carr III}Handbook of Automation, Computation, and ControlEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeChapter 2.Programming and Coding
@InCollection{Carr:1959:PC,
author = "John W. {Carr III}",
editor = "Eugene M. Grabbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pubWILEY,
address = pubWILEY:adr,
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = acknhfb,
bookpages = "????",
remark = "19581961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}
@
@ /%KfM
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author = "P. Ienne and M. A. Viredaz",
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volume = "43",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=338107",
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fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}re
@Article{Ide:2000:GMF,
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Shin ichi Yoshioka and Hiroaki Murakami and Atsushi
Kunimatsu and Toshinori Sato and Takayuki Kamei and
Toyoshi Okada and Masakazu Suzuoki",
title = "{2.44 GFLOPS 300MHz} FloatingPoint VectorProcessing
Unit for HighPerformance {$3$D} Graphics Computing",
journal = jIEEEJSOLIDSTATECIRCUITS,
volumv8q
@Article{Ikebe:1965:NTP,
author = "Yasuhiko Ikebe",
title = "Note on TriplePrecision FloatingPoint Arithmetic
with 132Bit Numbers",
journal = jCACM,
volume = "8",
number = "3",
pages = "175177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "68.00",
MRnumber = "30\#2701
@Article{Ignatowski:1994:CNA,
author = "R. Ignatowski and E. E. Swartzlander",
title = "Creating New Algorithms and Modifying Old Algorithms
to Use the Variable Precision Floating Point
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journal = "Conference record",
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year = "1994",
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}2e
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year = "1983",
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ISSN = "00127515, 03646637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "EDN",
}
Vs
W #/1]'O577EI;#1!C%1]Aarticlefparith.bibForsythe:1959:RNRGeorge E. ForsytheReprint of a Note on RoundingOff ErrorsjSIAMREVIEW1166671959SIREADhttp://dx.doi.org/10.1137/100101100361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 0036144565.00MR0099119 (20 \#5563)Thu Mar 27 09:04:24 MDT 2014http://epubs.siam.org/toc/siread/1/1; http://www.math.utah.edu/pub/bibnet/authors/f/forsythegeorgeelmer.bib; http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:04:24 MDTSIAM Reviewnumerical analysis0168.14002acknhfbhttp://epubs.siam.org/sirevJanuary 1959George E. ForsytheReprint of a Note on RoundingOff Errors
@Article{Forsythe:1959:RNR,
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title = "Reprint of a Note on RoundingOff Errors",
journal = jSIAMREVIEW,
volume = "1",
number = "1",
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month = "????",
year = "1959",
CODEN = "SIREAD",
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http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib;
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ZMnumber = "0168.14002",
acknowledgement = acknhfb,
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journalURL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis",
onlinedate = "January 1959",
}& Y#+I!57E;?cI!)articlefparith.bibErcoli:1959:BADPaolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial ComputerjCACM241315apr41959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#ErcoliV59; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Paolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial Computer
@Article{Ercoli:1959:BAD,
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title = "Binary Arithmetic for Discretely Variable Word Length
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journal = jCACM,
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pages = "1315",
month = apr,
year = "1959",
CODEN = "CACMA2",
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bibdate = "Wed Jul 14 15:48:22 MDT 2004",
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S SW #+?;a7E;]?aarticlefparith.bibGarner:1959:RNSHarvey L. GarnerThe Residue Number SystemjIRETRANSELECCOMPUTEC82140147jun61959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.521951503679950 OR 03679950Thu Jul 14 15:56:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515IRE Transactions on Electronic ComputersacknhfbHarvey L. GarnerThe Residue Number System
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "2",
pages = "140147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5219515",
ISSN = "03679950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}Y #+;a7E;]Oarticlefparith.bibGarner:1959:RMSHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement CodesjIRETRANSELECCOMPUTEC812530mar31959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.522275703679950 OR 03679950Thu Jul 14 15:56:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757IRE Transactions on Electronic ComputersacknhfbHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement Codes
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "1",
pages = "2530",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5222757",
ISSN = "03679950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
Y '#''U=m;M''Uinproceedingsfparith.bibHenrici:1959:TESPeter HenriciProceedings of the International Conference on Information Processing, UNESCOTheoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations36431959Fri Aug 20 09:11:32 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:11:32 ???Cited in cite Sterbenz:1974:FPC.acknhfbPeter HenriciProceedings of the International Conference on Information Processing, UNESCOTheoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations
@InProceedings{Henrici:1959:TES,
author = "Peter Henrici",
editor = "????",
booktitle = "Proceedings of the International Conference on
Information Processing, UNESCO",
title = "Theoretical and Experimental Studies on the
Accumulation of Error in the Numerical Solution of
Initial Value Problems for Systems of Ordinary
Differential Equations",
publisher = "????",
address = "????",
pages = "3643",
year = "1959",
LCCN = "????",
bibdate = "Fri Aug 20 09:11:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}e
Y'#'A7'%=m;A7einproceedingsfparith.bibGray:1959:NFPH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, MA, December 13, 1959Normalized floatingpoint arithmetic with an index of significance16pubAFIPSpubAFIPS:adr2442481959TK7885.A1 J6Tue Oct 09 09:43:31 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.10.09 09:43:31 ???acknhfbH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, MA, December 13, 1959Normalized floatingpoint arithmetic with an index of significance
@InProceedings{Gray:1959:NFP,
author = "H. L. Gray and C. Harrison",
booktitle = "Proceedings of the Eastern Joint Computer Conference,
Boston, MA, December 13, 1959",
title = "Normalized floatingpoint arithmetic with an index of
significance",
volume = "16",
publisher = pubAFIPS,
address = pubAFIPS:adr,
pages = "244248",
year = "1959",
LCCN = "TK7885.A1 J6",
bibdate = "Tue Oct 09 09:43:31 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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W W #)!57E1;?c!articlefparith.bibGurzi:1960:HSMFred GurziA HighSpeed Multiplication Process for Digital ComputersjCACM34241245apr41960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:26 MST 2005http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Gurzi60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:26 MSTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Fred GurziA HighSpeed Multiplication Process for Digital Computers
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author = "Fred Gurzi",
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}YY #+%57E5;??c%Ccarticlefparith.bibErcoli:1960:LEEPaolo ErcoliLetter to the Editor: Errors Due to Overflow in Arithmetic OperationsjCACM312A9A9dec121960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:29 MSTSee cite Ercoli:1957:EDO.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Paolo ErcoliSee \cite{Ercoli:1957:EDO}.Letter to the {Editor}: {Errors} Due to Overflow in Arithmetic Operations
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x!X !#+%m%1Em;m9%mktechreportfparith.bibJensen:1960:CIFB. A. JensenCoding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functionsGroup report30G0009Massachusetts Institute of Technology, Lincoln LaboratoryLexington, MA, USA71960Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTTrigonometrical functions  Computer programs.Cover title. ``Millstone Hill Radar Station.'' ``1 November 1960.'' Air Force ContractacknhfbB. A. JensenCoding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functions
@TechReport{Jensen:1960:CIF,
author = "B. A. Jensen",
title = "Coding instructions for floating point trigonometric,
inverse trigonometric hyperbolic and exponential
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type = "Group report",
number = "30G0009",
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Laboratory",
address = "Lexington, MA, USA",
pages = "7",
year = "1960",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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remark = "Cover title. ``Millstone Hill Radar Station.'' ``1
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bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Knuth60;
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note = "Errata, {\sl Commun\i\ca\tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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"[ #)+A57E[;7q?cq+WAarticlefparith.bibKnuth:1960:INSDonald E. KnuthAn Imaginary Number SystemjCACM34245247apr41960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.9923\#B554C. B. HaselgroveFri Nov 25 18:19:26 MST 2005http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Knuth60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database2005.11.25 18:19:26 MSTErrata, sl Communications of the ACM bf 4 (August 1961), 355 cite Knuth:1961:EIN. See cite Nadler:1961:DSR for extension to division and square root.For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.Donald E. KnuthErrata, {\sl Commun\i\ca\tions of the ACM\/ \bf 4} (August 1961), 355 \cite{Knuth:1961:EIN}. See \cite{Nadler:1961:DSR} for extension to division and square root.An Imaginary Number System
@Article{Knuth:1960:INS,
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http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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note = "Errata, {\sl Commun\i\ca\tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
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author = "I. E. Perlin and J. R. Garrett",
title = "High Precision Calculation of $ \operatorname {Arcsin}
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@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
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}(W#'AG57;K;?cAGarticlefparith.bibPope:1960:MPAD. A. Pope and M. L. SteinMultiple Precision ArithmeticjCACM312652654dec121960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:15:08 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:08 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79D. A. Pope and M. L. SteinMultiple Precision Arithmetic
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author = "D. A. Pope and M. L. Stein",
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}?+Y #+'57E5;?ac'karticlefparith.bibSilver:1960:LERRoland SilverLetter to the Editor: Rounding in FloatingPoint ArithmeticjCACM312A9A9dec121960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:29 MSTCommunications of the ACMfloatingpoint arithmetic; rounding errorsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Roland SilverLetter to the {Editor}: Rounding in FloatingPoint Arithmetic
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author = "Roland Silver",
title = "Letter to the {Editor}: Rounding in FloatingPoint
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@Article{Wilson:1988:FPS,
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month = mar,
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acknowledgement = acknhfb,
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@Article{Wilson:1970:OSA,
author = "M. Wayne Wilson",
title = "Optimal Starting Approximations for Generating Square
Root for Slow or No Divide",
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@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",
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@Article{Williams:1995:SBA,
author = "T. Williams and N. Patkar and G. Shen",
title = "{SPARC64}: a 64b 64activeinstruction
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@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
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@Article{Williamson:1985:NAB,
author = "D. Williamson and S. Sridharan and P. McCrea",
title = "A new approach for block floatingpoint arithmetic in
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pages = "719722",
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year = "1985",
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note = "See \cite{Sarafyan:1959:NMC}.",
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((TY #)#S57E1;C?c#GWkarticlefparith.bibTraub:1960:CNMJ. F. TraubComments on a recent paper [``A New Method of Computation of Square Roots Without Using Division'']jCACM328686feb21960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:25 MST 2005http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:25 MSTSee cite Sarafyan:1959:NMC.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79J. F. TraubSee \cite{Sarafyan:1959:NMC}.Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]
@Article{Traub:1960:CNM,
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abstract = "Three types of floatingpoint arithmetics with error
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h,h@/W #1+e!577=;7U+emarticlefparith.bibWilkinson:1960:EAFJ. H. WilkinsonError Analysis of FloatingPoint ComputationjNUMMATH2319340dec121960NUMMA70029599X (print), 09453245 (electronic) OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599X65.00MR0116477 (22 \#7264)C. B. HaselgroveFri May 14 17:18:08 2010http://www.math.utah.edu/pub/bibnet/authors/w/wilkinsonjameshardy.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.05.14 17:18:08 ???Numerische Mathematikacknhfbhttp://link.springer.com/journal/211J. H. WilkinsonError Analysis of FloatingPoint Computation
@Article{Wilkinson:1960:EAF,
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articlefparith.bibWadey:1960:FAW. G. WadeyFloatingPoint ArithmeticsjJACM72129139apr41960JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541165.00 (68.00)22\#6090Fri Dec 08 14:44:46 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 14:44:46 ???Three types of floatingpoint arithmetics with error control are discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.Journal of the ACMCited in cite Sterbenz:1974:FPC.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401C. B. HaselgroveThree types of floatingpoint arithmetics with error control are discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.W. G. WadeyFloatingPoint Arithmetics
@Article{Wadey:1960:FA,
author = "W. G. Wadey",
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MRclass = "65.00 (68.00)",
MRnumber = "22\#6090",
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}nt), 15729125 (electronic)",
ISSNL = "00063835",
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note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
xxpages = "220221??",
}
z+z1U !#1==E[=m;M= techreportfparith.bibAnonymous:1961:MCMAnonymousModern Computing MethodsNotes on Applied Science16National Physical LaboratoryHer Majesty's Stationery Office, London2202221961Fri Aug 20 10:05:25 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 10:05:25 ???Cited in cite Sterbenz:1974:FPC.acknhfbAnonymousModern Computing Methods
@TechReport{Anonymous:1961:MCM,
author = "Anonymous",
title = "Modern Computing Methods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}Q0Z#)C#I)U57C;cKqYCg{articlefparith.bibAmble:1961:AFPO. Amble and Jan V. GarwickOn the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp. 8788]jNORDISKTIDSKRINFORMBEHAND13220222sep91961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0193343400063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=3; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee cite Garwick:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543O. Amble and Jan V. GarwickSee \cite{Garwick:1961:AFP,Garwick:1961:RAF}.On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 8788]}
@Article{Amble:1961:AFP,
author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 8788]}",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "3",
pages = "220222",
month = sep,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01933434",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
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note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220",
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journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
xxpages = "220221??",
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;a7E;]=
iarticlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSignedDigit Number Representations for Fast Parallel ArithmeticjIRETRANSELECCOMPUTEC103389400sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521922703679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227IRE Transactions on Electronic ComputersacknhfbAlgirdas Avi{\v{z}}ienisSignedDigit Number Representations for Fast Parallel Arithmetic
@Article{Avizienis:1961:SDN,
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acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}T 2011",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
MM/3Y #+5{;a7E;=]=5{7articlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number SystemjIRETRANSELECCOMPUTEC1016370mar31961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521915403679950 OR 03679950Thu Jul 14 14:45:02 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:02 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154A system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.IRE Transactions on Electronic ComputersacknhfbA system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.Philip Warren CheneyA Digital Correlator Based on the Residue Number System
@Article{Cheney:1961:DCB,
author = "Philip Warren Cheney",
title = "A Digital Correlator Based on the Residue Number
System",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "1",
pages = "6370",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219154",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
[[!4V #/)c57=m;?c)carticlefparith.bibClarkson:1961:DMIW. K. ClarksonA Divisionless Method of Integer ConversionjCACM47315316jul71961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 08:14:59 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:59 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79W. K. ClarksonA Divisionless Method of Integer Conversion
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Method of Integer Conversion",
journal = jCACM,
volume = "4",
number = "7",
pages = "315316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision additionsubtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
''U5Y #%I[]57=;?cI[Warticlefparith.bibCox:1961:NMPAlbert G. Cox and H. A. LutherA Note on Multiple Precision ArithmeticjCACM48353353aug81961CACMA2http://doi.acm.org/10.1145/366678.36669300010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Sat Dec 03 14:07:44 2005ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.12.03 14:07:44 ???Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision additionsubtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a pm b = (a_0 pm b_0) + (a_1 pm b_1)t + cdots + (a_n pm b_n)t^n$. Here $ a_i pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision additionsubtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a \pm b = (a_0 \pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$. Here $ a_i \pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.Albert G. Cox and H. A. LutherA Note on Multiple Precision Arithmetic
@Article{Cox:1961:NMP,
author = "Albert G. Cox and H. A. Luther",
title = "A Note on Multiple Precision Arithmetic",
journal = jCACM,
volume = "4",
number = "8",
pages = "353353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/366678.366693",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision additionsubtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
{[7W #'!=m;+'
articlefparith.bibFreiman:1961:SACC. V. FreimanStatistical analysis of certain binary division algorithmsjIREPROC49191103jan11961Mon Sep 16 16:12:21 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.09.16 16:12:21 ???IRE ProceedingsacksfoC. V. FreimanStatistical analysis of certain binary division algorithms
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = jIREPROC,
volume = "49",
number = "1",
pages = "91103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}6Y #'%];a7E;]%]articlefparith.bibCroy:1961:RTMJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix ArithmeticjIRETRANSELECCOMPUTEC104777777dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521928603679950 OR 03679950Thu Jul 14 14:45:05 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:05 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286IRE Transactions on Electronic ComputersacknhfbJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix Arithmetic
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine BinarytoDecimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "777777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219286",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
0ti
@Article{Ferro:1986:DTF,
author = "F. Ferro",
title = "{DSP} tackles floatingpoint arithmetic",
journal = jCOMPDESIGN,
volume = "25",
number = "15",
pages = "5356",
day = "15",
month = aug,
year = "1986",
CODEN = "CMPDAM",
ISSN = "00104566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CDROM database (1991);
http://www)
@Article{Ferrari:1969:CDM,
author = "D. Ferrari",
title = "Correction to {``A Division Method Using a Parallel
Multiplier''}",
journal = jIEEETRANSCOMPUT,
volume = "C18",
number = "10",
pages = "960960",
month = oct,
year = "1969",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1969.222555",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL =Ď7o
@Article{Ferrari:1967:DMU,
author = "Domenico Ferrari",
title = "A Division Method Using a Parallel Multiplier",
journal = jIEEETRANSELECCOMPUT,
volume = "EC16",
number = "2",
pages = "224226",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1967.264580",
ISSN = "03677508",
bibdate = "Wed Jul 13 21:15:02 MDT 2011",
bibsource = "vK
@Article{Fernandez:2003:FPA,
author = "Jos{\'e}Jes{\'u}s Fern{\'a}ndez and Inmaculada
Garc{\'\i}a and Ester M. Garz{\'o}n",
title = "Floating point arithmetic teaching for computational
science",
journal = jFUTGENCOMPSYS,
volume = "19",
number = "8",
pages = "13211334",
month = nov,
year = "2003",
CODEN = "FGSEVI",
ISSN = "0167739X (print), 18727115 (eՄU+
@Article{Fenwick:1972:BRD,
author = "Peter M. Fenwick",
title = "A Binary Representation for Decimal Numbers",
journal = jAUSTRALIANCOMPJ,
volume = "4",
number = "4",
pages = "146149",
month = nov,
year = "1972",
CODEN = "ACMJB2",
ISSN = "00048917",
bibdate = "Fri Nov 28 11:31:38 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Australian Computer Journal",
keywords = "decimal floatingpoint arithmetic",
}YN
@Article{Ferguson:1991:SMC,
author = "Warren E. {Ferguson, Jr.}",
title = "Selecting math coprocessors",
journal = jIEEESPECTRUM,
volume = "28",
number = "7",
pages = "3841",
month = jul,
year = "1991",
CODEN = "IEESAM",
DOI = "http://dx.doi.org/10.1109/6.83469",
ISSN = "00189235 (print), 19399340 (electronic)",
ISSNL = "00189235",
bibdate = "Thu Sep 01 16:17:34 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "IEEE Spectrum",
keywords = "floatingpoint arithmetic",
remark = "Contains performancecomparison tables for Cyrix,
Intel, Motorola, and Weitek floatingpoint coprocessor
chips.",
} ڄ~}
@Article{Ferguson:1984:SFP,
author = "Kenneth M. Ferguson",
title = "{Savage} floatingpoint benchmark deficiencies of in
{16BST}",
journal = jDDJ,
volume = "9",
number = "8",
pages = "107??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}>ibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = acknhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}His work was supported by this contract, and led to the Ph.D..acknhfbThe purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.H. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computers
@TechReport{Garner:1961:RNS,
author = "H. L. Garner and R. F. Arnold and B. C. Benson and C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = acknhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}
g8\!#+[U51=m;#yy[Uw
techreportfparith.bibGarner:1961:RNSH. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computersASD Technical Report61483Electronic Technology Laboratory, The University of MichiganAnn Arbor, MI, USA91103oct101961Thu Nov 18 09:27:06 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:27:06 ???http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txtThe purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.This report represents the results of research performed by the group at The University of Michigan under the direction of Professor H. L. Garner. Concurrently, research on the same subject was being conducted at Harvard University under the direction of Professor Howard Aiken, and at the Lockheed Missile System Division under the direction of Dr. Richard Tanaka. There was a considerable exchange of information among the above groups during the course of the research effort. The efforts attained exhibit little overlap, rather they are complementary. A portion of this report was extracted from the doctoral dissertation of D. P. Rozenberg. = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}
:Y #'AI)57=I;_qY'cK[articlefparith.bibGarwick:1961:RAFJ. V. GarwickReply to ``On the Accuracy of Floating Point Computers'' [BIT bf 1(3), 1961, pp. 220221]jNORDISKTIDSKRINFORMBEHAND132222221961BITTEL, NBITAB00063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Mon Nov 16 14:36:22 1998http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.11.16 14:36:22 ???See cite Garwick:1961:AFP,Amble:1961:AFP.floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543J. V. GarwickSee \cite{Garwick:1961:AFP,Amble:1961:AFP}.Reply to {``On the Accuracy of Floating Point Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "3",
pages = "222222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}T9Z #)]I)U57C;
IqY)]{articlefparith.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point ComputersjNORDISKTIDSKRINFORMBEHAND128788jun61961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0193922100063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee also comment and reply cite Amble:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543Jan V. GarwickSee also comment and reply \cite{Amble:1961:AFP,Garwick:1961:RAF}.The Accuracy of Floating Point Computers
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "2",
pages = "8788",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01939221",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}.bib",
abstract = "Error checking codes based on residues have the
advantage over paritybased codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect bursttype errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
singledigit error in a decimal operation.",
acknowledgement = acknhfb,
keywords = "decimal arithmetic",
}
Q5Q`> ?
@Article{Madhukumar:2004:EAR,
author = "A. S. Madhukumar and F. Chin",
title = "Enhanced architecture for residue number systembased
{CDMA} for highrate data transmission",
journal = "IEEE Transactions on Wireless Communications",
volume = "3",
number = "5",
pages = "13631368",
month = sep,
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1109/TWC.2004.833509",
dI
@Article{Madhukumar:2002:RNS,
author = "A. S. Madhukumar and F. Chin",
title = "Residue number systembased multicarrier {CDMA} system
for highspeed broadband wireless access",
journal = jIEEETRANSBROADCAST,
volume = "48",
number = "1",
pages = "4652",
month = mar,
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acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
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c csY#1Y#'O57E#;#C%Y#7 articlefparith.bibLindamood:1963:MCOGeorge E. Lindamood and George ShapiroMagnitude Comparison and Overflow Detection in Modular Arithmetic ComputersjSIAMREVIEW543423501963SIREADhttp://dx.doi.org/10.1137/100509500361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 00361445Thu Mar 27 09:05:07 MDT 2014http://epubs.siam.org/toc/siread/5/4; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:05:07 MDTSIAM Reviewacknhfbhttp://epubs.siam.org/sirevOctober 1963George E. Lindamood and George ShapiroMagnitude Comparison and Overflow Detection in Modular Arithmetic Computers
@Article{Lindamood:1963:MCO,
author = "George E. Lindamood and George Shapiro",
title = "Magnitude Comparison and Overflow Detection in Modular
Arithmetic Computers",
journal = jSIAMREVIEW,
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month = "????",
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acknowledgement = acknhfb,
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}.263592",
ISSN = "03677508",
bibdate = "Thu Jul 14 08:10:44 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multiprecision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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1tZ#3Qw=97E);a_M!aQws articlefparith.bibMetropolis:1963:BOUN. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic SystemjIEEETRANSELECCOMPUTEC126896904dec121963IEECA8http://dx.doi.org/10.1109/PGEC.1963.263593; http://dx.doi.org/10.1109/PGEC.1963.26359203677508 OR 03677508Thu Jul 14 08:10:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037A particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.IEEE Transactions on Electronic ComputersCited in cite Sterbenz:1974:FPC.0124.07910acknhfbA particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.N. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic System
@Article{Metropolis:1963:BOU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Basic Operations in an Unnormalized Arithmetic
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pages = "896904",
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bibdate = "Thu Jul 14 08:10:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multiprecision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
L2C+W
@Book{Thies:1985:NPE,
author = "KlausDieter Thies",
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microfiche)",
LCCN = "QA76.6 .C633 1990",
bhQ
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editor =