# bibtab

bibtype: inproceedings
filename: fparith.bib
label: Metropolis:1972:ABCc
author: Nicholas C. Metropolis
title: Analyzed binary computing
crossref: IEEE:1972:ITS
pages: 1--14
year: 1972
DOI: https://doi.org/10.1109/ARITH.1972.6153912
bibdate: Tue Mar 5 08:31:37 MST 2013
bibtimestamp: 2013.03.05 08:31:37 MST
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543
rawauthor: Nicholas C. Metropolis
rawtitle: Analyzed binary computing
entry:
@InProceedings{Metropolis:1972:ABCc,
  author =       "Nicholas C. Metropolis",
  title =        "Analyzed binary computing",
  crossref =     "IEEE:1972:ITS",
  pages =        "1--14",
  year =         "1972",
  DOI =          "https://doi.org/10.1109/ARITH.1972.6153912",
  bibdate =      "Tue Mar 5 08:31:37 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543",
}


bibtype: mastersthesis
filename: fparith.bib
label: Miller:1972:DFD
author: Peter Edwin Miller
type: Thesis (M.S.)
school: Ohio State University
address: Columbus, OH, USA
pages: 83
year: 1972
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Arithmetic --- Computer programs; PDP-9 (Computer)
acknowledgement: ack-nhfb
rawauthor: Peter Edwin Miller
title:
The design of a floating-point, double-precision arithmetic unit for the Digital Equipment Corporation's PDP-9 computer

rawtitle:
The design of a floating-point, double-precision arithmetic unit for the {Digital Equipment Corporation}'s {PDP-9} computer

entry:
@MastersThesis{Miller:1972:DFD,
  author =       "Peter Edwin Miller",
  title =        "The design of a floating-point, double-precision
                 arithmetic unit for the {Digital Equipment
                 Corporation}'s {PDP-9} computer",
  type =         "Thesis ({M.S.})",
  school =       "Ohio State University",
  address =      "Columbus, OH, USA",
  pages =        "83",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic --- Computer programs; PDP-9 (Computer)",
}


bibtype: inproceedings
filename: fparith.bib
label: Neely:1972:CSN
author: Peter M. Neely
title: On conventions for systems of numerical representation
crossref: ACM:1972:PAA
pages: 644--561
year: 1972
bibdate: Fri Nov 28 11:28:06 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:28:06 ???
acknowledgement: ack-nhfb
rawauthor: Peter M. Neely
rawtitle: On conventions for systems of numerical representation
abstract:
Present conventions for numeric representation are considered inadequate to serve the needs of applied computing. Thus an augmented digital number system is proposed for use in programming languages and in digital computers. Special symbols are proposed for numbers too large, too small or too close to zero to be represented in the normal digital number system, or which are undefined. Properties of mappings among and between digital number systems are used to justify the augments chosen. Finally a suggestion is made for a new floating point word format that will serve all the above needs and will greatly extend the exponent range of floating point numbers.

rawabstract:
Present conventions for numeric representation are considered inadequate to serve the needs of applied computing. Thus an augmented digital number system is proposed for use in programming languages and in digital computers. Special symbols are proposed for numbers too large, too small or too close to zero to be represented in the normal digital number system, or which are undefined. Properties of mappings among and between digital number systems are used to justify the augments chosen. Finally a suggestion is made for a new floating point word format that will serve all the above needs and will greatly extend the exponent range of floating point numbers.

entry:
@InProceedings{Neely:1972:CSN,
  author =       "Peter M. Neely",
  title =        "On conventions for systems of numerical
                 representation",
  crossref =     "ACM:1972:PAA",
  pages =        "644--561",
  year =         "1972",
  bibdate =      "Fri Nov 28 11:28:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Present conventions for numeric representation are
                 considered inadequate to serve the needs of applied
                 computing. Thus an augmented digital number system is
                 proposed for use in programming languages and in
                 digital computers. Special symbols are proposed for
                 numbers too large, too small or too close to zero to be
                 represented in the normal digital number system, or
                 which are undefined. Properties of mappings among and
                 between digital number systems are used to justify the
                 augments chosen. Finally a suggestion is made for a new
                 floating point word format that will serve all the
                 above needs and will greatly extend the exponent range
                 of floating point numbers.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Oberman:1972:FRM
author: R. M. M. Oberman
title: A Flexible Rate Multiplier Circuit with Uniform Pulse Distribution Outputs
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 8
pages: 896--899
month: aug
monthnumber: 8
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009048
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:46 MDT 2011
bibtimestamp: 2011.07.12 18:58:46 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. M. M. Oberman
rawtitle: A Flexible Rate Multiplier Circuit with Uniform Pulse Distribution Outputs
entry:
@Article{Oberman:1972:FRM,
  author =       "R. M. M. Oberman",
  title =        "A Flexible Rate Multiplier Circuit with Uniform Pulse
                 Distribution Outputs",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "896--899",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009048",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Paris:1972:MA
author: J. B. Paris
title: On models of arithmetic
journal: j-LECT-NOTES-MATH
volume: 255
pages: 251--280
year: 1972
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0059548
ISBN: 3-540-05744-7 (print), 3-540-37162-1 (e-book) OR 3540057447 (print), 3540371621 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
MRclass: 02H05 (02H13)
MRnumber: 0392552 (52 \#13369)
MRreviewer: W. Marek
bibdate: Fri May 9 19:07:09 MDT 2014
bibtimestamp: 2014.05.09 19:07:09 MDT
URL: http://link.springer.com/chapter/10.1007/BFb0059548/
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0059533
bookURL: http://www.springerlink.com/content/978-3-540-37162-5
journalURL: http://link.springer.com/bookseries/304
rawauthor: J. B. Paris
rawtitle: On models of arithmetic
ISBN13:
978-3-540-05744-4 (print), 978-3-540-37162-5 (e-book) OR 9783540057444 (print), 9783540371625 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/lnm1970.bib

entry:
@Article{Paris:1972:MA,
  author =       "J. B. Paris",
  title =        "On models of arithmetic",
  journal =      j-LECT-NOTES-MATH,
  volume =       "255",
  pages =        "251--280",
  year =         "1972",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0059548",
  ISBN =         "3-540-05744-7 (print), 3-540-37162-1 (e-book)",
  ISBN-13 =      "978-3-540-05744-4 (print), 978-3-540-37162-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "02H05 (02H13)",
  MRnumber =     "0392552 (52 \#13369)",
  MRreviewer =   "W. Marek",
  bibdate =      "Fri May 9 19:07:09 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0059548/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0059533",
  book-URL =     "http://www.springerlink.com/content/978-3-540-37162-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}


bibtype: article
filename: fparith.bib
label: Pettus:1972:IDC
author: C. Pettus
title: Indeterminate $ 0 div 0 $ check in APL
journal: j-SIGPLAN
volume: 7
number: 4
pages: 40--41
month: apr
monthnumber: 4
year: 1972
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Thu May 25 06:58:23 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.25 06:58:23 MDT
fjournal: ACM SIGPLAN Notices
keywords: floating-point arithmetic; zero divide
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: C. Pettus
rawtitle: Indeterminate $ 0 \div 0 $ check in {APL}
abstract:
One unique feature of the APL system is the definition $ (0 div 0) = 1 $. Although there is obvious merit in this decision, in real analysis $ (0 div 0) $ is indeterminate. If one wishes to be alerted to the fact that a denominator is zero and does not want the result $1$ if the numerator is also zero, one can replace the expression $ X div Y $ with $ X times div Y $. Then if $X$ and $Y$ are both zero, a Domain Error will be reported instead of yielding.

rawabstract:
One unique feature of the APL system is the definition $ (0 \div 0) = 1 $. Although there is obvious merit in this decision, in real analysis $ (0 \div 0) $ is indeterminate. If one wishes to be alerted to the fact that a denominator is zero and does not want the result $1$ if the numerator is also zero, one can replace the expression $ X \div Y $ with $ X \times \div Y $. Then if $X$ and $Y$ are both zero, a Domain Error will be reported instead of yielding.

entry:
@Article{Pettus:1972:IDC,
  author =       "C. Pettus",
  title =        "Indeterminate $ 0 \div 0 $ check in {APL}",
  journal =      j-SIGPLAN,
  volume =       "7",
  number =       "4",
  pages =        "40--41",
  month =        apr,
  year =         "1972",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu May 25 06:58:23 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One unique feature of the APL system is the definition
                 $ (0 \div 0) = 1 $. Although there is obvious merit in
                 this decision, in real analysis $ (0 \div 0) $ is
                 indeterminate. If one wishes to be alerted to the fact
                 that a denominator is zero and does not want the result
                 $1$ if the numerator is also zero, one can replace the
                 expression $ X \div Y $ with $ X \times \div Y $. Then
                 if $X$ and $Y$ are both zero, a Domain Error will be
                 reported instead of yielding.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "floating-point arithmetic; zero divide",
}


bibtype: article
filename: fparith.bib
label: Phillips:1972:ICF
author: C. Phillips
title: Instabilities caused by floating-point arithmetic quantization
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 17
number: 2
pages: 242--243
month: apr
monthnumber: 4
year: 1972
CODEN: IETAA9
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Automatic Control
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: C. Phillips
rawtitle: Instabilities caused by floating-point arithmetic quantization
entry:
@Article{Phillips:1972:ICF,
  author =       "C. Phillips",
  title =        "Instabilities caused by floating-point arithmetic
                 quantization",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "17",
  number =       "2",
  pages =        "242--243",
  month =        apr,
  year =         "1972",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "It is shown that an otherwise stable digital control
                 system may become unstable due to signal quantization
                 if the controller operates on floating-point
                 arithmetic. Sufficient conditions for instability are
                 developed \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Pichat:1972:CSA
author: M. Pichat
journal: j-NUM-MATH
volume: 19
number: 5
pages: 400--406
year: 1972
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sat Sep 17 18:30:51 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.17 18:30:51 ???
fjournal: Numerische Mathematik
language: French
acknowledgement: ack-nhfb
corpsource: Conservatoire Nat. Arts Metiers, Paris, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: M. Pichat
title:
Correction d'une Somme en Arithmetique a Virgule Flottante. (French) [Correction of a Sum in Floating-Point Arithmetic]

note:
From Douglas Priest: (path =Douglas.Priest@eng.sun.com=) writing in Usenet newsgroup sci.math.num-analysis on 13 Sep 1994 16:04:56 GMT: ``ldots An iterative algorithm for computing a protracted sum to working precision by repeatedly applying the sum-and-roundoff method.''

keywords:
accurate floating-point summation; correct rounding; correction; digital arithmetic; floating point arithmetic; rounding off law; sum; truncature with guard digit

rawnote:
From Douglas Priest: (\path=Douglas.Priest@eng.sun.com=) writing in Usenet newsgroup sci.math.num-analysis on 13 Sep 1994 16:04:56 GMT: ``\ldots{} An iterative algorithm for computing a protracted sum to working precision by repeatedly applying the sum-and-roundoff method.''

rawtitle:
Correction d'une Somme en Arithm{\'e}tique {\`a} Virgule Flottante. ({French}) {[Correction of a Sum in Floating-Point Arithmetic]}

entry:
@Article{Pichat:1972:CSA,
  author =       "M. Pichat",
  title =        "Correction d'une Somme en Arithm{\'e}tique {\`a}
                 Virgule Flottante. ({French}) {[Correction of a Sum in
                 Floating-Point Arithmetic]}",
  journal =      j-NUM-MATH,
  volume =       "19",
  number =       "5",
  pages =        "400--406",
  year =         "1972",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Sep 17 18:30:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From Douglas Priest:
                 (\path=Douglas.Priest@eng.sun.com=) writing in Usenet
                 newsgroup sci.math.num-analysis on 13 Sep 1994 16:04:56
                 GMT: ``\ldots{} An iterative algorithm for computing a
                 protracted sum to working precision by repeatedly
                 applying the sum-and-roundoff method.''",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Conservatoire Nat. Arts M{\'e}tiers, Paris, France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "accurate floating-point summation; correct rounding;
                 correction; digital arithmetic; floating point
                 arithmetic; rounding off law; sum; truncature with
                 guard digit",
  language =     "French",
  treatment =    "T Theoretical or Mathematical",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}


bibtype: article
filename: fparith.bib
label: Ramamoorthy:1972:SPI
author: C. V. Ramamoorthy and James R. Goodman and K. H. Kim
title: Some Properties of Iterative Square-Rooting Methods Using High-Speed Multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 8
pages: 837--847
month: aug
monthnumber: 8
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009039
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:45 MDT 2011
bibtimestamp: 2011.07.12 18:58:45 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. V. Ramamoorthy and James R. Goodman and K. H. Kim
rawtitle: Some Properties of Iterative Square-Rooting Methods Using High-Speed Multiplication
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

entry:
@Article{Ramamoorthy:1972:SPI,
  author =       "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
  title =        "Some Properties of Iterative Square-Rooting Methods
                 Using High-Speed Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "837--847",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:45 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Randell:1972:ATO
author: Brian Randell
title: On Alan Turing and the origins of digital computers
type: Technical report
number: 33
institution: University of Newcastle upon Tyne, Computing Laboratory
address: Newcastle upon Tyne, UK
pages: 36
year: 1972
LCCN: TK7888.3 .R35
bibdate: Wed Oct 13 09:24:25 MDT 2010
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 09:24:25 MDT
series: University of Newcastle upon Tyne. Computing Laboratory. Technical report series
subject: Von Neumann, John; Turing, Alan Mathison; Electronic digital computers; History
acknowledgement: ack-nhfb
subjectdates: 1903--1957 (John von Neumann); 1912--1954 (Alan Turing)
rawauthor: Brian Randell
rawtitle: On {Alan Turing} and the origins of digital computers
entry:
@TechReport{Randell:1972:ATO,
  author =       "Brian Randell",
  title =        "On {Alan Turing} and the origins of digital
                 computers",
  type =         "Technical report",
  number =       "33",
  institution =  "University of Newcastle upon Tyne, Computing
                 Laboratory",
  address =      "Newcastle upon Tyne, UK",
  pages =        "36",
  year =         "1972",
  LCCN =         "TK7888.3 .R35",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "University of Newcastle upon Tyne. Computing
                 Laboratory. Technical report series",
  acknowledgement = ack-nhfb,
  subject =      "Von Neumann, John; Turing, Alan Mathison; Electronic
                 digital computers; History",
  subject-dates = "1903--1957 (John von Neumann); 1912--1954 (Alan
                 Turing)",
}


bibtype: techreport
filename: fparith.bib
label: Randell:1972:ODC
author: Brian Randell
title: The origins of digital computers: a bibliography
type: Technical report
number: 38
institution: Computing Laboratory, University of Newcastle upon Tyne
address: Newcastle upon Tyne, UK
pages: iii + 59
year: 1972
LCCN: TK7888.3 .R35
bibdate: Wed Oct 13 09:24:25 MDT 2010
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 09:24:25 MDT
series: University of Newcastle upon Tyne, Computing laboratory. Technical report series
subject: Electronic digital computers; History; Bibliography
acknowledgement: ack-nhfb
rawauthor: Brian Randell
rawtitle: The origins of digital computers: a bibliography
entry:
@TechReport{Randell:1972:ODC,
  author =       "Brian Randell",
  title =        "The origins of digital computers: a bibliography",
  type =         "Technical report",
  number =       "38",
  institution =  "Computing Laboratory, University of Newcastle upon
                 Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "iii + 59",
  year =         "1972",
  LCCN =         "TK7888.3 .R35",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "University of Newcastle upon Tyne, Computing
                 laboratory. Technical report series",
  acknowledgement = ack-nhfb,
  subject =      "Electronic digital computers; History; Bibliography",
}


bibtype: article
filename: fparith.bib
label: Richman:1972:AEA
author: Paul L. Richman
title: Automatic Error Analysis for Determining Precision
journal: j-CACM
volume: 15
number: 9
pages: 813--817
month: sep
monthnumber: 9
year: 1972
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65G05
MRnumber: 47 2808
bibdate: Mon Jan 22 07:15:56 MST 2001
bibtimestamp: 2001.01.22 07:15:56 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
corpsource: Bell Telephone Labs. Inc., Denver, CO, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: T Theoretical or Mathematical
rawauthor: Paul L. Richman
rawtitle: Automatic Error Analysis for Determining Precision
bibsource:
Compendex database; http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Richman72; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The problem considered is that of evaluating a rational expression to within any desired tolerance on a computer which performs variable-precision floating-point arithmetic operations. An automatic error analysis technique is given for determining, directly from the results of a trial low-precision interval arithmetic calculation, just how much precision and data accuracy are required to achieve a desired final accuracy. The technique given generalize easily to the evaluation of many nonrational expressions.

keywords:
automatic error analysis; control; digital arithmetic; error analysis; floating point arithmetic; interval arithmetic; mathematical techniques; precision; precision control

classcodes:
B0290B (Error analysis in numerical methods); C4110 (Error analysis in numerical methods); C5230 (Digital arithmetic methods)

rawabstract:
The problem considered is that of evaluating a rational expression to within any desired tolerance on a computer which performs variable-precision floating-point arithmetic operations. An automatic error analysis technique is given for determining, directly from the results of a trial low-precision interval arithmetic calculation, just how much precision and data accuracy are required to achieve a desired final accuracy. The technique given generalize easily to the evaluation of many nonrational expressions.

entry:
@Article{Richman:1972:AEA,
  author =       "Paul L. Richman",
  title =        "Automatic Error Analysis for Determining Precision",
  journal =      j-CACM,
  volume =       "15",
  number =       "9",
  pages =        "813--817",
  month =        sep,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05",
  MRnumber =     "47 2808",
  bibdate =      "Mon Jan 22 07:15:56 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Richman72;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The problem considered is that of evaluating a
                 rational expression to within any desired tolerance on
                 a computer which performs variable-precision
                 floating-point arithmetic operations. An automatic
                 error analysis technique is given for determining,
                 directly from the results of a trial low-precision
                 interval arithmetic calculation, just how much
                 precision and data accuracy are required to achieve a
                 desired final accuracy. The technique given generalize
                 easily to the evaluation of many nonrational
                 expressions.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods); C5230 (Digital
                 arithmetic methods)",
  classification = "921",
  corpsource =   "Bell Telephone Labs. Inc., Denver, CO, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "automatic error analysis; control; digital arithmetic;
                 error analysis; floating point arithmetic; interval
                 arithmetic; mathematical techniques; precision;
                 precision control",
  oldlabel =     "Richman72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman72",
}


bibtype: phdthesis
filename: fparith.bib
label: Ripley:1972:PFP
author: Jerald Lester Ripley
title: On proofs of floating-point program correctness and a measure of their relative efficiency
type: Thesis (Ph.D.)
school: University of Oklahoma
pages: vi + 105
year: 1972
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Numerical calculations.
acknowledgement: ack-nhfb
rawauthor: Jerald Lester Ripley
rawtitle: On proofs of floating-point program correctness and a measure of their relative efficiency
entry:
@PhdThesis{Ripley:1972:PFP,
  author =       "Jerald Lester Ripley",
  title =        "On proofs of floating-point program correctness and a
                 measure of their relative efficiency",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Oklahoma",
  address =      "????",
  pages =        "vi + 105",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Numerical calculations.",
}


bibtype: article
filename: fparith.bib
label: Rohl:1972:NCA
author: J. S. Rohl and J. A. Linn
title: A Note on Compiling Arithmetic Expressions
journal: j-COMP-J
volume: 15
number: 1
pages: 13--14
month: feb
monthnumber: 2
year: 1972
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/15.1.13
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:49 MST 2012
bibtimestamp: 2012.12.04 14:47:49 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
corpsource: Univ. Manchester, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: J. S. Rohl and J. A. Linn
rawtitle: A Note on Compiling Arithmetic Expressions
bibsource:
http://comjnl.oxfordjournals.org/content/15/1.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/15/1/13.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/150013.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/13.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/14.tif

keywords:
arithmetic expressions; compilers; compiling; data handling; digital arithmetic; minimisation; minimization; program; single accumulator; storing; temporary

classcodes:
C5230 (Digital arithmetic methods); C6130 (Data handling techniques); C6150C (Compilers, interpreters and other processors)

entry:
@Article{Rohl:1972:NCA,
  author =       "J. S. Rohl and J. A. Linn",
  title =        "A Note on Compiling Arithmetic Expressions",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "1",
  pages =        "13--14",
  month =        feb,
  year =         "1972",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/15.1.13",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:49 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/15/1.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/15/1/13.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/150013.sgm.abs.html;
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  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C6150C (Compilers, interpreters
                 and other processors)",
  corpsource =   "Univ. Manchester, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic expressions; compilers; compiling; data
                 handling; digital arithmetic; minimisation;
                 minimization; program; single accumulator; storing;
                 temporary",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Samet:1972:CDL
author: P. A. Samet and D. W. Honey
journal: j-COMP-J
volume: 15
number: 2
pages: 116--116
month: may
monthnumber: 5
year: 1972
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/15.2.116
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:49 MST 2012
bibtimestamp: 2012.12.04 14:47:49 MST
fjournal: The Computer Journal
keywords: digital arithmetic; double length; precision techniques; single; square root
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Univ. Coll., London, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: P. A. Samet and D. W. Honey
title:
Calculation of a Double-Length Square Root from Double-Length Number using Single Precision Techniques

bibsource:
http://comjnl.oxfordjournals.org/content/15/2.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif

rawtitle:
Calculation of a Double-Length Square Root from Double-Length Number using Single Precision Techniques

entry:
@Article{Samet:1972:CDL,
  author =       "P. A. Samet and D. W. Honey",
  title =        "Calculation of a Double-Length Square Root from
                 Double-Length Number using Single Precision
                 Techniques",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "2",
  pages =        "116--116",
  month =        may,
  year =         "1972",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/15.2.116",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:49 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/15/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Coll., London, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "digital arithmetic; double length; precision
                 techniques; single; square root",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: fparith.bib
label: Schulenberg:1972:RSS
author: Craig Schulenberg and James E. Kernan
title: Results of space shuttle computer floating-point precision study
type: Report
number: E-2637
institution: M.I.T. Charles Stark Draper Laboratory
address: Cambridge
pages: various
year: 1972
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Electronic data processing --- Space trajectories.; Reusable space vehicles.
remark: At head of title: Apollo guidance, navigation and control.
acknowledgement: ack-nhfb
rawauthor: Craig Schulenberg and James E. Kernan
rawtitle: Results of space shuttle computer floating-point precision study
entry:
@TechReport{Schulenberg:1972:RSS,
  author =       "Craig Schulenberg and James E. Kernan",
  title =        "Results of space shuttle computer floating-point
                 precision study",
  type =         "Report",
  number =       "E-2637",
  institution =  "M.I.T. Charles Stark Draper Laboratory",
  address =      "Cambridge",
  pages =        "various",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic data processing --- Space trajectories.;
                 Reusable space vehicles.",
  remark =       "At head of title: Apollo guidance, navigation and
                 control.",
}


bibtype: article
filename: fparith.bib
label: Schurmann:1972:MEA
author: A. Schurmann
title: On the minimum error in addition processes of positive floating-point numbers
journal: j-ZASTOS-MAT
volume: 13
pages: 351--366
year: 1972 -- 1973
CODEN: ZAMTAK
MRclass: 65G05
MRnumber: 48 3242
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
fjournal: Zastosowania Matematyki
acknowledgement: ack-nhfb
reviewer: A. D. Booth
rawauthor: A. Schurmann
rawtitle: On the minimum error in addition processes of positive floating-point numbers
entry:
@Article{Schurmann:1972:MEA,
  author =       "A. Schurmann",
  title =        "On the minimum error in addition processes of positive
                 floating-point numbers",
  journal =      j-ZASTOS-MAT,
  volume =       "13",
  pages =        "351--366",
  year =         "1972--1973",
  CODEN =        "ZAMTAK",
  MRclass =      "65G05",
  MRnumber =     "48 3242",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zastosowania Matematyki",
  reviewer =     "A. D. Booth",
}


bibtype: article
filename: fparith.bib
label: Shaham:1972:NDA
author: Z. Shaham and Z. Riesel
title: A Note on Division Algorithms Based on Multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 5
pages: 513--514
month: may
monthnumber: 5
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1972.223557
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:43 MDT 2011
bibtimestamp: 2011.07.12 18:58:43 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Z. Shaham and Z. Riesel
rawtitle: A Note on Division Algorithms Based on Multiplication
entry:
@Article{Shaham:1972:NDA,
  author =       "Z. Shaham and Z. Riesel",
  title =        "A Note on Division Algorithms Based on
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "5",
  pages =        "513--514",
  month =        may,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223557",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Stallings:1972:CPM
author: W. T. Stallings and T. L. Boullion
title: Computation of Pseudoinverse Matrices Using Residue Arithmetic
journal: j-SIAM-REVIEW
volume: 14
number: 1
pages: 152--163
year: 1972
CODEN: SIREAD
DOI: https://doi.org/10.1137/1014005
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:06:35 MDT 2014
bibtimestamp: 2014.03.27 09:06:35 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1972
rawauthor: W. T. Stallings and T. L. Boullion
rawtitle: Computation of Pseudoinverse Matrices Using Residue Arithmetic
bibsource:
http://epubs.siam.org/toc/siread/14/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Stallings:1972:CPM,
  author =       "W. T. Stallings and T. L. Boullion",
  title =        "Computation of Pseudoinverse Matrices Using Residue
                 Arithmetic",
  journal =      j-SIAM-REVIEW,
  volume =       "14",
  number =       "1",
  pages =        "152--163",
  month =        "????",
  year =         "1972",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1014005",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:35 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/14/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1972",
}


bibtype: article
filename: fparith.bib
label: Stefanelli:1972:SHS
author: R. Stefanelli
title: A Suggestion for a High-Speed Parallel Binary Divider
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 1
pages: 42--55
month: jan
monthnumber: 1
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1972.223430
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jan 08 22:42:31 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 22:42:31 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. Stefanelli
rawtitle: A Suggestion for a High-Speed Parallel Binary Divider
abstract:
family of four procedures to compute the inverse $ 1 / X $ of a given binary number $X$ normalized between 0.5 and 1 is described. The quotient is obtained in redundant binary form, i.e., in a base 2 code in which digits can assume any positive or negative integer value. All methods here described can be implemented by combinatorial networks; the dividers realized in this way are very fast because all carry propagations take place at the same time.

rawabstract:
family of four procedures to compute the inverse $ 1 / X $ of a given binary number $X$ normalized between 0.5 and 1 is described. The quotient is obtained in redundant binary form, i.e., in a base 2 code in which digits can assume any positive or negative integer value. All methods here described can be implemented by combinatorial networks; the dividers realized in this way are very fast because all carry propagations take place at the same time.

entry:
@Article{Stefanelli:1972:SHS,
  author =       "R. Stefanelli",
  title =        "A Suggestion for a High-Speed Parallel Binary
                 Divider",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "1",
  pages =        "42--55",
  month =        jan,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223430",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jan 08 22:42:31 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "family of four procedures to compute the inverse $ 1 /
                 X $ of a given binary number $X$ normalized between 0.5
                 and 1 is described. The quotient is obtained in
                 redundant binary form, i.e., in a base 2 code in which
                 digits can assume any positive or negative integer
                 value. All methods here described can be implemented by
                 combinatorial networks; the dividers realized in this
                 way are very fast because all carry propagations take
                 place at the same time.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: incollection
filename: fparith.bib
label: Tung:1972:A
author: C. Tung
title: Arithmetic
crossref: Cardenas:1972:CS
pages: ??--??
year: 1972
bibdate: Sat May 18 14:39:14 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:39:14 ???
acknowledgement: ack-nhfb
rawauthor: C. Tung
rawtitle: Arithmetic
entry:
@InCollection{Tung:1972:A,
  author =       "C. Tung",
  title =        "Arithmetic",
  crossref =     "Cardenas:1972:CS",
  pages =        "??--??",
  year =         "1972",
  bibdate =      "Sat May 18 14:39:14 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Urabae:1972:CEA
author: Minoru Urabae
title: Component-wise error analysis of iterative methods practiced on a floating-point system
type: MRC Technical Summary Report
number: 1268
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 57
year: 1972
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Error analysis (Mathematics); Floating-point arithmetic.; Iterative methods (Mathematics)
remark: ``Received August 11, 1972.'' Sponsored by Army Research Office, Durham, N.C.
acknowledgement: ack-nhfb
rawauthor: Minoru Urabae
rawtitle: Component-wise error analysis of iterative methods practiced on a floating-point system
entry:
@TechReport{Urabae:1972:CEA,
  author =       "Minoru Urabae",
  title =        "Component-wise error analysis of iterative methods
                 practiced on a floating-point system",
  type =         "{MRC} Technical Summary Report",
  number =       "1268",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "57",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Error analysis (Mathematics); Floating-point
                 arithmetic.; Iterative methods (Mathematics)",
  remark =       "``Received August 11, 1972.'' Sponsored by Army
                 Research Office, Durham, N.C.",
}


bibtype: article
filename: fparith.bib
label: Varian:1972:LEB
author: Hal R. Varian
title: Letter to the Editor: Benford's Law
journal: j-AMER-STAT
volume: 26
number: 3
pages: 65--66
month: jun
monthnumber: 6
year: 1972
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Fri Mar 30 11:34:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.30 11:34:37 ???
URL: http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q
fjournal: The American Statistician
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: Hal R. Varian
rawtitle: Letter to the {Editor}: {Benford's Law}
abstract:
Around 1938 the physicist Frank Benford observed a rather strange fact: tables of logarithms in libraries tend to be dirtier at the beginning than at the end. This indicated to Benford that people had more occasion to calculate with numbers beginning with 1 or 2 than with 8 or 9.par Benford also found that the frequency of the digit p being the first digit of a decimal number was very closely approximated by $ log (p + 1) - log p $ [i.e., $ log (1 + 1 / p) $ ]. This has become known as Benford's law.

rawabstract:
Around 1938 the physicist Frank Benford observed a rather strange fact: tables of logarithms in libraries tend to be dirtier at the beginning than at the end. This indicated to Benford that people had more occasion to calculate with numbers beginning with 1 or 2 than with 8 or 9.\par Benford also found that the frequency of the digit p being the first digit of a decimal number was very closely approximated by $ \log (p + 1) - \log p $ [i.e., $ \log (1 + 1 / p) $ ]. This has become known as Benford's law.

entry:
@Article{Varian:1972:LEB,
  author =       "Hal R. Varian",
  title =        "Letter to the {Editor}: {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "26",
  number =       "3",
  pages =        "65--66",
  month =        jun,
  year =         "1972",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Mar 30 11:34:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
  abstract =     "Around 1938 the physicist Frank Benford observed a
                 rather strange fact: tables of logarithms in libraries
                 tend to be dirtier at the beginning than at the end.
                 This indicated to Benford that people had more occasion
                 to calculate with numbers beginning with 1 or 2 than
                 with 8 or 9.\par

                 Benford also found that the frequency of the digit p
                 being the first digit of a decimal number was very
                 closely approximated by $ \log (p + 1) - \log p $
                 [i.e., $ \log (1 + 1 / p) $ ]. This has become known as
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: techreport
filename: fparith.bib
label: Wirth:1972:PCG
author: Niklaus Wirth
title: On ``Pascal'', Code Generation, and the CDC 6000 Computer
type: Report
number: STAN-CS-72-257
institution: inst-STAN-CS
address: inst-STAN-CS:adr
pages: i + 38
month: feb
monthnumber: 2
year: 1972
bibdate: Thu Jan 04 12:57:12 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2024.01.04 12:57:12 ???
acknowledgement: ack-nhfb
authordates: 15 February 1934--1 January 2024
rawauthor: Niklaus Wirth
rawtitle: On ``{Pascal}'', Code Generation, and the {CDC 6000} Computer
abstract:
``PASCAL'' is a general purpose programming language with characteristics similar to ALGOL 60, but with an enriched set of program- and data structuring facilities. It has been implemented on the CDC 6000 computer. This paper discusses selected topics of code generation, in particular the selection of instruction sequences to represent simple operations on arithmetic, Boolean, and powerset operands. Methods to implement recursive procedures are briefly described, and it is hinted that the more sophisticated solutions are not necessarily also the best. The CDC 6000 architecture appears as a frequent source of pitfalls and nuisances, and its main trouble spots are scrutinized and discussed.

remark:
This report contains an interesting discussion of the problems for compiler writers with a hardware arithmetic design that subsumes integer arithmetic inside one's complement floating-point arithmetic, and is unable to detect integer overflow. The CDC 6000 and 7000, and Burroughs 5000 and 6000 families, share some of these difficulties.

rawabstract:
``PASCAL'' is a general purpose programming language with characteristics similar to ALGOL 60, but with an enriched set of program- and data structuring facilities. It has been implemented on the CDC 6000 computer. This paper discusses selected topics of code generation, in particular the selection of instruction sequences to represent simple operations on arithmetic, Boolean, and powerset operands. Methods to implement recursive procedures are briefly described, and it is hinted that the more sophisticated solutions are not necessarily also the best. The CDC 6000 architecture appears as a frequent source of pitfalls and nuisances, and its main trouble spots are scrutinized and discussed.

entry:
@TechReport{Wirth:1972:PCG,
  author =       "Niklaus Wirth",
  title =        "On ``{Pascal}'', Code Generation, and the {CDC 6000}
                 Computer",
  type =         "Report",
  number =       "STAN-CS-72-257",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "i + 38",
  month =        feb,
  year =         "1972",
  bibdate =      "Thu Jan 04 12:57:12 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "``PASCAL'' is a general purpose programming language
                 with characteristics similar to ALGOL 60, but with an
                 enriched set of program- and data structuring
                 facilities. It has been implemented on the CDC 6000
                 computer. This paper discusses selected topics of code
                 generation, in particular the selection of instruction
                 sequences to represent simple operations on arithmetic,
                 Boolean, and powerset operands. Methods to implement
                 recursive procedures are briefly described, and it is
                 hinted that the more sophisticated solutions are not
                 necessarily also the best. The CDC 6000 architecture
                 appears as a frequent source of pitfalls and nuisances,
                 and its main trouble spots are scrutinized and
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "15 February 1934--1 January 2024",
  remark =       "This report contains an interesting discussion of the
                 problems for compiler writers with a hardware
                 arithmetic design that subsumes integer arithmetic
                 inside one's complement floating-point arithmetic, and
                 is unable to detect integer overflow. The CDC 6000 and
                 7000, and Burroughs 5000 and 6000 families, share some
                 of these difficulties.",
}


bibtype: book
filename: fparith.bib
label: Young:1972:SNM
author: David M. Young and Robert Todd Gregory
title: A Survey of Numerical Mathematics
publisher: pub-AW
address: pub-AW:adr
pages: x + 492 (A1--A18 and B1--B14 and I1--I19)
year: 1972
ISBN: 0-201-08773-1, 0-486-65691-8 (Dover paperback) OR 0201087731, 0486656918 (Dover paperback)
LCCN: QA297 .Y63 1972
MRclass: 65-02
MRnumber: 53 11954a
bibdate: Wed Jan 17 10:57:04 1996
bibtimestamp: 1996.01.17 10:57:04 ???
acknowledgement: ack-nhfb
reviewer: D. Greenspan
rawauthor: David M. Young and Robert Todd Gregory
rawtitle: A Survey of Numerical Mathematics
ISBN13:
978-0-201-08773-4, 978-0-486-65691-5 (Dover paperback) OR 9780201087734, 9780486656915 (Dover paperback)

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
1: Numerical Analysis as a Subject Area 1.1 Introduction 1.2 Some pitfalls in computation 1.3 Mathematical and computer aspects of an algorithm 1.4 Numerical instability of algorithms and ill-conditioned problems 1.5 Typical problems of interest to the numerical analyst 1.6 Iterative methods 2: Elementary Operations with Automatic Digital Computers 2.1 Introduction 2.2 Binary arithmetic 2.3 Conversion from base $D$ to base $B$ representation 2.4 Representation of integers on a binary computer 2.5 Floating-point representations 2.6 Computer-representable numbers 2.7 Floating-point arithmetic operations 2.8 Fortran analysis of a floating-point number 2.9 Calculation of elementary functions 3: Surveillance of Number Ranges 3.1 Introduction 3.2 Allowable number ranges 3.3 Basic real arithmetic operations 3.4 The quadratic equation 3.5 Complex arithmetic operations 4: Solution of Equations 4.1 Introduction 4.2 Attainable accuracy 4.3 Graphical methods 4.4 The method of bisection 4.5 The method of false position 4.6 The secant method 4.7 General properties of iterative methods 4.8 Generation of iterative methods 4.9 The Newton method 4.10 Muller's method 4.11 Orders of convergence of iterative methods 4.12 Acceleration of the convergence 4.13 Systems of nonlinear equations 5: Roots of Polynomial Equations 5.1 Introduction 5.2 General properties of polynomials 5.3 The Newton method and related methods 5.4 Muller's method and Cauchy's method 5.5 Location of the roots 5.6 Root acceptance and refinement 5.7 Matrix related methods: the modified Bernoulli method 5.8 Matrix related methods: the IP method 5.9 Polyalgorithms 5.10 Other methods 6: Interpolation and Approximation 6.1 Introduction 6.2 Linear interpolation 6.3 Convergence and accuracy of linear interpolation 6.4 Lagrangian interpolation 6.5 Convergence and accuracy of Lagrangian interpolation 6.6 Interpolation with equal intervals 6.7 Hermite interpolation 6.8 Limitations on polynomial interpolation: smooth interpolation 6.9 Inverse interpolation 6.10 Approximation by polynomials 6.11 Least squares approximation by polynomials 6.12 Rational approximation 6.13 Trigonometric interpolation and approximation 6.14 Interpolation in two variables 7: Numerical Differentiation and Quadrature 7.1 Introduction 7.2 The method of undetermined weights 7.3 Numerical differentiation 7.4 Numerical quadrature --- equal intervals 7.5 The Euler--MacLaurin formula 7.6 Romberg integration 7.7 Error determination 7.8 Numerical quadrature --- unequal intervals 8: Ordinary Differential Equations 8.1 Introduction 8.2 Existence and uniqueness 8.3 Analytic methods 8.4 Integral equation formulation --- the Picard method of successive approximations 8.5 The Euler method 8.6 Methods based on numerical quadrature 8.7 Error estimation for predictor-corrector methods 8.8 A numerical example 8.9 Runge--Kutta methods 8.10 Methods based on numerical differentiation 8.11 Higher-order equations and systems of first-order equations 8.12 The use of high-speed computers Appendix A Appendix B Appendix C Bibliography Index

rawTOC:
1: Numerical Analysis as a Subject Area \\ 1.1 Introduction \\ 1.2 Some pitfalls in computation \\ 1.3 Mathematical and computer aspects of an algorithm \\ 1.4 Numerical instability of algorithms and ill-conditioned problems \\ 1.5 Typical problems of interest to the numerical analyst \\ 1.6 Iterative methods \\ 2: Elementary Operations with Automatic Digital Computers \\ 2.1 Introduction \\ 2.2 Binary arithmetic \\ 2.3 Conversion from base $D$ to base $B$ representation \\ 2.4 Representation of integers on a binary computer \\ 2.5 Floating-point representations \\ 2.6 Computer-representable numbers \\ 2.7 Floating-point arithmetic operations \\ 2.8 Fortran analysis of a floating-point number \\ 2.9 Calculation of elementary functions \\ 3: Surveillance of Number Ranges \\ 3.1 Introduction \\ 3.2 Allowable number ranges \\ 3.3 Basic real arithmetic operations \\ 3.4 The quadratic equation \\ 3.5 Complex arithmetic operations \\ 4: Solution of Equations \\ 4.1 Introduction \\ 4.2 Attainable accuracy \\ 4.3 Graphical methods \\ 4.4 The method of bisection \\ 4.5 The method of false position \\ 4.6 The secant method \\ 4.7 General properties of iterative methods \\ 4.8 Generation of iterative methods \\ 4.9 The Newton method \\ 4.10 Muller's method \\ 4.11 Orders of convergence of iterative methods \\ 4.12 Acceleration of the convergence \\ 4.13 Systems of nonlinear equations \\ 5: Roots of Polynomial Equations \\ 5.1 Introduction \\ 5.2 General properties of polynomials \\ 5.3 The Newton method and related methods \\ 5.4 Muller's method and Cauchy's method \\ 5.5 Location of the roots \\ 5.6 Root acceptance and refinement \\ 5.7 Matrix related methods: the modified Bernoulli method \\ 5.8 Matrix related methods: the IP method \\ 5.9 Polyalgorithms \\ 5.10 Other methods \\ 6: Interpolation and Approximation \\ 6.1 Introduction \\ 6.2 Linear interpolation \\ 6.3 Convergence and accuracy of linear interpolation \\ 6.4 Lagrangian interpolation \\ 6.5 Convergence and accuracy of Lagrangian interpolation \\ 6.6 Interpolation with equal intervals \\ 6.7 Hermite interpolation \\ 6.8 Limitations on polynomial interpolation: smooth interpolation \\ 6.9 Inverse interpolation \\ 6.10 Approximation by polynomials \\ 6.11 Least squares approximation by polynomials \\ 6.12 Rational approximation \\ 6.13 Trigonometric interpolation and approximation \\ 6.14 Interpolation in two variables \\ 7: Numerical Differentiation and Quadrature \\ 7.1 Introduction \\ 7.2 The method of undetermined weights \\ 7.3 Numerical differentiation \\ 7.4 Numerical quadrature --- equal intervals \\ 7.5 The Euler--MacLaurin formula \\ 7.6 Romberg integration \\ 7.7 Error determination \\ 7.8 Numerical quadrature --- unequal intervals \\ 8: Ordinary Differential Equations \\ 8.1 Introduction \\ 8.2 Existence and uniqueness \\ 8.3 Analytic methods \\ 8.4 Integral equation formulation --- the Picard method of successive approximations \\ 8.5 The Euler method \\ 8.6 Methods based on numerical quadrature \\ 8.7 Error estimation for predictor-corrector methods \\ 8.8 A numerical example \\ 8.9 Runge--Kutta methods \\ 8.10 Methods based on numerical differentiation \\ 8.11 Higher-order equations and systems of first-order equations \\ 8.12 The use of high-speed computers \\ Appendix A \\ Appendix B \\ Appendix C \\ Bibliography \\ Index

entry:
@Book{Young:1972:SNM,
  author =       "David M. Young and Robert Todd Gregory",
  title =        "A Survey of Numerical Mathematics",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "x + 492 (A1--A18 and B1--B14 and I1--I19)",
  year =         "1972",
  ISBN =         "0-201-08773-1, 0-486-65691-8 (Dover paperback)",
  ISBN-13 =      "978-0-201-08773-4, 978-0-486-65691-5 (Dover
                 paperback)",
  LCCN =         "QA297 .Y63 1972",
  MRclass =      "65-02",
  MRnumber =     "53 11954a",
  bibdate =      "Wed Jan 17 10:57:04 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "D. Greenspan",
  tableofcontents = "1: Numerical Analysis as a Subject Area \\
                 1.1 Introduction \\
                 1.2 Some pitfalls in computation \\
                 1.3 Mathematical and computer aspects of an algorithm
                 \\
                 1.4 Numerical instability of algorithms and
                 ill-conditioned problems \\
                 1.5 Typical problems of interest to the numerical
                 analyst \\
                 1.6 Iterative methods \\
                 2: Elementary Operations with Automatic Digital
                 Computers \\
                 2.1 Introduction \\
                 2.2 Binary arithmetic \\
                 2.3 Conversion from base $D$ to base $B$ representation
                 \\
                 2.4 Representation of integers on a binary computer \\
                 2.5 Floating-point representations \\
                 2.6 Computer-representable numbers \\
                 2.7 Floating-point arithmetic operations \\
                 2.8 Fortran analysis of a floating-point number \\
                 2.9 Calculation of elementary functions \\
                 3: Surveillance of Number Ranges \\
                 3.1 Introduction \\
                 3.2 Allowable number ranges \\
                 3.3 Basic real arithmetic operations \\
                 3.4 The quadratic equation \\
                 3.5 Complex arithmetic operations \\
                 4: Solution of Equations \\
                 4.1 Introduction \\
                 4.2 Attainable accuracy \\
                 4.3 Graphical methods \\
                 4.4 The method of bisection \\
                 4.5 The method of false position \\
                 4.6 The secant method \\
                 4.7 General properties of iterative methods \\
                 4.8 Generation of iterative methods \\
                 4.9 The Newton method \\
                 4.10 Muller's method \\
                 4.11 Orders of convergence of iterative methods \\
                 4.12 Acceleration of the convergence \\
                 4.13 Systems of nonlinear equations \\
                 5: Roots of Polynomial Equations \\
                 5.1 Introduction \\
                 5.2 General properties of polynomials \\
                 5.3 The Newton method and related methods \\
                 5.4 Muller's method and Cauchy's method \\
                 5.5 Location of the roots \\
                 5.6 Root acceptance and refinement \\
                 5.7 Matrix related methods: the modified Bernoulli
                 method \\
                 5.8 Matrix related methods: the IP method \\
                 5.9 Polyalgorithms \\
                 5.10 Other methods \\
                 6: Interpolation and Approximation \\
                 6.1 Introduction \\
                 6.2 Linear interpolation \\
                 6.3 Convergence and accuracy of linear interpolation
                 \\
                 6.4 Lagrangian interpolation \\
                 6.5 Convergence and accuracy of Lagrangian
                 interpolation \\
                 6.6 Interpolation with equal intervals \\
                 6.7 Hermite interpolation \\
                 6.8 Limitations on polynomial interpolation: smooth
                 interpolation \\
                 6.9 Inverse interpolation \\
                 6.10 Approximation by polynomials \\
                 6.11 Least squares approximation by polynomials \\
                 6.12 Rational approximation \\
                 6.13 Trigonometric interpolation and approximation \\
                 6.14 Interpolation in two variables \\
                 7: Numerical Differentiation and Quadrature \\
                 7.1 Introduction \\
                 7.2 The method of undetermined weights \\
                 7.3 Numerical differentiation \\
                 7.4 Numerical quadrature --- equal intervals \\
                 7.5 The Euler--MacLaurin formula \\
                 7.6 Romberg integration \\
                 7.7 Error determination \\
                 7.8 Numerical quadrature --- unequal intervals \\
                 8: Ordinary Differential Equations \\
                 8.1 Introduction \\
                 8.2 Existence and uniqueness \\
                 8.3 Analytic methods \\
                 8.4 Integral equation formulation --- the Picard method
                 of successive approximations \\
                 8.5 The Euler method \\
                 8.6 Methods based on numerical quadrature \\
                 8.7 Error estimation for predictor-corrector methods
                 \\
                 8.8 A numerical example \\
                 8.9 Runge--Kutta methods \\
                 8.10 Methods based on numerical differentiation \\
                 8.11 Higher-order equations and systems of first-order
                 equations \\
                 8.12 The use of high-speed computers \\
                 Appendix A \\
                 Appendix B \\
                 Appendix C \\
                 Bibliography \\
                 Index",
}


bibtype: article
filename: fparith.bib
label: Aird:1973:SUM
author: T. Aird and D. Dodson and E. Houstis and J. Rice
title: Statistics on the Use of Mathematical Subroutines from a Computer Center Library
journal: j-SIGNUM
volume: 8
number: 4
pages: 8--9
month: oct
monthnumber: 10
year: 1973
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:14:44 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:44 ???
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: T. Aird and D. Dodson and E. Houstis and J. Rice
rawtitle: Statistics on the Use of Mathematical Subroutines from a Computer Center Library
entry:
@Article{Aird:1973:SUM,
  author =       "T. Aird and D. Dodson and E. Houstis and J. Rice",
  title =        "Statistics on the Use of Mathematical Subroutines from
                 a Computer Center Library",
  journal =      j-SIGNUM,
  volume =       "8",
  number =       "4",
  pages =        "8--9",
  month =        oct,
  year =         "1973",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:14:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: mastersthesis
filename: fparith.bib
label: Anjoorian:1973:EME
author: Harry Anjoorian
title: An example of microprogrammed extended-precision floating-point arithmetic
type: Thesis (M.A.)
school: California State University, Chico
address: Chico, CA, USA
pages: ix + 94
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic and logic units.; Electronic digital computers --- Design and construction.
acknowledgement: ack-nhfb
rawauthor: Harry Anjoorian
rawtitle: An example of microprogrammed extended-precision floating-point arithmetic
entry:
@MastersThesis{Anjoorian:1973:EME,
  author =       "Harry Anjoorian",
  title =        "An example of microprogrammed extended-precision
                 floating-point arithmetic",
  type =         "Thesis ({M.A.})",
  school =       "California State University, Chico",
  address =      "Chico, CA, USA",
  pages =        "ix + 94",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Electronic
                 digital computers --- Design and construction.",
}


bibtype: article
filename: fparith.bib
label: Atkins:1973:PCA
author: David E. Atkins, III and Harvey L. Garner
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 549--551
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009104
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibtimestamp: 2007.11.09 19:18:24 ???
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: David E. {Atkins, III} and Harvey L. Garner
title:
Preface: Computer Arithmetic: An Introduction and Overview [Second IEEE Symposium on Computer Arithmetic, May 15--16, 1972, University of Maryland]

URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009104; http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Atkins.pdf

rawtitle:
Preface: Computer Arithmetic: An Introduction and Overview [{Second IEEE Symposium on Computer Arithmetic, May 15--16, 1972, University of Maryland}]

entry:
@Article{Atkins:1973:PCA,
  author =       "David E. {Atkins, III} and Harvey L. Garner",
  title =        "Preface: Computer Arithmetic: An Introduction and
                 Overview [{Second IEEE Symposium on Computer
                 Arithmetic, May 15--16, 1972, University of
                 Maryland}]",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "549--551",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009104",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009104;
                 http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Atkins.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: article
filename: fparith.bib
label: Avizienis:1973:AAE
author: Algirdas Avizienis
title: Arithmetic Algorithms for Error-Coded Operands
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 567--572
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009108
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:18:24 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Algirdas Avi{\v{z}}ienis
rawtitle: Arithmetic Algorithms for Error-Coded Operands
entry:
@Article{Avizienis:1973:AAE,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Arithmetic Algorithms for Error-Coded Operands",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "567--572",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009108",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: book
filename: fparith.bib
label: Barna:1973:ICD
author: Arpad Barna and Dan I. Porat
title: Integrated Circuits in Digital Electronics
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xi + 483
year: 1973
ISBN: 0-471-05050-4 OR 0471050504
ISBN13: 978-0-471-05050-6 OR 9780471050506
LCCN: TK7868.D5 B43
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: Arpad Barna and Dan I. Porat
rawtitle: Integrated Circuits in Digital Electronics
entry:
@Book{Barna:1973:ICD,
  author =       "Arpad Barna and Dan I. Porat",
  title =        "Integrated Circuits in Digital Electronics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 483",
  year =         "1973",
  ISBN =         "0-471-05050-4",
  ISBN-13 =      "978-0-471-05050-6",
  LCCN =         "TK7868.D5 B43",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Barsi:1973:ECP
author: F. Barsi and P. Maestrini
title: Error Correcting Properties of Redundant Residue Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 3
pages: 307--315
month: mar
monthnumber: 3
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1973.223711
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:18 MDT 2011
bibtimestamp: 2011.07.12 16:45:18 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. Barsi and P. Maestrini
rawtitle: Error Correcting Properties of Redundant Residue Number Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672304; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35074

entry:
@Article{Barsi:1973:ECP,
  author =       "F. Barsi and P. Maestrini",
  title =        "Error Correcting Properties of Redundant Residue
                 Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "3",
  pages =        "307--315",
  month =        mar,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1973.223711",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672304;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35074",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The error correcting properties of the redundant
                 residue number systems (RNS) are investigated through a
                 more natural a approach than was previously known. The
                 necessary and sufficient condition for the correction
                 of a given error affecting a single \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Baugh:1973:TCP
author: C. R. Baugh and B. A. Wooley
title: A Two's Complement Parallel Array Multiplication Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 12
pages: 1045--1047
month: dec
monthnumber: 12
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1973.223648
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:37 MDT 2011
bibtimestamp: 2011.07.12 16:45:37 MDT
note: See comments cite Blankenship:1974:CTC,Kroft:1974:CTC.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672241
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. R. Baugh and B. A. Wooley
rawnote: See comments \cite{Blankenship:1974:CTC,Kroft:1974:CTC}.
rawtitle: A Two's Complement Parallel Array Multiplication Algorithm
entry:
@Article{Baugh:1973:TCP,
  author =       "C. R. Baugh and B. A. Wooley",
  title =        "A Two's Complement Parallel Array Multiplication
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "12",
  pages =        "1045--1047",
  month =        dec,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223648",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments
                 \cite{Blankenship:1974:CTC,Kroft:1974:CTC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672241",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Besslich:1973:MDS
author: P. W. Besslich and S. Raman
title: Multiplication, Division and Square Root Extraction Methods for Electronic Desk Calculators
journal: Journal of the Institution of Telecommunication Engineers (India)
volume: 19
number: 4
pages: 1045--1047
month: apr
monthnumber: 4
year: 1973
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
acknowledgement: ack-nj
rawauthor: P. W. Besslich and S. Raman
rawtitle: Multiplication, Division and Square Root Extraction Methods for Electronic Desk Calculators
entry:
@Article{Besslich:1973:MDS,
  author =       "P. W. Besslich and S. Raman",
  title =        "Multiplication, Division and Square Root Extraction
                 Methods for Electronic Desk Calculators",
  journal =      "Journal of the Institution of Telecommunication
                 Engineers (India)",
  volume =       "19",
  number =       "4",
  month =        apr,
  year =         "1973",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Brent:1973:PAV
author: Richard P. Brent
title: On the Precision Attainable with Various Floating-Point Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 601--607
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009113
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:14:15 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:15 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Richard P. Brent
rawtitle: On the Precision Attainable with Various Floating-Point Number Systems
entry:
@Article{Brent:1973:PAV,
  author =       "Richard P. Brent",
  title =        "On the Precision Attainable with Various
                 Floating-Point Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "601--607",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009113",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: article
filename: fparith.bib
label: Brent:1973:PEA
author: R. Brent and D. Kuck and K. Maruyama
title: The Parallel Evaluation of Arithmetic Expressions Without Division
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 5
pages: 532--534
month: may
monthnumber: 5
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1973.223757
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:23 MDT 2011
bibtimestamp: 2011.07.12 16:45:23 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. Brent and D. Kuck and K. Maruyama
rawtitle: The Parallel Evaluation of Arithmetic Expressions Without Division
entry:
@Article{Brent:1973:PEA,
  author =       "R. Brent and D. Kuck and K. Maruyama",
  title =        "The Parallel Evaluation of Arithmetic Expressions
                 Without Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "5",
  pages =        "532--534",
  month =        may,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223757",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Cappa:1973:AIA
author: M. Cappa and V. C. Hamacher
title: An Augmented Iterative Array for High-Speed Binary Division
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 2
pages: 172--175
month: feb
monthnumber: 2
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1973.223680
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:15 MDT 2011
bibtimestamp: 2011.07.12 16:45:15 MDT
note: See comments cite Gardiner:1974:CAI.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672273
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Cappa and V. C. Hamacher
rawnote: See comments \cite{Gardiner:1974:CAI}.
rawtitle: An Augmented Iterative Array for High-Speed Binary Division
entry:
@Article{Cappa:1973:AIA,
  author =       "M. Cappa and V. C. Hamacher",
  title =        "An Augmented Iterative Array for High-Speed Binary
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "172--175",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223680",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Gardiner:1974:CAI}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672273",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Cody:1973:SDN
author: William J. Cody, Jr.
title: Static and Dynamic Numerical Characteristics of Floating-Point Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 598--601
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009112
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:14:15 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:15 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: William J. {Cody, Jr.}
rawtitle: Static and Dynamic Numerical Characteristics of Floating-Point Arithmetic
entry:
@Article{Cody:1973:SDN,
  author =       "William J. {Cody, Jr.}",
  title =        "Static and Dynamic Numerical Characteristics of
                 Floating-Point Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "598--601",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009112",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: article
filename: fparith.bib
label: Dorr:1973:REC
author: Fred W. Dorr and Cleve B. Moler
title: Roundoff error on the CDC 6600 / 7600 computers
journal: j-SIGNUM
volume: 8
number: 2
pages: 24--26
month: apr
monthnumber: 4
year: 1973
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:49:59 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:49:59 MDT
fjournal: ACM SIGNUM Newsletter
keywords: arithmetic; CDC 6600/7600 computers; computer; digital arithmetic; program; roundoff error
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Univ. California, Los Alamos, NM, USA
journalURL: https://dl.acm.org/loi/signum
treatment: P Practical; X Experimental
rawauthor: Fred W. Dorr and Cleve B. Moler
rawtitle: Roundoff error on the {CDC 6600\slash 7600} computers
entry:
@Article{Dorr:1973:REC,
  author =       "Fred W. Dorr and Cleve B. Moler",
  title =        "Roundoff error on the {CDC 6600\slash 7600}
                 computers",
  journal =      j-SIGNUM,
  volume =       "8",
  number =       "2",
  pages =        "24--26",
  month =        apr,
  year =         "1973",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:49:59 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. California, Los Alamos, NM, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; CDC 6600/7600 computers; computer; digital
                 arithmetic; program; roundoff error",
  treatment =    "P Practical; X Experimental",
}


bibtype: article
filename: fparith.bib
label: Du:1973:CSS
author: Min-Wen Du and C. Dennis Weiss
title: Circuit Structure and Switching Function Verification
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 618--625
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009116
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:18:24 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Min-Wen Du and C. Dennis Weiss
rawtitle: Circuit Structure and Switching Function Verification
entry:
@Article{Du:1973:CSS,
  author =       "Min-Wen Du and C. Dennis Weiss",
  title =        "Circuit Structure and Switching Function
                 Verification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "618--625",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009116",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1973:REC
author: Milos D. Ercegovac
title: Radix-16 Evaluation of Certain Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 561--566
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009107
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:39 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:39 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milo{\v{s}} D. Ercegovac
rawtitle: Radix-16 Evaluation of Certain Elementary Functions
entry:
@Article{Ercegovac:1973:REC,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "Radix-16 Evaluation of Certain Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "561--566",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009107",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: techreport
filename: fparith.bib
label: Erkio:1973:EAV
author: Hannu Erkio
title: An extension of ALGOL with variable precision floating-point arithmetic
type: Series A. Report
number: 1973/2
institution: University of Helsinki, Department of Computer Science
address: Helsinki
pages: ii + 20
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: ALGOL (Computer program language); Floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Hannu Erkio
rawtitle: An extension of {ALGOL} with variable precision floating-point arithmetic
entry:
@TechReport{Erkio:1973:EAV,
  author =       "Hannu Erkio",
  title =        "An extension of {ALGOL} with variable precision
                 floating-point arithmetic",
  type =         "Series {A}. Report",
  number =       "1973/2",
  institution =  "University of Helsinki, Department of Computer
                 Science",
  address =      "Helsinki",
  pages =        "ii + 20",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ALGOL (Computer program language); Floating-point
                 arithmetic",
}


bibtype: article
filename: fparith.bib
label: Fettweis:1973:RNA
author: A. Fettweis
title: Roundoff noise and attenuation sensitivity in digital filters with fixed-point arithmetic
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 20
number: 2
pages: 174--175
month: mar
monthnumber: 3
year: 1973
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: A. Fettweis
rawtitle: Roundoff noise and attenuation sensitivity in digital filters with fixed-point arithmetic
entry:
@Article{Fettweis:1973:RNA,
  author =       "A. Fettweis",
  title =        "Roundoff noise and attenuation sensitivity in digital
                 filters with fixed-point arithmetic",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "20",
  number =       "2",
  pages =        "174--175",
  month =        mar,
  year =         "1973",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "A general expression is established which relates the
                 output roundoff noise generated by a fixed-point
                 multiplier in a digital filter to the sensitivity of
                 the filter attenuation with respect to the
                 corresponding multiplier coefficient. It confirms
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gelenbe:1973:UAE
author: Erol Gelenbe
title: A Unified Approach to the Evaluation of a Class of Replacement Algorithms
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 611--618
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009115
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:18:24 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Erol Gelenbe
rawtitle: A Unified Approach to the Evaluation of a Class of Replacement Algorithms
entry:
@Article{Gelenbe:1973:UAE,
  author =       "Erol Gelenbe",
  title =        "A Unified Approach to the Evaluation of a Class of
                 Replacement Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "611--618",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009115",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: article
filename: fparith.bib
label: Green:1973:NTF
author: D. H. Green and R. G. Kelsch
title: Nonlinear Ternary Feedback Shift Registers
journal: j-COMP-J
volume: 16
number: 4
pages: 360--367
month: nov
monthnumber: 11
year: 1973
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:52:16 MDT 2000
bibtimestamp: 2000.09.29 08:52:16 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
corpsource: Univ. Manchester Inst. Sci. Technol., UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: D. H. Green and R. G. Kelsch
rawtitle: Nonlinear Ternary Feedback Shift Registers
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/160360.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/360.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/361.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/362.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/363.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/364.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/365.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/366.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/367.tif

keywords:
arithmetic; coding theory; communications; computers, digital; digital arithmetic; digital computers; feedback shift registers; functions; nonlinear; polynomial domain representation; shift registers; ternary

classcodes:
B1260 (Pulse circuits); B1265 (Digital electronics); C5120 (Logic and switching circuits); C5230 (Digital arithmetic methods)

entry:
@Article{Green:1973:NTF,
  author =       "D. H. Green and R. G. Kelsch",
  title =        "Nonlinear Ternary Feedback Shift Registers",
  journal =      j-COMP-J,
  volume =       "16",
  number =       "4",
  pages =        "360--367",
  month =        nov,
  year =         "1973",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:52:16 MDT 2000",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/160360.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/360.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/361.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/362.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/363.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/364.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/365.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/366.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/367.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "B1260 (Pulse circuits); B1265 (Digital electronics);
                 C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  classification = "722",
  corpsource =   "Univ. Manchester Inst. Sci. Technol., UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic; coding theory; communications; computers,
                 digital; digital arithmetic; digital computers;
                 feedback shift registers; functions; nonlinear;
                 polynomial domain representation; shift registers;
                 ternary",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: fparith.bib
label: Hamming:1973:NMS
author: R. W. (Richard Wesley) Hamming
title: Numerical methods for scientists and engineers
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
edition: Second
pages: ix + 721
year: 1973
ISBN: 0-07-025887-2 OR 0070258872
ISBN13: 978-0-07-025887-7 OR 9780070258877
LCCN: QA297 .H28 1973
bibdate: Fri Aug 20 09:12:08 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:12:08 MDT
series: International series in pure and applied mathematics
subject: Numerical analysis; Data processing
acknowledgement: ack-nhfb
rawauthor: R. W. (Richard Wesley) Hamming
rawtitle: Numerical methods for scientists and engineers
entry:
@Book{Hamming:1973:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "ix + 721",
  year =         "1973",
  ISBN =         "0-07-025887-2",
  ISBN-13 =      "978-0-07-025887-7",
  LCCN =         "QA297 .H28 1973",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Data processing",
}


bibtype: article
filename: fparith.bib
label: Hwang:1973:RRS
author: W. G. Hwang and John Todd
title: A recurrence relation for the square root
journal: j-J-APPROX-THEORY
volume: 9
pages: 299--306
year: 1973
CODEN: JAXTAZ
DOI: https://doi.org/10.1016/0021-9045(73)90075-0
ISSN: 0021-9045,1096-0430 OR 00219045,10960430
ISSNL: 0021-9045 OR 00219045
MRclass: 65H05
MRnumber: 373270
MRreviewer: L. Fox
bibdate: Sat Oct 21 14:25:01 2023
bibtimestamp: 2023.10.21 14:25:01 ???
fjournal: Journal of Approximation Theory
ZMnumber: 0271.65032
acknowledgement: ack-nhfb
authordates: John Todd (16 May 1911--21 June 2007)
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: W. G. Hwang and John Todd
rawtitle: A recurrence relation for the square root
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Hwang:1973:RRS,
  author =       "W. G. Hwang and John Todd",
  title =        "A recurrence relation for the square root",
  journal =      j-J-APPROX-THEORY,
  volume =       "9",
  pages =        "299--306",
  year =         "1973",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(73)90075-0",
  ISSN =         "0021-9045,1096-0430",
  ISSN-L =       "0021-9045",
  MRclass =      "65H05",
  MRnumber =     "373270",
  MRreviewer =   "L. Fox",
  bibdate =      "Sat Oct 21 14:25:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0271.65032",
  acknowledgement = ack-nhfb,
  author-dates = "John Todd (16 May 1911--21 June 2007)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  received =     "19 April 1971",
  ZBmath =       "3426800",
}


bibtype: article
filename: fparith.bib
label: Jacobsohn:1973:CDA
author: David H. Jacobsohn
title: A Combinatoric Division Algorithm for Fixed-Integer Divisors
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 608--610
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009114
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:18:24 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: David H. Jacobsohn
rawtitle: A Combinatoric Division Algorithm for Fixed-Integer Divisors
entry:
@Article{Jacobsohn:1973:CDA,
  author =       "David H. Jacobsohn",
  title =        "A Combinatoric Division Algorithm for Fixed-Integer
                 Divisors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "608--610",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009114",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1973:IAL
author: W. Kahan
title: Implementation of algorithms (lecture notes by W. S. Haugeland and D. Hough)
type: Technical report
number: 20
institution: Department of Computer Science
address: Berkeley, CA, USA
pages: 608--610
year: 1973
bibdate: Tue Aug 28 05:28:07 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.28 05:28:07 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Implementation of algorithms (lecture notes by {W. S. Haugeland} and {D. Hough})
remark:
This paper contains the modified compensating summation algorithm wherein `e = (temp - s) + y' is replaced by `f = 0; if (sign(temp) == sign(y)) f = (0.46*s - s) + s e = ((temp - f) - (s - f)) + y', cited in e.g., cite Dalhquist:1974:NM,Higham:1993:AFP. Kahan remarks ``The mysterious constant 0.46, which could perhaps be any number between 0.25 and 0.50, and the fact that the proof requires a consideration of known machines designs, indicate that this algorithm is not an advance in computer science.''

entry:
@TechReport{Kahan:1973:IAL,
  author =       "W. Kahan",
  title =        "Implementation of algorithms (lecture notes by {W. S.
                 Haugeland} and {D. Hough})",
  type =         "Technical report",
  number =       "20",
  institution =  "Department of Computer Science",
  address =      "Berkeley, CA, USA",
  year =         "1973",
  bibdate =      "Tue Aug 28 05:28:07 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  remark =       "This paper contains the modified compensating
                 summation algorithm wherein `e = (temp - s) + y' is
                 replaced by `f = 0; if (sign(temp) == sign(y)) {f =
                 (0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
                 cited in e.g.,
                 \cite{Dalhquist:1974:NM,Higham:1993:AFP}. Kahan remarks
                 ``The mysterious constant 0.46, which could perhaps be
                 any number between 0.25 and 0.50, and the fact that the
                 proof requires a consideration of known machines
                 designs, indicate that this algorithm is not an advance
                 in computer science.''",
}


bibtype: article
filename: fparith.bib
label: Kan:1973:CEA
author: E. Kan and J. Aggarwal
title: Correction to ``Error Analysis of Digital Filters Employing Floating-Point Arithmetic''
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 20
number: 5
pages: 617--618
month: sep
monthnumber: 9
year: 1973
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
note: See cite Kan:1971:EAD.
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: E. Kan and J. Aggarwal
rawnote: See \cite{Kan:1971:EAD}.
rawtitle: Correction to {``Error Analysis of Digital Filters Employing Floating-Point Arithmetic''}
entry:
@Article{Kan:1973:CEA,
  author =       "E. Kan and J. Aggarwal",
  title =        "Correction to {``Error Analysis of Digital Filters
                 Employing Floating-Point Arithmetic''}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "20",
  number =       "5",
  pages =        "617--618",
  month =        sep,
  year =         "1973",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Kan:1971:EAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
}


bibtype: article
filename: fparith.bib
label: Kanani:1973:NCS
author: Dhirubhai V. Kanani and Kenneth H. O'Keefe
title: A Note on Conditional-Sum Addition for Base $ - 2 $ Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 626--626
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009117
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:26 MDT 2011
bibtimestamp: 2011.07.12 16:45:26 MDT
fjournal: IEEE Transactions on Computers
keywords: ARITH-2; negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Dhirubhai V. Kanani and Kenneth H. O'Keefe
rawtitle: A Note on Conditional-Sum Addition for Base $ - 2 $ Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009117; http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf

entry:
@Article{Kanani:1973:NCS,
  author =       "Dhirubhai V. Kanani and Kenneth H. O'Keefe",
  title =        "A Note on Conditional-Sum Addition for Base $ - 2 $
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "626--626",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009117",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009117;
                 http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; negative base",
}


bibtype: article
filename: fparith.bib
label: Kaneko:1973:LCO
author: T. Kaneko
title: Limit-cycle oscillations in floating-point digital filters
journal: j-IEEE-TRANS-AUDIO-ELECTROACOUST
volume: 21
number: 2
pages: 100--106
month: apr
monthnumber: 4
year: 1973
CODEN: ITADAS
ISSN: 0018-9278 (print), 1558-2582 (electronic) OR 00189278 (print), 15582582 (electronic)
ISSNL: 0018-9278 OR 00189278
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Audio and Electroacoustics
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337
rawauthor: T. Kaneko
rawtitle: Limit-cycle oscillations in floating-point digital filters
entry:
@Article{Kaneko:1973:LCO,
  author =       "T. Kaneko",
  title =        "Limit-cycle oscillations in floating-point digital
                 filters",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "21",
  number =       "2",
  pages =        "100--106",
  month =        apr,
  year =         "1973",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "In a digital filter realized with fixed-point
                 arithmetic, there is a peculiar phenomenon known as
                 limit-cycle oscillation, which is due to roundoff
                 errors. For floating-point arithmetic, it has been
                 conjectured that its amplitude is negligibly small,
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Kaneko:1973:LRE
author: Toyohisa Kaneko and Bede Liu
title: On Local Roundoff Errors in Floating-Point Arithmetic
journal: j-J-ACM
volume: 20
number: 3
pages: 391--398
month: jul
monthnumber: 7
year: 1973
CODEN: JACOAH
DOI: https://doi.org/10.1145/321765.321771
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65G05
MRnumber: 49 8318
bibdate: Tue Oct 09 10:18:49 2007
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.09 10:18:49 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
reviewer: V. V. Ivanov
rawauthor: Toyohisa Kaneko and Bede Liu
rawtitle: On Local Roundoff Errors in Floating-Point Arithmetic
abstract:
A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator. A statistical model for the roundoff error in double-precision multiplication and addition is also derived. The model is confirmed by experimental measurements.

rawabstract:
A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator. A statistical model for the roundoff error in double-precision multiplication and addition is also derived. The model is confirmed by experimental measurements.

entry:
@Article{Kaneko:1973:LRE,
  author =       "Toyohisa Kaneko and Bede Liu",
  title =        "On Local Roundoff Errors in Floating-Point
                 Arithmetic",
  journal =      j-J-ACM,
  volume =       "20",
  number =       "3",
  pages =        "391--398",
  month =        jul,
  year =         "1973",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321765.321771",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "49 8318",
  bibdate =      "Tue Oct 09 10:18:49 2007",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A bound on the relative error in floating-point
                 addition using a single-precision accumulator with
                 guard digits is derived. It is shown that even with a
                 single guard digit, the accuracy can be almost as good
                 as that using a double-precision accumulator. A
                 statistical model for the roundoff error in
                 double-precision multiplication and addition is also
                 derived. The model is confirmed by experimental
                 measurements.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  reviewer =     "V. V. Ivanov",
}


bibtype: techreport
filename: fparith.bib
label: Kent:1973:PDS
author: Jan G. Kent
title: Procedures for the description and simulation of floating point instructions
type: Report
number: 426
institution: Norwegian Computing Center
address: Oslo, Norway
pages: 391--398
month: sep
monthnumber: 9
year: 1973
bibdate: Sat Jan 09 06:27:20 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2021.01.09 06:27:20 ???
acknowledgement: ack-nhfb
rawauthor: Jan G. Kent
rawtitle: Procedures for the description and simulation of floating point instructions
entry:
@TechReport{Kent:1973:PDS,
  author =       "Jan G. Kent",
  title =        "Procedures for the description and simulation of
                 floating point instructions",
  type =         "Report",
  number =       "426",
  institution =  "Norwegian Computing Center",
  address =      "Oslo, Norway",
  month =        sep,
  year =         "1973",
  bibdate =      "Sat Jan 09 06:27:20 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Kent:1973:TDA
author: Jan G. Kent
title: Theoretical definition, analysis and comparison of floating point instructions
type: Report
number: 425
institution: Norwegian Computing Center
address: Oslo, Norway
pages: 391--398
month: sep
monthnumber: 9
year: 1973
bibdate: Sat Jan 09 06:27:20 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2021.01.09 06:27:20 ???
acknowledgement: ack-nhfb
rawauthor: Jan G. Kent
rawtitle: Theoretical definition, analysis and comparison of floating point instructions
entry:
@TechReport{Kent:1973:TDA,
  author =       "Jan G. Kent",
  title =        "Theoretical definition, analysis and comparison of
                 floating point instructions",
  type =         "Report",
  number =       "425",
  institution =  "Norwegian Computing Center",
  address =      "Oslo, Norway",
  month =        sep,
  year =         "1973",
  bibdate =      "Sat Jan 09 06:27:20 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kielbasinski:1973:SAC
author: Andrzej Kielbasinski
title: Summation algorithm with corrections and some of its applications
journal: j-MATH-STOS
volume: 1
pages: 22--41
year: 1973
bibdate: Tue Aug 28 06:06:57 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.28 06:06:57 ???
note: In Polish.
fjournal: Math. Stos.
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: Andrzej Kie{\l}basi{\'n}ski
rawnote: In Polish.
rawtitle: Summation algorithm with corrections and some of its applications
remark:
The author's name is correct [verified by a Polish colleague who knows the author]: some references have it incorrectly as Kielbaszinski.

entry:
@Article{Kielbasinski:1973:SAC,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Summation algorithm with corrections and some of its
                 applications",
  journal =      j-MATH-STOS,
  volume =       "1",
  pages =        "22--41",
  year =         "1973",
  bibdate =      "Tue Aug 28 06:06:57 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "In Polish.",
  acknowledgement = ack-nhfb,
  fjournal =     "Math. Stos.",
  keywords =     "accurate floating-point summation",
  remark =       "The author's name is correct [verified by a Polish
                 colleague who knows the author]: some references have
                 it incorrectly as Kie{\l}baszi{\'n}ski.",
}


bibtype: article
filename: fparith.bib
label: Kinoshita:1973:GDS
author: E. Kinoshita and H. Kosako and Y. Kojima
title: General Division in the Symmetric Residue Number System
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 2
pages: 134--142
month: feb
monthnumber: 2
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1973.223674
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 9 11:38:57 MST 2007
bibtimestamp: 2007.11.09 11:38:57 MST
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Kinoshita and H. Kosako and Y. Kojima
rawtitle: General Division in the Symmetric Residue Number System
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672267; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35073

entry:
@Article{Kinoshita:1973:GDS,
  author =       "E. Kinoshita and H. Kosako and Y. Kojima",
  title =        "General Division in the Symmetric Residue Number
                 System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "134--142",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1973.223674",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672267;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35073",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "In the residue number system, the arithmetic
                 operations of addition, subtraction, and multiplication
                 are executed in the same period of time without the
                 need for interpositional carry. There is a hope for
                 high-speed operation if residue arithmetic \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Kreifelts:1973:OBF
author: T. Kreifelts
journal: j-COMPUTING
volume: 11
pages: 353--363
year: 1973
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Fri Sep 16 16:30:39 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:39 ???
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/607
rawauthor: T. Kreifelts
title:
Optimale Basiswahl fur eine Gleitkomma-Arithmetik toenglish Optimal Choice of Basis for a Floating-Point Arithmetic endtoenglish 

rawtitle:
{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik} \toenglish {Optimal Choice of Basis for a Floating-Point Arithmetic} \endtoenglish

entry:
@Article{Kreifelts:1973:OBF,
  author =       "T. Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine
                 Gleitkomma-Arithmetik} \toenglish {Optimal Choice of
                 Basis for a Floating-Point Arithmetic} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "??",
  pages =        "353--363",
  month =        "????",
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: article
filename: fparith.bib
label: Kreifelts:1973:OBG
author: Thomas Kreifelts
journal: j-COMPUTING
volume: 11
number: 4
pages: 353--363
month: dec
monthnumber: 12
year: 1973
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:51 MST 2001
bibtimestamp: 2001.01.02 17:40:51 MST
note: See correction cite Kreifelts:1975:OBF.
fjournal: Computing
language: German
acknowledgement: ack-nj
affiliation: Inst. Numerische Datenverarbeitung, Bonn, West Germany
journalURL: http://link.springer.com/journal/607
journalabr: Comput (Vienna/NY)
rawauthor: Thomas Kreifelts
rawnote: See correction \cite{Kreifelts:1975:OBF}.
title:
Optimale Basiswahl fur eine Gleitkomma-Arithmetik. (German) [Optimal Choice of Basis for a Floating-Point Arithmetic]

bibsource:
Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)

keywords:
base; computer programming; correct rounding; floating point arithmetic; mathematical techniques; optimal choice; rounding errors

rawtitle:
{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of Basis for a Floating-Point Arithmetic]

entry:
@Article{Kreifelts:1973:OBG,
  author =       "Thomas Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine
                 Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
                 Basis for a Floating-Point Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "4",
  pages =        "353--363",
  month =        dec,
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "See correction \cite{Kreifelts:1975:OBF}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Inst. Numerische Datenverarbeitung, Bonn, West
                 Germany",
  classification = "723; 921; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "base; computer programming; correct rounding; floating
                 point arithmetic; mathematical techniques; optimal
                 choice; rounding errors",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Kuki:1973:SSA
author: H. Kuki and W. J. Cody
title: A Statistical Study of the Accuracy of Floating Point Number Systems
journal: j-CACM
volume: 16
number: 4
pages: 223--230
month: apr
monthnumber: 4
year: 1973
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68A20 (65G05)
MRnumber: 51 2344
MRreviewer: I. Kaufmann
bibdate: Wed Aug 31 13:47:33 1994
bibtimestamp: 1994.08.31 13:47:33 ???
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Univ. Chicago, IL, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: T Theoretical or Mathematical
rawauthor: H. Kuki and W. J. Cody
rawtitle: A Statistical Study of the Accuracy of Floating Point Number Systems
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
This paper presents the statistical results of tests of the accuracy of certain arithmetic systems in evaluating sums, products and inner products, and analytic error estimates for some of the computations. The arithmetic systems studied are 6-digit hexadecimal and 22-digit binary floating point number representations combined with the usual chop and round modes of arithmetic with various numbers of guard digits, and with a modified round mode with guard digits. In a certain sense, arithmetic systems differing only in their use of binary or hexadecimal number representations are shown to be approximately statistically equivalent in accuracy. Further, the usual round mode with guard digits is shown to be statistically superior in accuracy to the usual chop mode in all cases save one. The modified round mode is found to be superior to the chop mode in all cases.

keywords:
accuracy; arithmetic; computer programming; digital arithmetic; error analysis; floating point arithmetic; floating point number systems; guard digits; number representation; rounding; statistical study

rawabstract:
This paper presents the statistical results of tests of the accuracy of certain arithmetic systems in evaluating sums, products and inner products, and analytic error estimates for some of the computations. The arithmetic systems studied are 6-digit hexadecimal and 22-digit binary floating point number representations combined with the usual chop and round modes of arithmetic with various numbers of guard digits, and with a modified round mode with guard digits. In a certain sense, arithmetic systems differing only in their use of binary or hexadecimal number representations are shown to be approximately statistically equivalent in accuracy. Further, the usual round mode with guard digits is shown to be statistically superior in accuracy to the usual chop mode in all cases save one. The modified round mode is found to be superior to the chop mode in all cases.

entry:
@Article{Kuki:1973:SSA,
  author =       "H. Kuki and W. J. Cody",
  title =        "A Statistical Study of the Accuracy of Floating Point
                 Number Systems",
  journal =      j-CACM,
  volume =       "16",
  number =       "4",
  pages =        "223--230",
  month =        apr,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68A20 (65G05)",
  MRnumber =     "51 2344",
  MRreviewer =   "I. Kaufmann",
  bibdate =      "Wed Aug 31 13:47:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents the statistical results of tests
                 of the accuracy of certain arithmetic systems in
                 evaluating sums, products and inner products, and
                 analytic error estimates for some of the computations.
                 The arithmetic systems studied are 6-digit hexadecimal
                 and 22-digit binary floating point number
                 representations combined with the usual chop and round
                 modes of arithmetic with various numbers of guard
                 digits, and with a modified round mode with guard
                 digits. In a certain sense, arithmetic systems
                 differing only in their use of binary or hexadecimal
                 number representations are shown to be approximately
                 statistically equivalent in accuracy. Further, the
                 usual round mode with guard digits is shown to be
                 statistically superior in accuracy to the usual chop
                 mode in all cases save one. The modified round mode is
                 found to be superior to the chop mode in all cases.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723",
  corpsource =   "Univ. Chicago, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "accuracy; arithmetic; computer programming; digital
                 arithmetic; error analysis; floating point arithmetic;
                 floating point number systems; guard digits; number
                 representation; rounding; statistical study",
  oldlabel =     "KukiC73",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/KukiC73",
}


bibtype: article
filename: fparith.bib
label: Larson:1973:HSM
author: R. H. Larson
title: High Speed Multiply Using Four Input Carry Save Adder
journal: j-IBM-TDB
pages: 2053--2054
month: dec
monthnumber: 12
year: 1973
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Fri Jun 24 20:46:32 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:46:32 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nhfb
rawauthor: R. H. Larson
rawtitle: High Speed Multiply Using Four Input Carry Save Adder
entry:
@Article{Larson:1973:HSM,
  author =       "R. H. Larson",
  title =        "High Speed Multiply Using Four Input Carry Save
                 Adder",
  journal =      j-IBM-TDB,
  volume =       "??",
  number =       "??",
  pages =        "2053--2054",
  month =        dec,
  year =         "1973",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Jun 24 20:46:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Larson:1973:MSM
author: R. H. Larson
title: Medium Speed Multiply
journal: j-IBM-TDB
pages: 2055--2055
month: dec
monthnumber: 12
year: 1973
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Fri Jun 24 20:42:28 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:42:28 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nhfb
rawauthor: R. H. Larson
rawtitle: Medium Speed Multiply
entry:
@Article{Larson:1973:MSM,
  author =       "R. H. Larson",
  title =        "Medium Speed Multiply",
  journal =      j-IBM-TDB,
  volume =       "??",
  number =       "??",
  pages =        "2055--2055",
  month =        dec,
  year =         "1973",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Jun 24 20:42:28 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: phdthesis
filename: fparith.bib
label: Lee:1973:SFP
author: Keng Ho Lee
title: Survey of floating-point software arithmetics and basic library mathematical functions
type: Thesis (Ph.D.)
school: Glasgow University
address: Glasgow, Scotland
pages: 2055--2055
year: 1973
bibdate: Thu May 09 08:34:15 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:34:15 ???
acknowledgement: ack-nhfb
rawauthor: Keng Ho Lee
rawtitle: Survey of floating-point software arithmetics and basic library mathematical functions
entry:
@PhdThesis{Lee:1973:SFP,
  author =       "Keng Ho Lee",
  title =        "Survey of floating-point software arithmetics and
                 basic library mathematical functions",
  type =         "Thesis ({Ph.D.})",
  school =       "Glasgow University",
  address =      "Glasgow, Scotland",
  year =         "1973",
  bibdate =      "Thu May 09 08:34:15 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Majithia:1973:NBL
author: J. C. Majithia and D. Levan
title: A note on base-2 logarithm computations
journal: j-PROC-IEEE
volume: 61
number: 10
pages: 1519--1520
month: oct
monthnumber: 10
year: 1973
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 18:05:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 18:05:03 MDT
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: J. C. Majithia and D. Levan
rawtitle: A note on base-2 logarithm computations
entry:
@Article{Majithia:1973:NBL,
  author =       "J. C. Majithia and D. Levan",
  title =        "A note on base-2 logarithm computations",
  journal =      j-PROC-IEEE,
  volume =       "61",
  number =       "10",
  pages =        "1519--1520",
  month =        oct,
  year =         "1973",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 18:05:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "The well-known methods of iteration used suitably can
                 yield a more accurate and rapidly convergent
                 computation for the values of many functions. One
                 typical example is the base-2 logarithm-antilogarithm
                 computation. Some recently proposed techniques
                 \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Malcolm:1973:MAP
author: Michael A. Malcolm
title: A machine-independent ALGOL procedure for accurate floating-point summation
type: Technical report
number: STAN-CS-73-374
institution: Stanford University, Computer Science Department
address: Stanford, CA, USA
pages: 6
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: ALGOL (Computer program language)
acknowledgement: ack-nhfb
rawauthor: Michael A. Malcolm
rawtitle: A machine-independent {ALGOL} procedure for accurate floating-point summation
entry:
@TechReport{Malcolm:1973:MAP,
  author =       "Michael A. Malcolm",
  title =        "A machine-independent {ALGOL} procedure for accurate
                 floating-point summation",
  type =         "Technical report",
  number =       "STAN-CS-73-374",
  institution =  "Stanford University, Computer Science Department",
  address =      "Stanford, CA, USA",
  pages =        "6",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ALGOL (Computer program language)",
}


bibtype: phdthesis
filename: fparith.bib
label: Malcolm:1973:PAF
author: Michael A. Malcolm
title: Part I: On accurate floating-point summation; Part II: Computation of nonlinear spline functions
type: Thesis (Ph.D.)
school: Department of Computer Science, Stanford University
address: Stanford, CA, USA
pages: ix + 129
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: accurate floating-point summation; Interpolation; spline theory
acknowledgement: ack-nhfb
rawauthor: Michael A. Malcolm
rawtitle:
Part {I}: On accurate floating-point summation; Part {II}: Computation of nonlinear spline functions

entry:
@PhdThesis{Malcolm:1973:PAF,
  author =       "Michael A. Malcolm",
  title =        "Part {I}: On accurate floating-point summation; Part
                 {II}: Computation of nonlinear spline functions",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "ix + 129",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Interpolation;
                 spline theory",
}


bibtype: article
filename: fparith.bib
label: Marasa:1973:SSC
author: John D. Marasa and David W. Matula
title: A simulated study of correlated error propagation in various finite-precision arithmetics
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 587--597
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009111
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon May 20 05:07:23 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.20 05:07:23 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: John D. Marasa and David W. Matula
rawtitle: A simulated study of correlated error propagation in various finite-precision arithmetics
entry:
@Article{Marasa:1973:SSC,
  author =       "John D. Marasa and David W. Matula",
  title =        "A simulated study of correlated error propagation in
                 various finite-precision arithmetics",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "587--597",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009111",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 05:07:23 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1973:ABC
author: Nicholas C. Metropolis
title: Analyzed Binary Computing
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 573--576
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009109
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Mar 21 09:24:37 2007
bibtimestamp: 2007.03.21 09:24:37 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Nicholas C. Metropolis
rawtitle: Analyzed Binary Computing
abstract:
A single format for the representation of numbers in a computer is proposed to accommodate both exact and inexact quantities. A consistent set of rules is described for addition (subtraction), multiplication, and division of such quantities, both within their separate types, as well as in combination. Error correlation aside, the propagation of inherent errors is monitored in operations with at least one imprecise value. A definitive algorithm must, of course take into account any correlations of inherent errors; these correlations must be recognized and incorporated into the algorithm by the numerical analyst, not by the logical designer of the computer.

keywords:
ARITH-2; control of propagated errors; floating-point representation; representation error; significant digit arithmetic

rawabstract:
A single format for the representation of numbers in a computer is proposed to accommodate both exact and inexact quantities. A consistent set of rules is described for addition (subtraction), multiplication, and division of such quantities, both within their separate types, as well as in combination. Error correlation aside, the propagation of inherent errors is monitored in operations with at least one imprecise value. A definitive algorithm must, of course take into account any correlations of inherent errors; these correlations must be recognized and incorporated into the algorithm by the numerical analyst, not by the logical designer of the computer.

entry:
@Article{Metropolis:1973:ABC,
  author =       "Nicholas C. Metropolis",
  title =        "Analyzed Binary Computing",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "573--576",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009109",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Mar 21 09:24:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A single format for the representation of numbers in a
                 computer is proposed to accommodate both exact and
                 inexact quantities. A consistent set of rules is
                 described for addition (subtraction), multiplication,
                 and division of such quantities, both within their
                 separate types, as well as in combination. Error
                 correlation aside, the propagation of inherent errors
                 is monitored in operations with at least one imprecise
                 value. A definitive algorithm must, of course take into
                 account any correlations of inherent errors; these
                 correlations must be recognized and incorporated into
                 the algorithm by the numerical analyst, not by the
                 logical designer of the computer.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; control of propagated errors; floating-point
                 representation; representation error; significant digit
                 arithmetic",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1973:SAC
author: N. Metropolis and Gian-Carlo Rota and S. Tanny
title: Significance arithmetic: the carrying algorithm
journal: j-J-COMB-THEORY-A
volume: 14
pages: 386--421
month: may
monthnumber: 5
year: 1973
CODEN: JCBTA7
ISSN: 0097-3165 (print), 1096-0899 (electronic) OR 00973165 (print), 10960899 (electronic)
ISSNL: 0097-3165 OR 00973165
MRclass: 10A30 (02E10)
MRnumber: MR0321857 (48 \#222)
MRreviewer: R. L. Goodstein
bibdate: Thu Nov 8 14:50:22 2007
bibtimestamp: 2007.11.08 14:50:22 ???
fjournal: Journal of Combinatorial Theory. Series A
ZMnumber: 0259.00001
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00973165
rawauthor: N. Metropolis and Gian-Carlo Rota and S. Tanny
rawtitle: Significance arithmetic: the carrying algorithm
abstract:
It has been remarked that, in mathematics, a notational deficiency is often a symptom of conceptual obscurity. The starting point of this work is one such deficiency. In ordinary binary arithmetic, a number ending in a string of ones, such as $ 0.0110111 ldots $ is equal to the number obtained by replacing the digit zero next to the string of ones by the digit one, and the string of succeeding ones by zeros; in the example, $ 0.0111000 $

rawabstract:
It has been remarked that, in mathematics, a notational deficiency is often a symptom of conceptual obscurity. The starting point of this work is one such deficiency. In ordinary binary arithmetic, a number ending in a string of ones, such as $ 0.0110111 \ldots {} $ is equal to the number obtained by replacing the digit zero next to the string of ones by the digit one, and the string of succeeding ones by zeros; in the example, $ 0.0111000 $

entry:
@Article{Metropolis:1973:SAC,
  author =       "N. Metropolis and Gian-Carlo Rota and S. Tanny",
  title =        "Significance arithmetic: the carrying algorithm",
  journal =      j-J-COMB-THEORY-A,
  volume =       "14",
  pages =        "386--421",
  month =        may,
  year =         "1973",
  CODEN =        "JCBTA7",
  ISSN =         "0097-3165 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  MRclass =      "10A30 (02E10)",
  MRnumber =     "MR0321857 (48 \#222)",
  MRreviewer =   "R. L. Goodstein",
  bibdate =      "Thu Nov 8 14:50:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0259.00001",
  abstract =     "It has been remarked that, in mathematics, a
                 notational deficiency is often a symptom of conceptual
                 obscurity. The starting point of this work is one such
                 deficiency. In ordinary binary arithmetic, a number
                 ending in a string of ones, such as $ 0.0110111 \ldots
                 {} $ is equal to the number obtained by replacing the
                 digit zero next to the string of ones by the digit one,
                 and the string of succeeding ones by zeros; in the
                 example, $ 0.0111000 $",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory. Series A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
}


bibtype: article
filename: fparith.bib
label: Mifsud:1973:AMP
author: Charles J. Mifsud and Michael J. Bohlen
title: Addendum to a Multiple-Precision Division Algorithm
journal: j-CACM
volume: 16
number: 10
pages: 628--??
year: 1973
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:04:18 MST 2001
bibtimestamp: 2001.01.22 07:04:18 MST
note: See cite Mifsud:1970:MDA.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Charles J. Mifsud and Michael J. Bohlen
rawnote: See \cite{Mifsud:1970:MDA}.
rawtitle: Addendum to a Multiple-Precision Division Algorithm
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#MifsudB73; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Mifsud:1973:AMP,
  author =       "Charles J. Mifsud and Michael J. Bohlen",
  title =        "Addendum to a Multiple-Precision Division Algorithm",
  journal =      j-CACM,
  volume =       "16",
  number =       "10",
  pages =        "628--??",
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:04:18 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#MifsudB73;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Mifsud:1970:MDA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "MifsudB73",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/MifsudB73",
}


bibtype: article
filename: fparith.bib
label: Newbery:1973:EAF
author: A. C. R. Newbery
title: Error Analysis for Fourier Series Evaluation
journal: j-MATH-COMPUT
volume: 27
number: 123
pages: 639--644
month: jul
monthnumber: 7
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: B0290B (Error analysis in numerical methods); C4110 (Error analysis in numerical methods)
corpsource: Univ. Kentucky, Lexington, KY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: A. C. R. Newbery
rawtitle: Error Analysis for {Fourier} Series Evaluation
keywords:
error analysis; evaluation; floating point; Fourier series evaluation; numerical methods; polynomials; recursive method; series (mathematics); trigonometric polynomials

entry:
@Article{Newbery:1973:EAF,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for {Fourier} Series Evaluation",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "123",
  pages =        "639--644",
  month =        jul,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Univ. Kentucky, Lexington, KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "error analysis; evaluation; floating point; Fourier
                 series evaluation; numerical methods; polynomials;
                 recursive method; series (mathematics); trigonometric
                 polynomials",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: OKeefe:1973:RBE
author: Kenneth H. O'Keefe and John L. Wright
title: Remarks on Base Extension for Modular Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 9
pages: 833--835
month: sep
monthnumber: 9
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009173
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:31 MDT 2011
bibtimestamp: 2011.07.12 16:45:31 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Kenneth H. O'Keefe and John L. Wright
rawtitle: Remarks on Base Extension for Modular Arithmetic
entry:
@Article{OKeefe:1973:RBE,
  author =       "Kenneth H. O'Keefe and John L. Wright",
  title =        "Remarks on Base Extension for Modular Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "9",
  pages =        "833--835",
  month =        sep,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009173",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: mastersthesis
filename: fparith.bib
label: Parker:1973:DHF
author: Tony Edwin Parker
title: Design of a hardware floating point processor for the PDP-8s
type: Thesis (B.S.)
school: Massachusetts Institute of Technology. Dept. of Electrical Engineering
address: Cambridge, MA, USA
pages: 19
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Tony Edwin Parker
rawtitle: Design of a hardware floating point processor for the {PDP-8s}
entry:
@MastersThesis{Parker:1973:DHF,
  author =       "Tony Edwin Parker",
  title =        "Design of a hardware floating point processor for the
                 {PDP-8s}",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical Engineering",
  address =      "Cambridge, MA, USA",
  pages =        "19",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Paterson:1973:NNM
author: Michael S. Paterson and Larry J. Stockmeyer
title: On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials
journal: j-SIAM-J-COMPUT
volume: 2
number: 1
pages: 60--66
month: mar
monthnumber: 3
year: 1973
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
bibdate: Mon Nov 29 10:57:40 MST 2010
bibtimestamp: 2010.11.29 10:57:40 MST
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: Michael S. Paterson and Larry J. Stockmeyer
rawtitle: On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/2/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; Theory/Matrix.bib

entry:
@Article{Paterson:1973:NNM,
  author =       "Michael S. Paterson and Larry J. Stockmeyer",
  title =        "On the Number of Nonscalar Multiplications Necessary
                 to Evaluate Polynomials",
  journal =      j-SIAM-J-COMPUT,
  volume =       "2",
  number =       "1",
  pages =        "60--66",
  month =        mar,
  year =         "1973",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Mon Nov 29 10:57:40 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/2/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  kwds =         "na, polynomial, complexity",
  xxnote =       "Cited in \cite{govl:89}.",
}


bibtype: article
filename: fparith.bib
label: Pittnauer:1973:AA
author: E. Pittnauer
title: Eine Aussage uber Alternanten toenglish ?? endtoenglish
journal: j-NUM-MATH
volume: 23
pages: 427--432
year: 1973
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Sep 16 16:30:40 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/211
rawauthor: E. Pittnauer
rawtitle: {Eine Aussage {\"u}ber Alternanten} \toenglish {??} \endtoenglish
entry:
@Article{Pittnauer:1973:AA,
  author =       "E. Pittnauer",
  title =        "{Eine Aussage {\"u}ber Alternanten} \toenglish {??}
                 \endtoenglish",
  journal =      j-NUM-MATH,
  volume =       "23",
  number =       "??",
  pages =        "427--432",
  month =        "????",
  year =         "1973",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: fparith.bib
label: Pittnauer:1973:NPK
author: E. Pittnauer
journal: j-NUM-MATH
volume: 21
number: 3
pages: 256--263
year: 1973
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Sep 16 16:30:40 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/211
rawauthor: E. Pittnauer
title:
Numerische Polynomapproximation mit Knotenpolynomen toenglish Numerical Polynomial Approximations with Knot Polynomials endtoenglish 

rawtitle:
{Numerische Polynomapproximation mit Knotenpolynomen} \toenglish {Numerical Polynomial Approximations with Knot Polynomials} \endtoenglish

entry:
@Article{Pittnauer:1973:NPK,
  author =       "E. Pittnauer",
  title =        "{Numerische Polynomapproximation mit Knotenpolynomen}
                 \toenglish {Numerical Polynomial Approximations with
                 Knot Polynomials} \endtoenglish",
  journal =      j-NUM-MATH,
  volume =       "21",
  number =       "3",
  pages =        "256--263",
  year =         "1973",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  xxmonth =      "(none)",
}


bibtype: book
filename: fparith.bib
label: Randell:1973:ODC
editor: Brian Randell
title: The origins of digital computers: selected papers
publisher: pub-SV
address: pub-SV:adr
pages: xvi + 464
year: 1973
ISBN: 0-387-06169-X, 3-540-06169-X OR 038706169X, 354006169X
ISBN13: 978-0-387-06169-6, 978-3-540-06169-4 OR 9780387061696, 9783540061694
LCCN: TK7888.3 .R36
bibdate: Wed Oct 13 09:24:25 MDT 2010
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 09:24:25 MDT
remark: See also later editions cite Randell:1975:ODC,Randell:1982:ODC.
acknowledgement: ack-nhfb
raweditor: Brian Randell
rawtitle: The origins of digital computers: selected papers
entry:
@Book{Randell:1973:ODC,
  editor =       "Brian Randell",
  title =        "The origins of digital computers: selected papers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 464",
  year =         "1973",
  ISBN =         "0-387-06169-X, 3-540-06169-X",
  ISBN-13 =      "978-0-387-06169-6, 978-3-540-06169-4",
  LCCN =         "TK7888.3 .R36",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "See also later editions
                 \cite{Randell:1975:ODC,Randell:1982:ODC}.",
}


bibtype: article
filename: fparith.bib
label: Richman:1973:VPE
author: Paul L. Richman
title: Variable-Precision Exponentiation
journal: j-CACM
volume: 16
number: 1
pages: 38--40
month: jan
monthnumber: 1
year: 1973
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65D20
MRnumber: 51 4631
MRreviewer: V. V. Ivanov
bibdate: Mon Jan 22 07:15:57 MST 2001
bibtimestamp: 2001.01.22 07:15:57 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Bell Telephone Labs. Inc., Denver, CO, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: T Theoretical or Mathematical
rawauthor: Paul L. Richman
rawtitle: Variable-Precision Exponentiation
bibsource:
Compendex database; http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Richman73; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
A previous paper presented an efficient algorithm, called the Recomputation Algorithm, for evaluating a rational expression to within any desired tolerance on a computer which performs variable-precision arithmetic operations. The Recomputation Algorithm can be applied to expressions involving any variable-precision operations having $ O(10^( - p) + sum _i|E_i|) $ error bounds, where $p$ denotes the operation's precision and $ E_i $ denotes the error in the operation's $i$-th argument. par This paper presents an efficient variable-precision exponential operation with an error bound of the above order. Other operations such as log, sin, and cos, which have simple series expansions, can be handled similarly.

keywords:
computer programming; digital arithmetic; error analysis; exponential function; exponentiation; interval arithmetic; mathematical programming; variable precision; variable-precision

rawabstract:
A previous paper presented an efficient algorithm, called the Recomputation Algorithm, for evaluating a rational expression to within any desired tolerance on a computer which performs variable-precision arithmetic operations. The Recomputation Algorithm can be applied to expressions involving any variable-precision operations having $ O(10^( - p) + \sum_i|E_i|) $ error bounds, where $p$ denotes the operation's precision and $ E_i $ denotes the error in the operation's $i$-th argument. \par This paper presents an efficient variable-precision exponential operation with an error bound of the above order. Other operations such as log, sin, and cos, which have simple series expansions, can be handled similarly.

entry:
@Article{Richman:1973:VPE,
  author =       "Paul L. Richman",
  title =        "Variable-Precision Exponentiation",
  journal =      j-CACM,
  volume =       "16",
  number =       "1",
  pages =        "38--40",
  month =        jan,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20",
  MRnumber =     "51 4631",
  MRreviewer =   "V. V. Ivanov",
  bibdate =      "Mon Jan 22 07:15:57 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Richman73;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A previous paper presented an efficient algorithm,
                 called the Recomputation Algorithm, for evaluating a
                 rational expression to within any desired tolerance on
                 a computer which performs variable-precision arithmetic
                 operations. The Recomputation Algorithm can be applied
                 to expressions involving any variable-precision
                 operations having $ O(10^( - p) + \sum_i|E_i|) $ error
                 bounds, where $p$ denotes the operation's precision and
                 $ E_i $ denotes the error in the operation's $i$-th
                 argument. \par

                 This paper presents an efficient variable-precision
                 exponential operation with an error bound of the above
                 order. Other operations such as log, sin, and cos,
                 which have simple series expansions, can be handled
                 similarly.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723; 921",
  corpsource =   "Bell Telephone Labs. Inc., Denver, CO, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "computer programming; digital arithmetic; error
                 analysis; exponential function; exponentiation;
                 interval arithmetic; mathematical programming; variable
                 precision; variable-precision",
  oldlabel =     "Richman73",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman73",
}


bibtype: article
filename: fparith.bib
label: Robertson:1973:SIC
author: James E. Robertson and Kishor S. Trivedi
title: The status of investigations into computer hardware design based on the use of continued fractions
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 555--560
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009106
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 8 14:50:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:24 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2; continued fractions
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: James E. Robertson and Kishor S. Trivedi
rawtitle: The status of investigations into computer hardware design based on the use of continued fractions
entry:
@Article{Robertson:1973:SIC,
  author =       "James E. Robertson and Kishor S. Trivedi",
  title =        "The status of investigations into computer hardware
                 design based on the use of continued fractions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "555--560",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009106",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 8 14:50:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; continued fractions",
}


bibtype: article
filename: fparith.bib
label: Roy:1973:ARC
author: P. K. Sinha Roy and C. L. Sheng
title: Author's Reply to Comments on ``Decomposition Method of Determining Maximum Compatibles''
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 627--627
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009119
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:18:24 ???
note: See cite Sureshchander:1973:CDM.
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. K. Sinha Roy and C. L. Sheng
rawnote: See \cite{Sureshchander:1973:CDM}.
rawtitle: Author's Reply to Comments on {``Decomposition Method of Determining Maximum Compatibles''}
entry:
@Article{Roy:1973:ARC,
  author =       "P. K. Sinha Roy and C. L. Sheng",
  title =        "Author's Reply to Comments on {``Decomposition Method
                 of Determining Maximum Compatibles''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "627--627",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009119",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Sureshchander:1973:CDM}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: mastersthesis
filename: fparith.bib
label: Rubinfield:1973:FM
author: Louis P. Rubinfield
title: A floating-point macromodule
type: Thesis (M.S.)
school: Washington University, Department of Electrical Engineering
address: St. Louis, MO, USA
pages: vii + 111
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Electronic digital computers --- Design and construction.
acknowledgement: ack-nhfb
rawauthor: Louis P. Rubinfield
rawtitle: A floating-point macromodule
entry:
@MastersThesis{Rubinfield:1973:FM,
  author =       "Louis P. Rubinfield",
  title =        "A floating-point macromodule",
  type =         "Thesis ({M.S.})",
  school =       "Washington University, Department of Electrical
                 Engineering",
  address =      "St. Louis, MO, USA",
  pages =        "vii + 111",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Design and
                 construction.",
}


bibtype: article
filename: fparith.bib
label: Sankar:1973:AAN
author: P. V. Sankar and S. Chakrabarti and E. V. Krishnamurthy
title: Arithmetic Algorithms in a Negative Base
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 2
pages: 120--125
month: feb
monthnumber: 2
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1973.223671
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:14 MDT 2011
bibtimestamp: 2011.07.12 16:45:14 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. V. Sankar and S. Chakrabarti and E. V. Krishnamurthy
rawtitle: Arithmetic Algorithms in a Negative Base
entry:
@Article{Sankar:1973:AAN,
  author =       "P. V. Sankar and S. Chakrabarti and E. V.
                 Krishnamurthy",
  title =        "Arithmetic Algorithms in a Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "120--125",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223671",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Sankar:1973:DDA
author: P. V. Sankar and S. Chakrabarti and E. V. Krishnamurthy
title: Deterministic Division Algorithm in a Negative Base
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 2
pages: 125--128
month: feb
monthnumber: 2
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1973.223672
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:14 MDT 2011
bibtimestamp: 2011.07.12 16:45:14 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. V. Sankar and S. Chakrabarti and E. V. Krishnamurthy
rawtitle: Deterministic Division Algorithm in a Negative Base
entry:
@Article{Sankar:1973:DDA,
  author =       "P. V. Sankar and S. Chakrabarti and E. V.
                 Krishnamurthy",
  title =        "Deterministic Division Algorithm in a Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "125--128",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223672",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Schatte:1973:VMG
author: Peter Schatte
journal: j-Z-ANGE-MATH-MECH
volume: 53
pages: 553--565
year: 1973
CODEN: ZAMMAX
ISSN: 0044-2267 (print), 1521-4001 (electronic) OR 00442267 (print), 15214001 (electronic)
ISSNL: 0044-2267 OR 00442267
bibdate: Mon Nov 14 16:35:28 2011
bibtimestamp: 2011.11.14 16:35:28 ???
fjournal: Zeitschrift fur Angewandte Mathematik und Mechanik
language: German
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001
rawauthor: Peter Schatte
title:
Zur Verteilung der Mantisse in der Gleitkommadarstellung einer Zufallsgross e. (German) [Distribution of the mantissa in the floating-point representation of a random variable]

bibsource:
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
{Zur Verteilung der Mantisse in der Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}. ({German}) [Distribution of the mantissa in the floating-point representation of a random variable]

entry:
@Article{Schatte:1973:VMG,
  author =       "Peter Schatte",
  title =        "{Zur Verteilung der Mantisse in der
                 Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
                 ({German}) [Distribution of the mantissa in the
                 floating-point representation of a random variable]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "53",
  number =       "??",
  pages =        "553--565",
  month =        "????",
  year =         "1973",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Mon Nov 14 16:35:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Schmid:1973:BLIa
author: H. Schmid
title: BCD logic I: BCD -- logic of many uses
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 13
pages: 90--95
month: jun
monthnumber: 6
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 08 08:17:30 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:17:30 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {I}: {BCD} -- logic of many uses
entry:
@Article{Schmid:1973:BLIa,
  author =       "H. Schmid",
  title =        "{BCD} logic {I}: {BCD} -- logic of many uses",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "13",
  pages =        "90--95",
  month =        jun,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 08 08:17:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}


bibtype: article
filename: fparith.bib
label: Schmid:1973:BLIb
author: H. Schmid
title: BCD logic II: BCD multiplication
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 14
pages: 62--69
month: jul
monthnumber: 7
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {II}: {BCD} multiplication
entry:
@Article{Schmid:1973:BLIb,
  author =       "H. Schmid",
  title =        "{BCD} logic {II}: {BCD} multiplication",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "14",
  pages =        "62--69",
  month =        jul,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}


bibtype: article
filename: fparith.bib
label: Schmid:1973:BLIc
author: H. Schmid
title: BCD logic III: BCD division
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 15
pages: 86--92
month: jul
monthnumber: 7
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {III}: {BCD} division
entry:
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  author =       "H. Schmid",
  title =        "{BCD} logic {III}: {BCD} division",
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  number =       "15",
  pages =        "86--92",
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  year =         "1973",
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  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}


bibtype: article
filename: fparith.bib
label: Schmid:1973:BLId
author: H. Schmid
title: BCD logic IV: BCD decimal-point location
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 16
pages: 80--84
month: aug
monthnumber: 8
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronic Design
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {IV}: {BCD} decimal-point location
entry:
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  author =       "H. Schmid",
  title =        "{BCD} logic {IV}: {BCD} decimal-point location",
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  volume =       "21",
  number =       "16",
  pages =        "80--84",
  month =        aug,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
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  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Schmid:1973:BLVa
author: H. Schmid
title: BCD logic V: BCD square root
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 17
pages: 62--69
month: aug
monthnumber: 8
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {V}: {BCD} square root
entry:
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  author =       "H. Schmid",
  title =        "{BCD} logic {V}: {BCD} square root",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "17",
  pages =        "62--69",
  month =        aug,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}


bibtype: article
filename: fparith.bib
label: Schmid:1973:BLVb
author: H. Schmid
title: BCD logic VI: BCD logarithms and exponentials
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 18
pages: 118--123
month: sep
monthnumber: 9
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {VI}: {BCD} logarithms and exponentials
entry:
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  author =       "H. Schmid",
  title =        "{BCD} logic {VI}: {BCD} logarithms and exponentials",
  journal =      j-ELECTRONIC-DESIGN,
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  number =       "18",
  pages =        "118--123",
  month =        sep,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}


bibtype: article
filename: fparith.bib
label: Schmid:1973:BLVc
author: H. Schmid
title: BCD logic VII: BCD trig and hyperbolic functions
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 19
pages: 68--73
month: sep
monthnumber: 9
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:16:11 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronic Design
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {VII}: {BCD} trig and hyperbolic functions
entry:
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  author =       "H. Schmid",
  title =        "{BCD} logic {VII}: {BCD} trig and hyperbolic
                 functions",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "19",
  pages =        "68--73",
  month =        sep,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}


bibtype: article
filename: fparith.bib
label: Sentance:1973:FAB
author: W. A. Sentance
title: A Further Analysis of Benford's Law
journal: j-FIB-QUART
volume: 11
number: 5
pages: 490--494
month: dec
monthnumber: 12
year: 1973
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:58:46 MDT 2011
bibtimestamp: 2011.10.20 17:58:46 MDT
URL: http://www.fq.math.ca/Scanned/11-5/sentance.pdf
fjournal: The Fibonacci Quarterly
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: W. A. Sentance
rawtitle: A Further Analysis of {Benford's Law}
bibsource:
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entry:
@Article{Sentance:1973:FAB,
  author =       "W. A. Sentance",
  title =        "A Further Analysis of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "5",
  pages =        "490--494",
  month =        dec,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:46 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-5.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: fparith.bib
label: Shea:1973:NDN
author: Dale D. Shea
title: On the Number of Divisions Needed in Finding the Greatest Common Divisor
journal: j-FIB-QUART
volume: 11
number: 5
pages: 508--510
month: dec
monthnumber: 12
year: 1973
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:58:46 MDT 2011
bibtimestamp: 2011.10.20 17:58:46 MDT
URL: http://www.fq.math.ca/Scanned/11-5/shea.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Dale D. Shea
rawtitle: On the Number of Divisions Needed in Finding the Greatest Common Divisor
bibsource:
http://www.fq.math.ca/11-5.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Shea:1973:NDN,
  author =       "Dale D. Shea",
  title =        "On the Number of Divisions Needed in Finding the
                 Greatest Common Divisor",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "5",
  pages =        "508--510",
  month =        dec,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:46 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-5.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/11-5/shea.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: fparith.bib
label: Singh:1973:MOA
author: S. Singh and R. Waxman
title: Multiple Operand Addition and Multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 2
pages: 113--120
month: feb
monthnumber: 2
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1973.223670
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:14 MDT 2011
bibtimestamp: 2011.07.12 16:45:14 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Singh and R. Waxman
rawtitle: Multiple Operand Addition and Multiplication
entry:
@Article{Singh:1973:MOA,
  author =       "S. Singh and R. Waxman",
  title =        "Multiple Operand Addition and Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "113--120",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223670",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Sites:1973:FPS
author: Richard L. Sites
title: Floating point significance interrupt proposal
journal: j-COMP-ARCH-NEWS
volume: 2
number: 1
pages: 10--12
month: jan
monthnumber: 1
year: 1973
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Fri May 12 09:40:28 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.12 09:40:28 MDT
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J89
rawauthor: Richard L. Sites
rawtitle: Floating point significance interrupt proposal
abstract:
The purpose of this proposal is to aid numerical analysts in observing the significance of results in floating-point calculations. This proposal is not a cure-all, but it does attempt to a first, high-payoff step in understanding and analyzing floating-point algorithms. This proposal is specifically for IBM 360/370 architecture, but the ideas are applicable to all machines.

remark:
The author observes that register clearing by subtraction is common, and is one of the reasons that ``all IBM language processors execute with significance masked off.'' He proposes suppressing the significance interrupt in subtractions when both operands are equal.

rawabstract:
The purpose of this proposal is to aid numerical analysts in observing the significance of results in floating-point calculations. This proposal is not a cure-all, but it does attempt to a first, high-payoff step in understanding and analyzing floating-point algorithms. This proposal is specifically for IBM 360/370 architecture, but the ideas are applicable to all machines.

entry:
@Article{Sites:1973:FPS,
  author =       "Richard L. Sites",
  title =        "Floating point significance interrupt proposal",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "2",
  number =       "1",
  pages =        "10--12",
  month =        jan,
  year =         "1973",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:28 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The purpose of this proposal is to aid numerical
                 analysts in observing the significance of results in
                 floating-point calculations. This proposal is not a
                 cure-all, but it does attempt to a first, high-payoff
                 step in understanding and analyzing floating-point
                 algorithms. This proposal is specifically for IBM
                 360/370 architecture, but the ideas are applicable to
                 all machines.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
  remark =       "The author observes that register clearing by
                 subtraction is common, and is one of the reasons that
                 ``all IBM language processors execute with significance
                 masked off.'' He proposes suppressing the significance
                 interrupt in subtractions when both operands are
                 equal.",
}


bibtype: article
filename: fparith.bib
label: Sjoding:1973:NVR
author: T. Sjoding
title: Noise variance for rounded two's complement product quantization
journal: j-IEEE-TRANS-AUDIO-ELECTROACOUST
volume: 21
number: 4
pages: 378--380
month: aug
monthnumber: 8
year: 1973
CODEN: ITADAS
ISSN: 0018-9278 (print), 1558-2582 (electronic) OR 00189278 (print), 15582582 (electronic)
ISSNL: 0018-9278 OR 00189278
bibdate: Sat Jul 16 11:25:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:03 MDT
fjournal: IEEE Transactions on Audio and Electroacoustics
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337
rawauthor: T. Sjoding
rawtitle: Noise variance for rounded two's complement product quantization
entry:
@Article{Sjoding:1973:NVR,
  author =       "T. Sjoding",
  title =        "Noise variance for rounded two's complement product
                 quantization",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "21",
  number =       "4",
  pages =        "378--380",
  month =        aug,
  year =         "1973",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "The Halyo-McAlpine discrete model for product
                 quantization is reconstructed using an error variable
                 set having an even number of members. It is shown in
                 this case that the noise variance associated with a
                 continuous model becomes an upper rather \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Spira:1973:CTA
author: Philip M. Spira
title: Computation Times of Arithmetic and Boolean functions in $ (d, r) $ circuits
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 552--555
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009105
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:18:24 ???
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Philip M. Spira
rawtitle: Computation Times of Arithmetic and {Boolean} functions in $ (d, r) $ circuits
entry:
@Article{Spira:1973:CTA,
  author =       "Philip M. Spira",
  title =        "Computation Times of Arithmetic and {Boolean}
                 functions in $ (d, r) $ circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "552--555",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009105",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: book
filename: fparith.bib
label: Stone:1973:DMS
author: Harold S. Stone
title: Discrete mathematical structures and their applications
publisher: Science Research Associates
address: Chicago, IL, USA
pages: 401
year: 1973
LCCN: QA162 .S877d; QA162 .S77
bibdate: Fri Nov 9 19:24:02 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.11.09 19:24:02 MST
series: The SRA computer science series
subject: Algebra, Abstract; Group theory; Machine theory
acknowledgement: ack-nhfb
rawauthor: Harold S. Stone
rawtitle: Discrete mathematical structures and their applications
TOC:
Foundations of discrete mathematics. Groups. The Polya theory of enumeration. Applications of group theory to computer design. Group codes. Semigroups. Finite-state machines. Rings and fields. Linear -finite-state machines. Boolean algebra with applications to computer design.

rawTOC:
Foundations of discrete mathematics. \\ Groups. \\ The P\'olya theory of enumeration. \\ Applications of group theory to computer design. \\ Group codes. \\ Semigroups. \\ Finite-state machines. \\ Rings and fields. \\ Linear -finite-state machines. \\ Boolean algebra with applications to computer design.

entry:
@Book{Stone:1973:DMS,
  author =       "Harold S. Stone",
  title =        "Discrete mathematical structures and their
                 applications",
  publisher =    "Science Research Associates",
  address =      "Chicago, IL, USA",
  pages =        "401",
  year =         "1973",
  LCCN =         "QA162 .S877d; QA162 .S77",
  bibdate =      "Fri Nov 9 19:24:02 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "The SRA computer science series",
  acknowledgement = ack-nhfb,
  subject =      "Algebra, Abstract; Group theory; Machine theory",
  tableofcontents = "Foundations of discrete mathematics. \\
                 Groups. \\
                 The P\'olya theory of enumeration. \\
                 Applications of group theory to computer design. \\
                 Group codes. \\
                 Semigroups. \\
                 Finite-state machines. \\
                 Rings and fields. \\
                 Linear -finite-state machines. \\
                 Boolean algebra with applications to computer design.",
}


bibtype: article
filename: fparith.bib
label: Sureshchander:1973:CDM
author: Sureshchander
title: Comments on ``Decomposition Method of Determining Maximum Compatibles''
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 627--627
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009118
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:18:24 ???
note: See cite Roy:1973:ARC.
URL: http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Sureshchander
rawnote: See \cite{Roy:1973:ARC}.
rawtitle: Comments on {``Decomposition Method of Determining Maximum Compatibles''}
entry:
@Article{Sureshchander:1973:CDM,
  author =       "Sureshchander",
  title =        "Comments on {``Decomposition Method of Determining
                 Maximum Compatibles''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "627--627",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009118",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Roy:1973:ARC}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
  xxnote =       "Author has only a single name",
}


bibtype: article
filename: fparith.bib
label: Swartzlander:1973:QSM
author: E. E. Swartzlander, Jr.
title: The Quasi-Serial Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 4
pages: 317--321
month: apr
monthnumber: 4
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1973.223717
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:19 MDT 2011
bibtimestamp: 2011.07.12 16:45:19 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. E. {Swartzlander, Jr.}
rawtitle: The Quasi-Serial Multiplier
entry:
@Article{Swartzlander:1973:QSM,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "The Quasi-Serial Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "4",
  pages =        "317--321",
  month =        apr,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223717",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: Tanny:1973:SSA
author: Stephen Michael Tanny
title: Studies in Significance Arithmetic
type: Ph.D. thesis
school: Massachusetts Institute of Technology
address: Cambridge, MA, USA
pages: 195
year: 1973
bibdate: Tue Oct 22 06:18:19 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.10.22 06:18:19 ???
URL: https://search.proquest.com/pqdtglobal/docview/302720894
remark: Full text is not available in ProQuest.
acknowledgement: ack-nhfb
rawauthor: Stephen Michael Tanny
rawtitle: Studies in Significance Arithmetic
entry:
@PhdThesis{Tanny:1973:SSA,
  author =       "Stephen Michael Tanny",
  title =        "Studies in Significance Arithmetic",
  type =         "{Ph.D.} thesis",
  school =       "Massachusetts Institute of Technology",
  address =      "Cambridge, MA, USA",
  pages =        "195",
  year =         "1973",
  bibdate =      "Tue Oct 22 06:18:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/302720894",
  acknowledgement = ack-nhfb,
  remark =       "Full text is not available in ProQuest.",
}


bibtype: article
filename: fparith.bib
label: Urabe:1973:CEA
author: Minoru Urabe
title: Component-wise error analysis of iterative methods practiced on a floating-point system
journal: j-MEM-FAC-SCI-KYUSHU-UNIV-A
volume: 27
pages: 23--64
year: 1973
CODEN: MFKAAF
ISSN: 0373-6385 (print), 1883-2172 (electronic) OR 03736385 (print), 18832172 (electronic)
ISSNL: 0373-6385 OR 03736385
MRclass: 65H10
MRnumber: 48 1457
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
acknowledgement: ack-nhfb
reviewer: D. C. Handscomb
rawauthor: Minoru Urabe
rawtitle: Component-wise error analysis of iterative methods practiced on a floating-point system
fjournal:
Memoirs of the Faculty of Science, Kyushu Imperial University. Series A, Mathematics = Kyushu Teikoku Daigaku Rigakubu kiyo

entry:
@Article{Urabe:1973:CEA,
  author =       "Minoru Urabe",
  title =        "Component-wise error analysis of iterative methods
                 practiced on a floating-point system",
  journal =      j-MEM-FAC-SCI-KYUSHU-UNIV-A,
  volume =       "27",
  pages =        "23--64",
  year =         "1973",
  CODEN =        "MFKAAF",
  ISSN =         "0373-6385 (print), 1883-2172 (electronic)",
  ISSN-L =       "0373-6385",
  MRclass =      "65H10",
  MRnumber =     "48 1457",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Memoirs of the Faculty of Science, Kyushu Imperial
                 University. Series A, Mathematics = Kyushu Teikoku
                 Daigaku Rigakubu kiyo",
  reviewer =     "D. C. Handscomb",
}


bibtype: phdthesis
filename: fparith.bib
label: Wiatrowski:1973:DFP
author: Claude A. Wiatrowski
title: Design of a floating-point processor for digital simulation
type: Thesis (Ph.D. - Electrical Engineering)
school: University of Arizona
address: Tucson, AZ, USA
pages: 107
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic and logic units.; Computer storage devices.
acknowledgement: ack-nhfb
rawauthor: Claude A. Wiatrowski
rawtitle: Design of a floating-point processor for digital simulation
entry:
@PhdThesis{Wiatrowski:1973:DFP,
  author =       "Claude A. Wiatrowski",
  title =        "Design of a floating-point processor for digital
                 simulation",
  type =         "Thesis ({Ph.D.} - Electrical Engineering)",
  school =       "University of Arizona",
  address =      "Tucson, AZ, USA",
  pages =        "107",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Computer storage
                 devices.",
}


bibtype: article
filename: fparith.bib
label: Yau:1973:ECR
author: S. S.-S. Yau and Yu-Cheng Liu
title: Error Correction in Redundant Residue Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 1
pages: 5--11
month: jan
monthnumber: 1
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1973.223594
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:11 MDT 2011
bibtimestamp: 2011.07.12 16:45:11 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. S.-S. Yau and Yu-Cheng Liu
rawtitle: Error Correction in Redundant Residue Number Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672187; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35069

entry:
@Article{Yau:1973:ECR,
  author =       "S. S.-S. Yau and Yu-Cheng Liu",
  title =        "Error Correction in Redundant Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "1",
  pages =        "5--11",
  month =        jan,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1973.223594",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672187;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35069",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Two error-correcting algorithms for redundant residue
                 number systems are presented, one for single
                 residue-error correction and the other for burst
                 residue-error correction. Neither algorithm requires
                 table lookup, and hence their implementation \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Yohe:1973:FFPa
author: J. M. Yohe
title: Foundations of floating point computer arithmetic
type: MRC Technical Summary Report
number: 1302
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 25
month: jan
monthnumber: 1
year: 1973
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computers.; Floating-point arithmetic.
remark: January 1973. Sponsored by Army Research Office, Durham, NC, USA.
acknowledgement: ack-nhfb
rawauthor: J. M. Yohe
rawtitle: Foundations of floating point computer arithmetic
abstract:
A formal structure, within which computer arithmetic operations may be defined, is described. Several floating point arithmetic schemes are defined within this context. The structure described in the paper includes, as a sub-structure, the significance spaces of Matula.

rawabstract:
A formal structure, within which computer arithmetic operations may be defined, is described. Several floating point arithmetic schemes are defined within this context. The structure described in the paper includes, as a sub-structure, the significance spaces of Matula.

entry:
@TechReport{Yohe:1973:FFPa,
  author =       "J. M. Yohe",
  title =        "Foundations of floating point computer arithmetic",
  type =         "{MRC} Technical Summary Report",
  number =       "1302",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "25",
  month =        jan,
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A formal structure, within which computer arithmetic
                 operations may be defined, is described. Several
                 floating point arithmetic schemes are defined within
                 this context. The structure described in the paper
                 includes, as a sub-structure, the significance spaces
                 of Matula.",
  acknowledgement = ack-nhfb,
  keywords =     "Computers.; Floating-point arithmetic.",
  remark =       "January 1973. Sponsored by Army Research Office,
                 Durham, NC, USA.",
}


bibtype: article
filename: fparith.bib
label: Yohe:1973:IBS
author: J. M. Yohe
title: Interval Bounds for Square Roots and Cube Roots
journal: j-COMPUTING
volume: 11
number: 1
pages: 51--57
year: 1973
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:51 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)
bibtimestamp: 2001.01.02 17:40:51 MST
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-jr
affiliation: Univ. Wisconsin, Madison, WI, USA
journalURL: http://link.springer.com/journal/607
rawauthor: J. M. Yohe
rawtitle: Interval Bounds for Square Roots and Cube Roots
keywords:
binary computers; cube roots; error analysis; interval bounds; machine representable number; optimal upward directed rounding; smallest machine representable interval; square roots

entry:
@Article{Yohe:1973:IBS,
  author =       "J. M. Yohe",
  title =        "Interval Bounds for Square Roots and Cube Roots",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "1",
  pages =        "51--57",
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  affiliation =  "Univ. Wisconsin, Madison, WI, USA",
  classification = "C5230",
  description =  "digital arithmetic; error analysis",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "binary computers; cube roots; error analysis; interval
                 bounds; machine representable number; optimal upward
                 directed rounding; smallest machine representable
                 interval; square roots",
}


bibtype: article
filename: fparith.bib
label: Yohe:1973:RFP
author: J. Michael Yohe
title: Roundings in Floating-Point Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 577--586
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009110
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:25 MDT 2011
bibtimestamp: 2011.07.12 16:45:25 MDT
fjournal: IEEE Transactions on Computers
keywords: ARITH-2; correct rounding; floating-point arithmetic
acknowledgement: ack-jr
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. Michael Yohe
rawtitle: Roundings in Floating-Point Arithmetic
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009110; http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Yohe.pdf

abstract:
In this paper we discuss directed roundings and indicate how hardware might be designed to produce proper upward directed, downward directed, and certain commonly used symmetric roundings. Algorithms for the four binary arithmetic operations and for rounding are presented, together with proofs of their correctness; appropriate formulas for a priori error analysis of these algorithms are presented. Some of the basic applications of directed roundings are surveyed.

rawabstract:
In this paper we discuss directed roundings and indicate how hardware might be designed to produce proper upward directed, downward directed, and certain commonly used symmetric roundings. Algorithms for the four binary arithmetic operations and for rounding are presented, together with proofs of their correctness; appropriate formulas for a priori error analysis of these algorithms are presented. Some of the basic applications of directed roundings are surveyed.

entry:
@Article{Yohe:1973:RFP,
  author =       "J. Michael Yohe",
  title =        "Roundings in Floating-Point Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "577--586",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009110",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009110;
                 http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Yohe.pdf",
  abstract =     "In this paper we discuss directed roundings and
                 indicate how hardware might be designed to produce
                 proper upward directed, downward directed, and certain
                 commonly used symmetric roundings. Algorithms for the
                 four binary arithmetic operations and for rounding are
                 presented, together with proofs of their correctness;
                 appropriate formulas for a priori error analysis of
                 these algorithms are presented. Some of the basic
                 applications of directed roundings are surveyed.",
  acknowledgement = ack-jr # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; correct rounding; floating-point arithmetic",
}


bibtype: book
filename: fparith.bib
label: Zacher:1973:HDG
author: H. J. Zacher
publisher: V. Klostermann
address: Frankfurt am Main, West Germany
pages: viii + 384
year: 1973
LCCN: QA141.4.Z3; QA141.4.Z3 1973
bibdate: Fri Mar 17 09:19:21 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.03.17 09:19:21 ???
series: Veroffentlichungen des Leibniz-Archivs
language: German
remark: Selected original texts and correspondence in French, German or Latin.
acknowledgement: ack-nhfb
rawauthor: H. J. Zacher
title:
Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein Beitr. zur Geschichte des binaren Zahlen-systems. (German) [The main writings on the dyadic by G. W. Leibniz: a contribution to the history of the binary number system]

subject:
Leibniz, Gottfried Wilhelm; Freiherr von; Yi jing; Freiherr von,; Binary system (Mathematics); History; Sources; Systeme binaire (Mathematiques); Histoire; Binary system (Mathematics)

rawtitle:
{Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein Beitr. zur Geschichte des bin{\"a}ren Zahlen-systems}. ({German}) [{The} main writings on the dyadic by {G. W. Leibniz}: a contribution to the history of the binary number system]

entry:
@Book{Zacher:1973:HDG,
  author =       "H. J. Zacher",
  title =        "{Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein
                 Beitr. zur Geschichte des bin{\"a}ren Zahlen-systems}.
                 ({German}) [{The} main writings on the dyadic by {G. W.
                 Leibniz}: a contribution to the history of the binary
                 number system]",
  publisher =    "V. Klostermann",
  address =      "Frankfurt am Main, West Germany",
  pages =        "viii + 384",
  year =         "1973",
  LCCN =         "QA141.4.Z3; QA141.4.Z3 1973",
  bibdate =      "Fri Mar 17 09:19:21 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Ver{\"o}ffentlichungen des Leibniz-Archivs",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "Selected original texts and correspondence in French,
                 German or Latin.",
  subject =      "Leibniz, Gottfried Wilhelm; Freiherr von; Yi jing;
                 Freiherr von,; Binary system (Mathematics); History;
                 Sources; Syst{\'e}me binaire (Math{\'e}matiques);
                 Histoire; Binary system (Mathematics)",
}


bibtype: article
filename: fparith.bib
label: Zohar:1973:DCR
author: Shalhav Zohar
title: A/D Conversion for Radix ($ - 2$)
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 7
pages: 698--701
month: jul
monthnumber: 7
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009137
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 16:45:28 MDT 2011
bibtimestamp: 2011.07.12 16:45:28 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009137
fjournal: IEEE Transactions on Computers
keywords: negative base
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Shalhav Zohar
rawtitle: {A/D} Conversion for Radix ($ - 2$)
entry:
@Article{Zohar:1973:DCR,
  author =       "Shalhav Zohar",
  title =        "{A/D} Conversion for Radix ($ - 2$)",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "7",
  pages =        "698--701",
  month =        jul,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009137",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009137",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Agrawal:1974:NCL
author: D. P. Agrawal
title: Negabinary carry-look-ahead adder and fast multiplier
journal: j-ELECT-LETTERS
volume: 10
pages: 312--313
month: jul
monthnumber: 7
year: 1974
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Thu Nov 06 06:16:38 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2014.11.06 06:16:38 ???
fjournal: Electronics Letters
keywords: negative base
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: D. P. Agrawal
rawtitle: Negabinary carry-look-ahead adder and fast multiplier
entry:
@Article{Agrawal:1974:NCL,
  author =       "D. P. Agrawal",
  title =        "Negabinary carry-look-ahead adder and fast
                 multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "10",
  number =       "??",
  pages =        "312--313",
  month =        jul,
  year =         "1974",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Thu Nov 06 06:16:38 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Banerji:1974:NIM
author: D. K. Banerji
title: A Novel Implementation Method for Addition and Subtraction in Residue Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 1
pages: 106--109
month: jan
monthnumber: 1
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1974.223790
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:29 MDT 2011
bibtimestamp: 2011.07.12 11:27:29 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. K. Banerji
rawtitle: A Novel Implementation Method for Addition and Subtraction in Residue Number Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672383; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077

entry:
@Article{Banerji:1974:NIM,
  author =       "D. K. Banerji",
  title =        "A Novel Implementation Method for Addition and
                 Subtraction in Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "1",
  pages =        "106--109",
  month =        jan,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1974.223790",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672383;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This correspondence describes an implementation scheme
                 for the operations of addition and subtraction in the
                 residue number systems. The method is based on the
                 property that the set of residues modulo m form a
                 finite group under addition and \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Banerji:1974:URA
author: D. K. Banerji
title: On the Use of Residue Arithmetic for Computation
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 12
pages: 1315--1317
month: dec
monthnumber: 12
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.223855
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:38 MDT 2011
bibtimestamp: 2011.07.12 11:27:38 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. K. Banerji
rawtitle: On the Use of Residue Arithmetic for Computation
entry:
@Article{Banerji:1974:URA,
  author =       "D. K. Banerji",
  title =        "On the Use of Residue Arithmetic for Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1315--1317",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223855",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Barsi:1974:EDC
author: F. Barsi and P. Maestrini
title: Error Detection and Correction by Product Codes in Residue Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 9
pages: 915--924
month: sep
monthnumber: 9
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1974.224055
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:35 MDT 2011
bibtimestamp: 2011.07.12 11:27:35 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. Barsi and P. Maestrini
rawtitle: Error Detection and Correction by Product Codes in Residue Number Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672648; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35088

entry:
@Article{Barsi:1974:EDC,
  author =       "F. Barsi and P. Maestrini",
  title =        "Error Detection and Correction by Product Codes in
                 Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "9",
  pages =        "915--924",
  month =        sep,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1974.224055",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:35 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672648;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35088",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The arithmetic error detecting and correcting
                 capabilities of product (AN) codes in residue number
                 systems (RNS) are described. The redundancy necessary
                 and sufficient to allow single residue digit error
                 detection or correction is determined, under \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Bauer:1974:CGR
author: F. L. Bauer
title: Computational Graphs and Rounding Error
journal: j-SIAM-J-NUMER-ANAL
volume: 11
number: 1
pages: 87--96
month: mar
monthnumber: 3
year: 1974
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0711010
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65G05
MRnumber: 356482
MRreviewer: L. B. Rall
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibtimestamp: 1998.10.16 06:57:22 MDT
note: In memoriam George Forsythe.
URL: https://www.jstor.org/stable/2156433
fjournal: SIAM Journal on Numerical Analysis
ZMnumber: 0337.65028
acknowledgement: ack-nhfb
authordates: Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26 March 2015)
journalURL: http://epubs.siam.org/sinum
rawauthor: F. L. Bauer
rawnote: In memoriam George Forsythe.
rawtitle: Computational Graphs and Rounding Error
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib; https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database; Theory/auto.diff.bib

entry:
@Article{Bauer:1974:CGR,
  author =       "F. L. Bauer",
  title =        "Computational Graphs and Rounding Error",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "11",
  number =       "1",
  pages =        "87--96",
  month =        mar,
  year =         "1974",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0711010",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65G05",
  MRnumber =     "356482",
  MRreviewer =   "L. B. Rall",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database; Theory/auto.diff.bib",
  note =         "In memoriam George Forsythe.",
  URL =          "https://www.jstor.org/stable/2156433",
  ZMID =         "03527739",
  ZMnumber =     "0337.65028",
  acknowledgement = ack-nhfb,
  author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
                 March 2015)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  referred =     "[Char91a]; [Irim91a].",
}


bibtype: article
filename: fparith.bib
label: Blankenship:1974:CTC
author: P. E. Blankenship
title: Comments on ``A Two's Complement Parallel Array Multiplication Algorithm''
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 12
pages: 1327--1327
month: dec
monthnumber: 12
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.223862
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:38 MDT 2011
bibtimestamp: 2011.07.12 11:27:38 MDT
note: See cite Baugh:1973:TCP,Kroft:1974:CTC.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672455
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. E. Blankenship
rawnote: See \cite{Baugh:1973:TCP,Kroft:1974:CTC}.
rawtitle: Comments on {``A Two's Complement Parallel Array Multiplication Algorithm''}
entry:
@Article{Blankenship:1974:CTC,
  author =       "P. E. Blankenship",
  title =        "Comments on {``A Two's Complement Parallel Array
                 Multiplication Algorithm''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1327--1327",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223862",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Baugh:1973:TCP,Kroft:1974:CTC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672455",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Boyes:1974:BNS
author: J. D. Boyes
title: Binary Noise Sources Incorporating Modulo-$N$ Dividers
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 5
pages: 550--552
month: may
monthnumber: 5
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.223980
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:33 MDT 2011
bibtimestamp: 2011.07.12 11:27:33 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. D. Boyes
rawtitle: Binary Noise Sources Incorporating Modulo-{$N$} Dividers
entry:
@Article{Boyes:1974:BNS,
  author =       "J. D. Boyes",
  title =        "Binary Noise Sources Incorporating Modulo-{$N$}
                 Dividers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "5",
  pages =        "550--552",
  month =        may,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223980",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Brent:1974:FEP
author: Barry Brent
title: Functional Equations with Prime Roots from Arithmetic Expressions for $ G_alpha $
journal: j-FIB-QUART
volume: 12
number: 2
pages: 199--207
month: apr
monthnumber: 4
year: 1974
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:58:50 MDT 2011
bibtimestamp: 2011.10.20 17:58:50 MDT
URL: http://www.fq.math.ca/Scanned/12-2/brent1.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Barry Brent
rawtitle: Functional Equations with Prime Roots from Arithmetic Expressions for {$ G_\alpha $}
bibsource:
http://www.fq.math.ca/12-2.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Brent:1974:FEP,
  author =       "Barry Brent",
  title =        "Functional Equations with Prime Roots from Arithmetic
                 Expressions for {$ G_\alpha $}",
  journal =      j-FIB-QUART,
  volume =       "12",
  number =       "2",
  pages =        "199--207",
  month =        apr,
  year =         "1974",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:50 MDT 2011",
  bibsource =    "http://www.fq.math.ca/12-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/12-2/brent1.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: fparith.bib
label: Brown:1974:BDE
author: D. A. H. Brown
title: Biquinary Decimal Error Detection Codes with One, Two and Three Check Digits
journal: j-COMP-J
volume: 17
number: 3
pages: 201--204
month: aug
monthnumber: 8
year: 1974
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Mar 25 13:51:56 MST 1997
bibtimestamp: 1997.03.25 13:51:56 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Royal Radar Establ., Malvern, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: D. A. H. Brown
rawtitle: Biquinary Decimal Error Detection Codes with One, Two and Three Check Digits
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/201.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/202.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/203.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/204.tif

keywords:
biquinary decimal error detection codes; check digits; computer systems, digital; computers --- Debugging; decimal floating-point arithmetic; digital arithmetic; error detection codes; polynomial coding

entry:
@Article{Brown:1974:BDE,
  author =       "D. A. H. Brown",
  title =        "Biquinary Decimal Error Detection Codes with One, Two
                 and Three Check Digits",
  journal =      j-COMP-J,
  volume =       "17",
  number =       "3",
  pages =        "201--204",
  month =        aug,
  year =         "1974",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/201.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/202.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/203.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/204.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "722; 723",
  corpsource =   "Royal Radar Establ., Malvern, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "biquinary decimal error detection codes; check digits;
                 computer systems, digital; computers --- Debugging;
                 decimal floating-point arithmetic; digital arithmetic;
                 error detection codes; polynomial coding",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Brown:1974:SEC
author: D. A. H. Brown
title: Some Error Correcting Codes for Certain Transposition and Transcription Errors in Decimal Integers
journal: j-COMP-J
volume: 17
number: 1
pages: 9--12
month: feb
monthnumber: 2
year: 1974
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Nov 28 16:12:29 2003
bibtimestamp: 2003.11.28 16:12:29 ???
fjournal: The Computer Journal
acknowledgement: ack-mfc
classcodes: C5230 (Digital arithmetic methods); C6130 (Data handling techniques)
corpsource: Royal Radar Establ., Malvern, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: D. A. H. Brown
rawtitle: Some Error Correcting Codes for Certain Transposition and Transcription Errors in Decimal Integers
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/10.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/11.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/12.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/9.tif

keywords:
algorithm; block; codes, symbolic; cyclic; decimal floating-point arithmetic; decimal integers; digital arithmetic; error correcting codes; error correction codes; modulus 11; transcription; transposition

entry:
@Article{Brown:1974:SEC,
  author =       "D. A. H. Brown",
  title =        "Some Error Correcting Codes for Certain Transposition
                 and Transcription Errors in Decimal Integers",
  journal =      j-COMP-J,
  volume =       "17",
  number =       "1",
  pages =        "9--12",
  month =        feb,
  year =         "1974",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Nov 28 16:12:29 2003",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/10.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/11.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/12.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/9.tif",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  classification = "731",
  corpsource =   "Royal Radar Establ., Malvern, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algorithm; block; codes, symbolic; cyclic; decimal
                 floating-point arithmetic; decimal integers; digital
                 arithmetic; error correcting codes; error correction
                 codes; modulus 11; transcription; transposition",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Carta:1974:HLR
author: David G. Carta
title: Help!!: The Lost Reference: (A Modified Newton Method for Square Roots)
journal: j-SIGNUM
volume: 9
number: 4
pages: 9--9
month: oct
monthnumber: 10
year: 1974
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1206085.1206086
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Jun 17 18:47:00 MDT 2008
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.06.17 18:47:00 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: David G. Carta
rawtitle: Help!!: {The} Lost Reference: ({A} Modified {Newton} Method for Square Roots)
abstract:
Around 1970 I saw a journal article describing a modified Newton iteration for square roots. It involved changing the usual factor of 0.5 in $ x_n + 1 = 0.5 (x_n + a / x_n) $ to $ c_n $ where $ c_n rightarrow 0.5 $, thereby increasing the asymptotic rate of convergence from $ e_n + 1 = 0.5 e_n^2 $ to $ e_n + 1 = 0.25 e_n^2 $.

rawabstract:
Around 1970 I saw a journal article describing a modified Newton iteration for square roots. It involved changing the usual factor of 0.5 in $ x_{n + 1} = 0.5 (x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow 0.5 $, thereby increasing the asymptotic rate of convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n + 1} = 0.25 e_n^2 $.

entry:
@Article{Carta:1974:HLR,
  author =       "David G. Carta",
  title =        "Help!!: {The} Lost Reference: ({A} Modified {Newton}
                 Method for Square Roots)",
  journal =      j-SIGNUM,
  volume =       "9",
  number =       "4",
  pages =        "9--9",
  month =        oct,
  year =         "1974",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1206085.1206086",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Jun 17 18:47:00 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Around 1970 I saw a journal article describing a
                 modified Newton iteration for square roots. It involved
                 changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
                 (x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
                 0.5 $, thereby increasing the asymptotic rate of
                 convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
                 1} = 0.25 e_n^2 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: fparith.bib
label: Catlin:1974:MR
author: Paul A. Catlin
title: On the Multiplication of Recurrences
journal: j-FIB-QUART
volume: 12
number: 4
pages: 365--367
month: dec
monthnumber: 12
year: 1974
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:58:54 MDT 2011
bibtimestamp: 2011.10.20 17:58:54 MDT
URL: http://www.fq.math.ca/Scanned/12-4/catlin2.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Paul A. Catlin
rawtitle: On the Multiplication of Recurrences
bibsource:
http://www.fq.math.ca/12-4.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Catlin:1974:MR,
  author =       "Paul A. Catlin",
  title =        "On the Multiplication of Recurrences",
  journal =      j-FIB-QUART,
  volume =       "12",
  number =       "4",
  pages =        "365--367",
  month =        dec,
  year =         "1974",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:54 MDT 2011",
  bibsource =    "http://www.fq.math.ca/12-4.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/12-4/catlin2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: fparith.bib
label: Chakrabarti:1974:DCA
author: S. Chakrabarti
title: Divide-and-Correct Algorithm for Division in a Negative Base
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 9
pages: 981--983
month: sep
monthnumber: 9
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.224066
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:35 MDT 2011
bibtimestamp: 2011.07.12 11:27:35 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672659
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Chakrabarti
rawtitle: Divide-and-Correct Algorithm for Division in a Negative Base
entry:
@Article{Chakrabarti:1974:DCA,
  author =       "S. Chakrabarti",
  title =        "Divide-and-Correct Algorithm for Division in a
                 Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "9",
  pages =        "981--983",
  month =        sep,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.224066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:35 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672659",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Chan:1974:REM
author: O. Chan and E. Jury
title: Roundoff error in multidimensional generalized discrete transforms
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 21
number: 1
pages: 100--108
month: jan
monthnumber: 1
year: 1974
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: O. Chan and E. Jury
rawtitle: Roundoff error in multidimensional generalized discrete transforms
entry:
@Article{Chan:1974:REM,
  author =       "O. Chan and E. Jury",
  title =        "Roundoff error in multidimensional generalized
                 discrete transforms",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "21",
  number =       "1",
  pages =        "100--108",
  month =        jan,
  year =         "1974",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The analysis of rounding error in the one-dimensional
                 fast Fourier transform (FFT) is extended to a class of
                 generalized orthogonal transforms [1] with a common
                 fast algorithm similar to the FFT algorithm. This class
                 includes the BInary FOurier \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Dahlquist:1974:NM
author: Germund Dahlquist and AA ke Bjorck and Ned Anderson
title: Numerical Methods
publisher: pub-PH
address: pub-PH:adr
pages: xviii + 573
year: 1974
ISBN: 0-13-627315-7 OR 0136273157
ISBN13: 978-0-13-627315-8 OR 9780136273158
LCCN: QA297 .D131 1969
bibdate: Tue Dec 14 22:44:59 1993
bibtimestamp: 1993.12.14 22:44:59 ???
note: Translated by Ned Anderson.
series: Prentice-Hall Series in Automatic Computation
acknowledgement: ack-nhfb
rawauthor: Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned Anderson
rawnote: Translated by Ned Anderson.
rawtitle: Numerical Methods
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib

TOC:
Preface / xvii Conventions / xix 1: Some General Principles of Numerical Calculation / 1 1.1. Introduction / 1 1.2. Some Common Ideas and Concepts in Numerical Methods / 2 1.3. Numerical Problems and Algorithms / 13 1.3.1. Definitions / 13 1.3.2. Recursive Formulas; Homer's Rule / 14 1.3.3. An Example of Numerical Instability / 16 2: How to Obtain and Estimate Accuracy in Numerical Calculations / 21 2.1. Basic Concepts in Error Estimation / 21 2.1.1. Introduction / 21 2.1.2. Sources of Error / 22 2.1.3. Absolute and Relative Errors / 23 2.1.4. Rounding and Chopping / 24 2.2 Propagation of Errors / 26 2.2.1. Simple Examples of Error Analysis / 26 2.2.2. The General Formula for Error Propagation; Maximum Error and Standard Error / 29 2.2.3. On the Practical Application of Error Estimation / 34 2.2.4. The Use of Experimental Perturbations / 36 2.2.5. Automatic Control of Accuracy / 37 2.3. Number Systems; Floating and Fixed Representation / 42 2.3.1. The Position System / 42 2.3.2. Floating and Fixed Representation / 43 2.3.3. Floating Decimal Point / 44 2.3.4. Fixed Decimal Point / 46 2.3.5. Round-off Errors in Computation with Floating Arithmetic Operations / 46 2.4. Backward Error Analysis; Condition Numbers / 51 2.4.1. Backward Error Analysis / 51 2.4.2. Condition Numbers for Problems and Algorithms / 53 2.4.3. Geometrical Illustration of Error Analysis / 56 3: Numerical Uses of Series / 60 3.1. Elementary Uses of Series / 60 3.1.1. Simple Examples / 60 3.1.2. Estimating the Remainder / 62 3.1.3. Power Series / 65 3.2. Acceleration of Convergence / 71 3.2.1. Slowly Converging Alternating Series / 71 3.2.2. Slowly Converging Series with Positive Terms / 73 3.2.3. Other Simple Ways to Accelerate Convergence / 74 3.2.4. Ill-Conditioned Series / 75 3.2.5. Numerical Use of Divergent Series / 77 4: Approximation of Functions / 81 4.1. Basic Concepts in Approximation / 81 4.1.1. Introduction / 81 4.1.2. The Idea of a Function Space / 84 4.1.3. Norms and Seminorms / 85 4.1.4. Approximation of Functions as a Geometric Problem in Function Space / 87 4.2. The Approximation of Functions by the Method of Least Squares / 88 4.2.t. Statement of the Problems / 88 4.2.2. Orthogonal Systems / 89 4.2.3. Solution of the Approximation Problem / 92 4.3. Polynomials / 97 4.3.1. Basic Terminology; the Weierstrass Approximation Theorem / 97 4.3.2. Triangle Families of Polynomials / 98 4.3.3. A Triangle Family and Its Application to Interpolation / 99 4.3.4. Equidistant Interpolation and the Runge Phenomenon / 101 4.4. Orthogonal Polynomials and Applications / 104 4.4.1. Tchebycheff Polynomials / 104 4.4.2. Tchebycheff Interpolation and Smoothing / 106 4.4.3. General Theory of Orthogonal Polynomials / 108 4.4.4. Legendre Polynomials and Gram Polynomials / 113 4.5. Complementary Observations on Polynomial Approximation / 117 4.5.1. Summary of the Use of Polynomials / 117 4.5.2. Some Inequalities for $E_n(f)$ with Applications to the Computation of Linear Functionals / 120 4.5.3. Approximation in the Maximum Norm / 124 4.5.4. Economization of Power Series; Standard Functions / 125 4.5.5. Some Statistical Aspects of the Method of Least Squares / 126 4.6. Spline Functions / 131 5: Numerical Linear Algebra / 137 5,1. Introduction / 137 5.2. Basic Concepts of Linear Algebra / 138 5.2.1. Fundamental Definitions / 138 5.2.2. Partitioned Matrices / 140 5.2.3. Linear Vector Spaces / 141 5.2.4. Eigenvalues and Similarity Transformations / 142 5.2.5. Singular-Value Decomposition and Pseudo-Inverse / 143 5.3. Direct Methods for Solving Systems of Linear Equations / 146 5.3.1. Triangular Systems / 146 5.3.2. Gaussian Elimination / 147 5.3.3. Pivoting Strategies / 150 5.3.4. $L U$-Decomposition / 152 5.3.5. Compact Schemes for Gaussian Elimination / 157 5.3.6. Inverse Matrices / 159 5.4. Special Matrices / 162 5.4.1. Symmetric Positive-Definite Matrices / 162 5.4.2. Band Matrices / 165 5.4.3. Large-Scale Linear Systems / 168 5.4.4. Other Sparse Matrices / 169 5.5. Error Analysis for Linear Systems / 174 5.5.1. An Ill-Conditioned Example / 174 5.5.2. Vector and Matrix Norms / 175 5.5.3. Perturbation Analysis / 176 5.5.4. Rounding Errors in Gaussian Elimination / 177 5.5.5. Scaling of Linear Systems / 181 5.5.6. Iterative Improvement of a Solution / 183 5.6. Iterative Methods / 188 5.7. Overdetermined Linear Systems / 196 5.7.1. The Normal Equations / 197 5.7.2. Orthogonalization Methods / 201 5.7.3. Improvement of Least-Squares Solutions / 204 5.7.4. Least-Squares Problems with Linear Constraints / 205 5.8. Computation of Eigenvalues and Eigenvectors / 208 5.8.1. The Power Method / 209 5.8.2. Methods Based on Similarity Transformations / 211 5.8.3. Eigenvalues by Equation Solving / 215 5.8.4. The $Q R$-Algorithm / 216 6: Nonlinear Equations / 218 6.1. Introduction / 218 6.2. Initial Approximations; Starting Methods / 219 6.2.1. Introduction / 219 6.2.2. The Bisection Method / 220 6.3. Newton--Raphson's Method / 222 6.4. The Secant Method / 227 6.4.1. Description of the Method / 227 6.4.2. Error Analysis for the Secant Method / 228 6.4.3. Regula Falsi / 230 6.4.4. Other Related Methods / 230 6.5. General Theory of Iteration Methods / 233 6.6. Error Estimation and Attainable Accuracy in Iteration Methods / 238 6.6.1. Error Estimation / 238 6.6.2. Attainable Accuracy; Termination Criteria / 240 6.7. Multiple Roots / 242 6.8. Algebraic Equations / 243 6.8.1. Introduction / 243 6.8.2. Deflation / 245 6.8.3. Ill-Conditioned Algebraic Equations / 246 6.9. Systems of Nonlinear Equations / 248 6.9.1. Iteration / 249 6.9.2. Newton--Raphson's Method and Some Modifications / 249 6.9.3. Other Methods / 251 7: Finite Differences with Applications to Numerical Integration, Differentiation, and Interpolation / 255 7.1. Difference Operators and Their Simplest Properties / 255 7.2. Simple Methods for Deriving Approximation Formulas and Error Estimates / 263 7.2.1. Statement of the Problems and Some Typical Examples / 263 7.2.2, Repeated Richardson Extrapolation / 269 7.3. Interpolation / 275 7.3.1. Introduction / 275 7.3.2. When is Linear Interpolation Sufficient? / 276 7.3.3. Newton's General Interpolation Formula / 277 7.3.4. Formulas for Equidistant Interpolation / 279 7.3.5. Complementary Remarks on Interpolation / 282 7.3.6. Lagrange's Interpolation Formula / 284 7.3.7. Hermite Interpolation / 285 7.3.8. Inverse Interpolation / 286 7.4. Numerical Integration / 290 7.4.1. The Rectangle Rule, Trapezoidal Rule, and Romberg's Method / 291 7.4.2. The Truncation Error of the Trapezoidal Rule / 293 7.4.3. Some Difficulties and Possibilities in Numerical Integration / 294 7.4.4. The Euler--Maclaurin Summation Formula / 297 7.4.5. Uses of the Euler--Maclaurin Formula / 300 7.4.6. Other Methods for Numerical Integration / 302 7.5. Numerical Differentiation / 307 7.6. The Calculus of Operators / 311 7.6.1. Operator Algebra / 311 7.6.2. Operator Series with Applications / 312 7.7. Functions of Several Variables / 318 7.7.1. Working with One Variable at a Time / 319 7.7.2. Rectangular Grids / 319 7.7.3. Irregular Triangular Grids / 322 8: Differential Equations / 330 8.1. Theoretical Background / 330 8.1.1. Initial-Value Problems for Ordinary Differential Equations / 330 8.1.2. Error Propagation / 333 8.1.3. Other Differential Equation Problems / 337 8.2. Euler's Method, with Repeated Richardson Extrapolation / 338 8.3. Other Methods for Initial-Value Problems in Ordinary Differential Equations / 342 8.3.1. The Modified Midpoint Method / 342 8.3.2. The Power-Series Method / 345 8.3.3. Runge--Kutta Methods / 346 8.3.4. Implicit Methods / 347 8.3.5. Stiff Problems / 349 8.3.6. Control of Step Size / 350 8.3.7. A Finite-Difference Method for a Second-Order Equation / 352 8.4. Orientation on Boundary and Eigenvalue Problems for Ordinary Differential Equations / 359 8.4.1. Introduction / 359 8.4.2. The Shooting Method / 359 8.4.3. The Band Matrix Method / 361 8.4.4. Numerical Example of an Eigenvalue Problem / 363 8.5. Difference Equations / 367 8.5.1. Homogeneous Linear Difference Equations with Constant Coefficients / 368 8.5.2. General Linear Difference Equations / 370 8.5.3. Analysis of a Numerical Method with the Help of a Test Problem / 372 8.5.4. Linear Multistep Methods / 375 8.6. Partial Differential Equations / 383 8.6.1. Introduction / 383 8.6.2. An Example of an Initial-Value Problem / 384 8.6.3. An Example of a Boundary-Value Problem / 389 8.6.4. Methods of Undetermined Coefficients and Variational Methods / 392 8.6.5. Finite-Element Methods / 395 8.6.6. Integral Equations / 397 9: Fourier Methods / 405 9.1. Introduction / 405 9.2. Basic Formulas and Theorems in Fourier Analysis / 406 9.2.1. Functions of One Variable / 406 9.2.2. Functions of Several Variables / 411 9.3. Fast Fourier Analysis / 413 9.3.1. An Important Special Case / 413 9.3.2. Fast Fourier Analysis, General Case / 414 9.4. Periodic Continuation of a Nonperiodic Function / 417 9.5. The Fourier Integral Theorem / 419 10: Optimization / 422 10.1. Statement of the Problem, Definitions, and Normal Form / 422 10.2. The Simplex Method / 426 10.3. Duality / 435 10.4. The Transportation Problem and Some Other Optimization Problems / 436 10.5. Nonlinear Optimization Problems / 438 10.5.1. Basic Concepts and Introductory Examples / 438 10.5.2. Line Search / 440 10.5.3. Algorithms for Unconstrained Optimization / 441 10.5.4. Overdetermined Nonlinear Systems / 443 10.5.5. Constrained Optimization / 444 11: The Monte Carlo Method and Simulation / 448 11.1. Introduction / 448 11.2. Random Digits and Random Numbers / 449 11.3. Applications; Reduction of Variance / 455 11.4. Pseudorandom Numbers / 463 12: Solutions to Problems / 465 13: Bibliography and Published Algorithms / 536 13.1. Introduction / 536 13.2. General Literature in Numerical Analysis / 536 13.3. Tables, Collections of Formulas, and Problems / 539 13.4. Error Analysis and Approximation of Functions / 540 13.5. Linear Algebra and Nonlinear Systems of Equations / 541 13.6. Interpolation, Numerical Integration, and Numerical Treatment of Differential Equations / 543 13.7. Optimization; Simulation / 545 13.8. Reviews, Abstracts and Other Periodicals / 547 13.9. Survey of Published Algorithms / 548 Index by Subject to Algorithms, 1960--1970 / 548 Appendix Tables / 563 Index / 565

shortTOC:
1: Some General Principles of Numerical Calculation / 1 2: How to Obtain and Estimate Accuracy in Numerical Calculations / 21 3: Numerical Uses of Series / 60 4: Approximation of Functions / 81 5: Numerical Linear Algebra / 137 6: Nonlinear Equations / 218 7: Finite Differences with Applications to Numerical Integration, Differentiation, and Interpolation / 255 8: Differential Equations / 330 9: Fourier Methods / 405 10: Optimization / 422 11: The Monte Carlo Method and Simulation / 448 12: Solutions to Problems / 465 13: Bibliography and Published Algorithms / 536 Index by Subject to Algorithms, 1960--1970 / 548 Appendix Tables / 563 Index / 565

rawshortTOC:
1: Some General Principles of Numerical Calculation / 1 \\ 2: How to Obtain and Estimate Accuracy in Numerical Calculations / 21 \\ 3: Numerical Uses of Series / 60 \\ 4: Approximation of Functions / 81 \\ 5: Numerical Linear Algebra / 137 \\ 6: Nonlinear Equations / 218 \\ 7: Finite Differences with Applications to Numerical Integration, Differentiation, and Interpolation / 255 \\ 8: Differential Equations / 330 \\ 9: Fourier Methods / 405 \\ 10: Optimization / 422 \\ 11: The Monte Carlo Method and Simulation / 448 \\ 12: Solutions to Problems / 465 \\ 13: Bibliography and Published Algorithms / 536 \\ Index by Subject to Algorithms, 1960--1970 / 548 \\ Appendix Tables / 563 \\ Index / 565

rawTOC:
Preface / xvii \\ Conventions / xix \\ 1: Some General Principles of Numerical Calculation / 1 \\ 1.1. Introduction / 1 \\ 1.2. Some Common Ideas and Concepts in Numerical Methods / 2 \\ 1.3. Numerical Problems and Algorithms / 13 \\ 1.3.1. Definitions / 13 \\ 1.3.2. Recursive Formulas; Homer's Rule / 14 \\ 1.3.3. An Example of Numerical Instability / 16 \\ 2: How to Obtain and Estimate Accuracy in Numerical Calculations / 21 \\ 2.1. Basic Concepts in Error Estimation / 21 \\ 2.1.1. Introduction / 21 \\ 2.1.2. Sources of Error / 22 \\ 2.1.3. Absolute and Relative Errors / 23 \\ 2.1.4. Rounding and Chopping / 24 \\ 2.2 Propagation of Errors / 26 \\ 2.2.1. Simple Examples of Error Analysis / 26 \\ 2.2.2. The General Formula for Error Propagation; Maximum Error and Standard Error / 29 \\ 2.2.3. On the Practical Application of Error Estimation / 34 \\ 2.2.4. The Use of Experimental Perturbations / 36 \\ 2.2.5. Automatic Control of Accuracy / 37 \\ 2.3. Number Systems; Floating and Fixed Representation / 42 \\ 2.3.1. The Position System / 42 \\ 2.3.2. Floating and Fixed Representation / 43 \\ 2.3.3. Floating Decimal Point / 44 \\ 2.3.4. Fixed Decimal Point / 46 \\ 2.3.5. Round-off Errors in Computation with Floating Arithmetic Operations / 46 \\ 2.4. Backward Error Analysis; Condition Numbers / 51 \\ 2.4.1. Backward Error Analysis / 51 \\ 2.4.2. Condition Numbers for Problems and Algorithms / 53 \\ 2.4.3. Geometrical Illustration of Error Analysis / 56 \\ 3: Numerical Uses of Series / 60 \\ 3.1. Elementary Uses of Series / 60 \\ 3.1.1. Simple Examples / 60 \\ 3.1.2. Estimating the Remainder / 62 \\ 3.1.3. Power Series / 65 \\ 3.2. Acceleration of Convergence / 71 \\ 3.2.1. Slowly Converging Alternating Series / 71 \\ 3.2.2. Slowly Converging Series with Positive Terms / 73 \\ 3.2.3. Other Simple Ways to Accelerate Convergence / 74 \\ 3.2.4. Ill-Conditioned Series / 75 \\ 3.2.5. Numerical Use of Divergent Series / 77 \\ 4: Approximation of Functions / 81 \\ 4.1. Basic Concepts in Approximation / 81 \\ 4.1.1. Introduction / 81 \\ 4.1.2. The Idea of a Function Space / 84 \\ 4.1.3. Norms and Seminorms / 85 \\ 4.1.4. Approximation of Functions as a Geometric Problem in Function Space / 87 \\ 4.2. The Approximation of Functions by the Method of Least Squares / 88 \\ 4.2.t. Statement of the Problems / 88 \\ 4.2.2. Orthogonal Systems / 89 \\ 4.2.3. Solution of the Approximation Problem / 92 \\ 4.3. Polynomials / 97 \\ 4.3.1. Basic Terminology; the Weierstrass Approximation Theorem / 97 \\ 4.3.2. Triangle Families of Polynomials / 98 \\ 4.3.3. A Triangle Family and Its Application to Interpolation / 99 \\ 4.3.4. Equidistant Interpolation and the Runge Phenomenon / 101 \\ 4.4. Orthogonal Polynomials and Applications / 104 \\ 4.4.1. Tchebycheff Polynomials / 104 \\ 4.4.2. Tchebycheff Interpolation and Smoothing / 106 \\ 4.4.3. General Theory of Orthogonal Polynomials / 108 \\ 4.4.4. Legendre Polynomials and Gram Polynomials / 113 \\ 4.5. Complementary Observations on Polynomial Approximation / 117 \\ 4.5.1. Summary of the Use of Polynomials / 117 \\ 4.5.2. Some Inequalities for $E_n(f)$ with Applications to the Computation of Linear Functionals / 120 \\ 4.5.3. Approximation in the Maximum Norm / 124 \\ 4.5.4. Economization of Power Series; Standard Functions / 125 \\ 4.5.5. Some Statistical Aspects of the Method of Least Squares / 126 \\ 4.6. Spline Functions / 131 \\ 5: Numerical Linear Algebra / 137 \\ 5,1. Introduction / 137 \\ 5.2. Basic Concepts of Linear Algebra / 138 \\ 5.2.1. Fundamental Definitions / 138 \\ 5.2.2. Partitioned Matrices / 140 \\ 5.2.3. Linear Vector Spaces / 141 \\ 5.2.4. Eigenvalues and Similarity Transformations / 142 \\ 5.2.5. Singular-Value Decomposition and Pseudo-Inverse / 143 \\ 5.3. Direct Methods for Solving Systems of Linear Equations / 146 \\ 5.3.1. Triangular Systems / 146 \\ 5.3.2. Gaussian Elimination / 147 \\ 5.3.3. Pivoting Strategies / 150 \\ 5.3.4. $L U$-Decomposition / 152 \\ 5.3.5. Compact Schemes for Gaussian Elimination / 157 \\ 5.3.6. Inverse Matrices / 159 \\ 5.4. Special Matrices / 162 \\ 5.4.1. Symmetric Positive-Definite Matrices / 162 \\ 5.4.2. Band Matrices / 165 \\ 5.4.3. Large-Scale Linear Systems / 168 \\ 5.4.4. Other Sparse Matrices / 169 \\ 5.5. Error Analysis for Linear Systems / 174 \\ 5.5.1. An Ill-Conditioned Example / 174 \\ 5.5.2. Vector and Matrix Norms / 175 \\ 5.5.3. Perturbation Analysis / 176 \\ 5.5.4. Rounding Errors in Gaussian Elimination / 177 \\ 5.5.5. Scaling of Linear Systems / 181 \\ 5.5.6. Iterative Improvement of a Solution / 183 \\ 5.6. Iterative Methods / 188 \\ 5.7. Overdetermined Linear Systems / 196 \\ 5.7.1. The Normal Equations / 197 \\ 5.7.2. Orthogonalization Methods / 201 \\ 5.7.3. Improvement of Least-Squares Solutions / 204 \\ 5.7.4. Least-Squares Problems with Linear Constraints / 205 \\ 5.8. Computation of Eigenvalues and Eigenvectors / 208 \\ 5.8.1. The Power Method / 209 \\ 5.8.2. Methods Based on Similarity Transformations / 211 \\ 5.8.3. Eigenvalues by Equation Solving / 215 \\ 5.8.4. The $Q R$-Algorithm / 216 \\ 6: Nonlinear Equations / 218 \\ 6.1. Introduction / 218 \\ 6.2. Initial Approximations; Starting Methods / 219 \\ 6.2.1. Introduction / 219 \\ 6.2.2. The Bisection Method / 220 \\ 6.3. Newton--Raphson's Method / 222 \\ 6.4. The Secant Method / 227 \\ 6.4.1. Description of the Method / 227 \\ 6.4.2. Error Analysis for the Secant Method / 228 \\ 6.4.3. Regula Falsi / 230 \\ 6.4.4. Other Related Methods / 230 \\ 6.5. General Theory of Iteration Methods / 233 \\ 6.6. Error Estimation and Attainable Accuracy in Iteration Methods / 238 \\ 6.6.1. Error Estimation / 238 \\ 6.6.2. Attainable Accuracy; Termination Criteria / 240 \\ 6.7. Multiple Roots / 242 \\ 6.8. Algebraic Equations / 243 \\ 6.8.1. Introduction / 243 \\ 6.8.2. Deflation / 245 \\ 6.8.3. Ill-Conditioned Algebraic Equations / 246 \\ 6.9. Systems of Nonlinear Equations / 248 \\ 6.9.1. Iteration / 249 \\ 6.9.2. Newton--Raphson's Method and Some Modifications / 249 \\ 6.9.3. Other Methods / 251 \\ 7: Finite Differences with Applications to Numerical Integration, Differentiation, and Interpolation / 255 \\ 7.1. Difference Operators and Their Simplest Properties / 255 \\ 7.2. Simple Methods for Deriving Approximation Formulas and Error Estimates / 263 \\ 7.2.1. Statement of the Problems and Some Typical Examples / 263 \\ 7.2.2, Repeated Richardson Extrapolation / 269 \\ 7.3. Interpolation / 275 \\ 7.3.1. Introduction / 275 \\ 7.3.2. When is Linear Interpolation Sufficient? / 276 \\ 7.3.3. Newton's General Interpolation Formula / 277 \\ 7.3.4. Formulas for Equidistant Interpolation / 279 \\ 7.3.5. Complementary Remarks on Interpolation / 282 \\ 7.3.6. Lagrange's Interpolation Formula / 284 \\ 7.3.7. Hermite Interpolation / 285 \\ 7.3.8. Inverse Interpolation / 286 \\ 7.4. Numerical Integration / 290 \\ 7.4.1. The Rectangle Rule, Trapezoidal Rule, and Romberg's Method / 291 \\ 7.4.2. The Truncation Error of the Trapezoidal Rule / 293 \\ 7.4.3. Some Difficulties and Possibilities in Numerical Integration / 294 \\ 7.4.4. The Euler--Maclaurin Summation Formula / 297 \\ 7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\ 7.4.6. Other Methods for Numerical Integration / 302 \\ 7.5. Numerical Differentiation / 307 \\ 7.6. The Calculus of Operators / 311 \\ 7.6.1. Operator Algebra / 311 \\ 7.6.2. Operator Series with Applications / 312 \\ 7.7. Functions of Several Variables / 318 \\ 7.7.1. Working with One Variable at a Time / 319 \\ 7.7.2. Rectangular Grids / 319 \\ 7.7.3. Irregular Triangular Grids / 322 \\ 8: Differential Equations / 330 \\ 8.1. Theoretical Background / 330 \\ 8.1.1. Initial-Value Problems for Ordinary Differential Equations / 330 \\ 8.1.2. Error Propagation / 333 \\ 8.1.3. Other Differential Equation Problems / 337 \\ 8.2. Euler's Method, with Repeated Richardson Extrapolation / 338 \\ 8.3. Other Methods for Initial-Value Problems in Ordinary Differential Equations / 342 \\ 8.3.1. The Modified Midpoint Method / 342 \\ 8.3.2. The Power-Series Method / 345 \\ 8.3.3. Runge--Kutta Methods / 346 \\ 8.3.4. Implicit Methods / 347 \\ 8.3.5. Stiff Problems / 349 \\ 8.3.6. Control of Step Size / 350 \\ 8.3.7. A Finite-Difference Method for a Second-Order Equation / 352 \\ 8.4. Orientation on Boundary and Eigenvalue Problems for Ordinary Differential Equations / 359 \\ 8.4.1. Introduction / 359 \\ 8.4.2. The Shooting Method / 359 \\ 8.4.3. The Band Matrix Method / 361 \\ 8.4.4. Numerical Example of an Eigenvalue Problem / 363 \\ 8.5. Difference Equations / 367 \\ 8.5.1. Homogeneous Linear Difference Equations with Constant Coefficients / 368 \\ 8.5.2. General Linear Difference Equations / 370 \\ 8.5.3. Analysis of a Numerical Method with the Help of a Test Problem / 372 \\ 8.5.4. Linear Multistep Methods / 375 \\ 8.6. Partial Differential Equations / 383 \\ 8.6.1. Introduction / 383 \\ 8.6.2. An Example of an Initial-Value Problem / 384 \\ 8.6.3. An Example of a Boundary-Value Problem / 389 \\ 8.6.4. Methods of Undetermined Coefficients and Variational Methods / 392 \\ 8.6.5. Finite-Element Methods / 395 \\ 8.6.6. Integral Equations / 397 \\ 9: Fourier Methods / 405 \\ 9.1. Introduction / 405 \\ 9.2. Basic Formulas and Theorems in Fourier Analysis / 406 \\ 9.2.1. Functions of One Variable / 406 \\ 9.2.2. Functions of Several Variables / 411 \\ 9.3. Fast Fourier Analysis / 413 \\ 9.3.1. An Important Special Case / 413 \\ 9.3.2. Fast Fourier Analysis, General Case / 414 \\ 9.4. Periodic Continuation of a Nonperiodic Function / 417 \\ 9.5. The Fourier Integral Theorem / 419 \\ 10: Optimization / 422 \\ 10.1. Statement of the Problem, Definitions, and Normal Form / 422 \\ 10.2. The Simplex Method / 426 \\ 10.3. Duality / 435 \\ 10.4. The Transportation Problem and Some Other Optimization Problems / 436 \\ 10.5. Nonlinear Optimization Problems / 438 \\ 10.5.1. Basic Concepts and Introductory Examples / 438 \\ 10.5.2. Line Search / 440 \\ 10.5.3. Algorithms for Unconstrained Optimization / 441 \\ 10.5.4. Overdetermined Nonlinear Systems / 443 \\ 10.5.5. Constrained Optimization / 444 \\ 11: The Monte Carlo Method and Simulation / 448 \\ 11.1. Introduction / 448 \\ 11.2. Random Digits and Random Numbers / 449 \\ 11.3. Applications; Reduction of Variance / 455 \\ 11.4. Pseudorandom Numbers / 463 \\ 12: Solutions to Problems / 465 \\ 13: Bibliography and Published Algorithms / 536 \\ 13.1. Introduction / 536 \\ 13.2. General Literature in Numerical Analysis / 536 \\ 13.3. Tables, Collections of Formulas, and Problems / 539 \\ 13.4. Error Analysis and Approximation of Functions / 540 \\ 13.5. Linear Algebra and Nonlinear Systems of Equations / 541 \\ 13.6. Interpolation, Numerical Integration, and Numerical Treatment of Differential Equations / 543 \\ 13.7. Optimization; Simulation / 545 \\ 13.8. Reviews, Abstracts and Other Periodicals / 547 \\ 13.9. Survey of Published Algorithms / 548 \\ Index by Subject to Algorithms, 1960--1970 / 548 \\ Appendix Tables / 563 \\ Index / 565

entry:
@Book{Dahlquist:1974:NM,
  author =       "Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned
                 Anderson",
  title =        "Numerical Methods",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xviii + 573",
  year =         "1974",
  ISBN =         "0-13-627315-7",
  ISBN-13 =      "978-0-13-627315-8",
  LCCN =         "QA297 .D131 1969",
  bibdate =      "Tue Dec 14 22:44:59 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Translated by Ned Anderson.",
  series =       "Prentice-Hall Series in Automatic Computation",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Some General Principles of Numerical
                 Calculation / 1 \\
                 2: How to Obtain and Estimate Accuracy in Numerical
                 Calculations / 21 \\
                 3: Numerical Uses of Series / 60 \\
                 4: Approximation of Functions / 81 \\
                 5: Numerical Linear Algebra / 137 \\
                 6: Nonlinear Equations / 218 \\
                 7: Finite Differences with Applications to Numerical
                 Integration, Differentiation, and Interpolation / 255
                 \\
                 8: Differential Equations / 330 \\
                 9: Fourier Methods / 405 \\
                 10: Optimization / 422 \\
                 11: The Monte Carlo Method and Simulation / 448 \\
                 12: Solutions to Problems / 465 \\
                 13: Bibliography and Published Algorithms / 536 \\
                 Index by Subject to Algorithms, 1960--1970 / 548 \\
                 Appendix Tables / 563 \\
                 Index / 565",
  tableofcontents = "Preface / xvii \\
                 Conventions / xix \\
                 1: Some General Principles of Numerical Calculation / 1
                 \\
                 1.1. Introduction / 1 \\
                 1.2. Some Common Ideas and Concepts in Numerical
                 Methods / 2 \\
                 1.3. Numerical Problems and Algorithms / 13 \\
                 1.3.1. Definitions / 13 \\
                 1.3.2. Recursive Formulas; Homer's Rule / 14 \\
                 1.3.3. An Example of Numerical Instability / 16 \\
                 2: How to Obtain and Estimate Accuracy in Numerical
                 Calculations / 21 \\
                 2.1. Basic Concepts in Error Estimation / 21 \\
                 2.1.1. Introduction / 21 \\
                 2.1.2. Sources of Error / 22 \\
                 2.1.3. Absolute and Relative Errors / 23 \\
                 2.1.4. Rounding and Chopping / 24 \\
                 2.2 Propagation of Errors / 26 \\
                 2.2.1. Simple Examples of Error Analysis / 26 \\
                 2.2.2. The General Formula for Error Propagation;
                 Maximum Error and Standard Error / 29 \\
                 2.2.3. On the Practical Application of Error Estimation
                 / 34 \\
                 2.2.4. The Use of Experimental Perturbations / 36 \\
                 2.2.5. Automatic Control of Accuracy / 37 \\
                 2.3. Number Systems; Floating and Fixed Representation
                 / 42 \\
                 2.3.1. The Position System / 42 \\
                 2.3.2. Floating and Fixed Representation / 43 \\
                 2.3.3. Floating Decimal Point / 44 \\
                 2.3.4. Fixed Decimal Point / 46 \\
                 2.3.5. Round-off Errors in Computation with Floating
                 Arithmetic Operations / 46 \\
                 2.4. Backward Error Analysis; Condition Numbers / 51
                 \\
                 2.4.1. Backward Error Analysis / 51 \\
                 2.4.2. Condition Numbers for Problems and Algorithms /
                 53 \\
                 2.4.3. Geometrical Illustration of Error Analysis / 56
                 \\
                 3: Numerical Uses of Series / 60 \\
                 3.1. Elementary Uses of Series / 60 \\
                 3.1.1. Simple Examples / 60 \\
                 3.1.2. Estimating the Remainder / 62 \\
                 3.1.3. Power Series / 65 \\
                 3.2. Acceleration of Convergence / 71 \\
                 3.2.1. Slowly Converging Alternating Series / 71 \\
                 3.2.2. Slowly Converging Series with Positive Terms /
                 73 \\
                 3.2.3. Other Simple Ways to Accelerate Convergence / 74
                 \\
                 3.2.4. Ill-Conditioned Series / 75 \\
                 3.2.5. Numerical Use of Divergent Series / 77 \\
                 4: Approximation of Functions / 81 \\
                 4.1. Basic Concepts in Approximation / 81 \\
                 4.1.1. Introduction / 81 \\
                 4.1.2. The Idea of a Function Space / 84 \\
                 4.1.3. Norms and Seminorms / 85 \\
                 4.1.4. Approximation of Functions as a Geometric
                 Problem in Function Space / 87 \\
                 4.2. The Approximation of Functions by the Method of
                 Least Squares / 88 \\
                 4.2.t. Statement of the Problems / 88 \\
                 4.2.2. Orthogonal Systems / 89 \\
                 4.2.3. Solution of the Approximation Problem / 92 \\
                 4.3. Polynomials / 97 \\
                 4.3.1. Basic Terminology; the Weierstrass Approximation
                 Theorem / 97 \\
                 4.3.2. Triangle Families of Polynomials / 98 \\
                 4.3.3. A Triangle Family and Its Application to
                 Interpolation / 99 \\
                 4.3.4. Equidistant Interpolation and the Runge
                 Phenomenon / 101 \\
                 4.4. Orthogonal Polynomials and Applications / 104 \\
                 4.4.1. Tchebycheff Polynomials / 104 \\
                 4.4.2. Tchebycheff Interpolation and Smoothing / 106
                 \\
                 4.4.3. General Theory of Orthogonal Polynomials / 108
                 \\
                 4.4.4. Legendre Polynomials and Gram Polynomials / 113
                 \\
                 4.5. Complementary Observations on Polynomial
                 Approximation / 117 \\
                 4.5.1. Summary of the Use of Polynomials / 117 \\
                 4.5.2. Some Inequalities for $E_n(f)$ with Applications
                 to the Computation of Linear Functionals / 120 \\
                 4.5.3. Approximation in the Maximum Norm / 124 \\
                 4.5.4. Economization of Power Series; Standard
                 Functions / 125 \\
                 4.5.5. Some Statistical Aspects of the Method of Least
                 Squares / 126 \\
                 4.6. Spline Functions / 131 \\
                 5: Numerical Linear Algebra / 137 \\
                 5,1. Introduction / 137 \\
                 5.2. Basic Concepts of Linear Algebra / 138 \\
                 5.2.1. Fundamental Definitions / 138 \\
                 5.2.2. Partitioned Matrices / 140 \\
                 5.2.3. Linear Vector Spaces / 141 \\
                 5.2.4. Eigenvalues and Similarity Transformations / 142
                 \\
                 5.2.5. Singular-Value Decomposition and Pseudo-Inverse
                 / 143 \\
                 5.3. Direct Methods for Solving Systems of Linear
                 Equations / 146 \\
                 5.3.1. Triangular Systems / 146 \\
                 5.3.2. Gaussian Elimination / 147 \\
                 5.3.3. Pivoting Strategies / 150 \\
                 5.3.4. $L U$-Decomposition / 152 \\
                 5.3.5. Compact Schemes for Gaussian Elimination / 157
                 \\
                 5.3.6. Inverse Matrices / 159 \\
                 5.4. Special Matrices / 162 \\
                 5.4.1. Symmetric Positive-Definite Matrices / 162 \\
                 5.4.2. Band Matrices / 165 \\
                 5.4.3. Large-Scale Linear Systems / 168 \\
                 5.4.4. Other Sparse Matrices / 169 \\
                 5.5. Error Analysis for Linear Systems / 174 \\
                 5.5.1. An Ill-Conditioned Example / 174 \\
                 5.5.2. Vector and Matrix Norms / 175 \\
                 5.5.3. Perturbation Analysis / 176 \\
                 5.5.4. Rounding Errors in Gaussian Elimination / 177
                 \\
                 5.5.5. Scaling of Linear Systems / 181 \\
                 5.5.6. Iterative Improvement of a Solution / 183 \\
                 5.6. Iterative Methods / 188 \\
                 5.7. Overdetermined Linear Systems / 196 \\
                 5.7.1. The Normal Equations / 197 \\
                 5.7.2. Orthogonalization Methods / 201 \\
                 5.7.3. Improvement of Least-Squares Solutions / 204 \\
                 5.7.4. Least-Squares Problems with Linear Constraints /
                 205 \\
                 5.8. Computation of Eigenvalues and Eigenvectors / 208
                 \\
                 5.8.1. The Power Method / 209 \\
                 5.8.2. Methods Based on Similarity Transformations /
                 211 \\
                 5.8.3. Eigenvalues by Equation Solving / 215 \\
                 5.8.4. The $Q R$-Algorithm / 216 \\
                 6: Nonlinear Equations / 218 \\
                 6.1. Introduction / 218 \\
                 6.2. Initial Approximations; Starting Methods / 219 \\
                 6.2.1. Introduction / 219 \\
                 6.2.2. The Bisection Method / 220 \\
                 6.3. Newton--Raphson's Method / 222 \\
                 6.4. The Secant Method / 227 \\
                 6.4.1. Description of the Method / 227 \\
                 6.4.2. Error Analysis for the Secant Method / 228 \\
                 6.4.3. Regula Falsi / 230 \\
                 6.4.4. Other Related Methods / 230 \\
                 6.5. General Theory of Iteration Methods / 233 \\
                 6.6. Error Estimation and Attainable Accuracy in
                 Iteration Methods / 238 \\
                 6.6.1. Error Estimation / 238 \\
                 6.6.2. Attainable Accuracy; Termination Criteria / 240
                 \\
                 6.7. Multiple Roots / 242 \\
                 6.8. Algebraic Equations / 243 \\
                 6.8.1. Introduction / 243 \\
                 6.8.2. Deflation / 245 \\
                 6.8.3. Ill-Conditioned Algebraic Equations / 246 \\
                 6.9. Systems of Nonlinear Equations / 248 \\
                 6.9.1. Iteration / 249 \\
                 6.9.2. Newton--Raphson's Method and Some Modifications
                 / 249 \\
                 6.9.3. Other Methods / 251 \\
                 7: Finite Differences with Applications to Numerical
                 Integration, Differentiation, and Interpolation / 255
                 \\
                 7.1. Difference Operators and Their Simplest Properties
                 / 255 \\
                 7.2. Simple Methods for Deriving Approximation Formulas
                 and Error Estimates / 263 \\
                 7.2.1. Statement of the Problems and Some Typical
                 Examples / 263 \\
                 7.2.2, Repeated Richardson Extrapolation / 269 \\
                 7.3. Interpolation / 275 \\
                 7.3.1. Introduction / 275 \\
                 7.3.2. When is Linear Interpolation Sufficient? / 276
                 \\
                 7.3.3. Newton's General Interpolation Formula / 277 \\
                 7.3.4. Formulas for Equidistant Interpolation / 279 \\
                 7.3.5. Complementary Remarks on Interpolation / 282 \\
                 7.3.6. Lagrange's Interpolation Formula / 284 \\
                 7.3.7. Hermite Interpolation / 285 \\
                 7.3.8. Inverse Interpolation / 286 \\
                 7.4. Numerical Integration / 290 \\
                 7.4.1. The Rectangle Rule, Trapezoidal Rule, and
                 Romberg's Method / 291 \\
                 7.4.2. The Truncation Error of the Trapezoidal Rule /
                 293 \\
                 7.4.3. Some Difficulties and Possibilities in Numerical
                 Integration / 294 \\
                 7.4.4. The Euler--Maclaurin Summation Formula / 297 \\
                 7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\
                 7.4.6. Other Methods for Numerical Integration / 302
                 \\
                 7.5. Numerical Differentiation / 307 \\
                 7.6. The Calculus of Operators / 311 \\
                 7.6.1. Operator Algebra / 311 \\
                 7.6.2. Operator Series with Applications / 312 \\
                 7.7. Functions of Several Variables / 318 \\
                 7.7.1. Working with One Variable at a Time / 319 \\
                 7.7.2. Rectangular Grids / 319 \\
                 7.7.3. Irregular Triangular Grids / 322 \\
                 8: Differential Equations / 330 \\
                 8.1. Theoretical Background / 330 \\
                 8.1.1. Initial-Value Problems for Ordinary Differential
                 Equations / 330 \\
                 8.1.2. Error Propagation / 333 \\
                 8.1.3. Other Differential Equation Problems / 337 \\
                 8.2. Euler's Method, with Repeated Richardson
                 Extrapolation / 338 \\
                 8.3. Other Methods for Initial-Value Problems in
                 Ordinary Differential Equations / 342 \\
                 8.3.1. The Modified Midpoint Method / 342 \\
                 8.3.2. The Power-Series Method / 345 \\
                 8.3.3. Runge--Kutta Methods / 346 \\
                 8.3.4. Implicit Methods / 347 \\
                 8.3.5. Stiff Problems / 349 \\
                 8.3.6. Control of Step Size / 350 \\
                 8.3.7. A Finite-Difference Method for a Second-Order
                 Equation / 352 \\
                 8.4. Orientation on Boundary and Eigenvalue Problems
                 for Ordinary Differential Equations / 359 \\
                 8.4.1. Introduction / 359 \\
                 8.4.2. The Shooting Method / 359 \\
                 8.4.3. The Band Matrix Method / 361 \\
                 8.4.4. Numerical Example of an Eigenvalue Problem / 363
                 \\
                 8.5. Difference Equations / 367 \\
                 8.5.1. Homogeneous Linear Difference Equations with
                 Constant Coefficients / 368 \\
                 8.5.2. General Linear Difference Equations / 370 \\
                 8.5.3. Analysis of a Numerical Method with the Help of
                 a Test Problem / 372 \\
                 8.5.4. Linear Multistep Methods / 375 \\
                 8.6. Partial Differential Equations / 383 \\
                 8.6.1. Introduction / 383 \\
                 8.6.2. An Example of an Initial-Value Problem / 384 \\
                 8.6.3. An Example of a Boundary-Value Problem / 389 \\
                 8.6.4. Methods of Undetermined Coefficients and
                 Variational Methods / 392 \\
                 8.6.5. Finite-Element Methods / 395 \\
                 8.6.6. Integral Equations / 397 \\
                 9: Fourier Methods / 405 \\
                 9.1. Introduction / 405 \\
                 9.2. Basic Formulas and Theorems in Fourier Analysis /
                 406 \\
                 9.2.1. Functions of One Variable / 406 \\
                 9.2.2. Functions of Several Variables / 411 \\
                 9.3. Fast Fourier Analysis / 413 \\
                 9.3.1. An Important Special Case / 413 \\
                 9.3.2. Fast Fourier Analysis, General Case / 414 \\
                 9.4. Periodic Continuation of a Nonperiodic Function /
                 417 \\
                 9.5. The Fourier Integral Theorem / 419 \\
                 10: Optimization / 422 \\
                 10.1. Statement of the Problem, Definitions, and Normal
                 Form / 422 \\
                 10.2. The Simplex Method / 426 \\
                 10.3. Duality / 435 \\
                 10.4. The Transportation Problem and Some Other
                 Optimization Problems / 436 \\
                 10.5. Nonlinear Optimization Problems / 438 \\
                 10.5.1. Basic Concepts and Introductory Examples / 438
                 \\
                 10.5.2. Line Search / 440 \\
                 10.5.3. Algorithms for Unconstrained Optimization / 441
                 \\
                 10.5.4. Overdetermined Nonlinear Systems / 443 \\
                 10.5.5. Constrained Optimization / 444 \\
                 11: The Monte Carlo Method and Simulation / 448 \\
                 11.1. Introduction / 448 \\
                 11.2. Random Digits and Random Numbers / 449 \\
                 11.3. Applications; Reduction of Variance / 455 \\
                 11.4. Pseudorandom Numbers / 463 \\
                 12: Solutions to Problems / 465 \\
                 13: Bibliography and Published Algorithms / 536 \\
                 13.1. Introduction / 536 \\
                 13.2. General Literature in Numerical Analysis / 536
                 \\
                 13.3. Tables, Collections of Formulas, and Problems /
                 539 \\
                 13.4. Error Analysis and Approximation of Functions /
                 540 \\
                 13.5. Linear Algebra and Nonlinear Systems of Equations
                 / 541 \\
                 13.6. Interpolation, Numerical Integration, and
                 Numerical Treatment of Differential Equations / 543 \\
                 13.7. Optimization; Simulation / 545 \\
                 13.8. Reviews, Abstracts and Other Periodicals / 547
                 \\
                 13.9. Survey of Published Algorithms / 548 \\
                 Index by Subject to Algorithms, 1960--1970 / 548 \\
                 Appendix Tables / 563 \\
                 Index / 565",
}


bibtype: article
filename: fparith.bib
label: Davis:1974:USN
author: R. L. Davis
title: Uniform Shift Networks
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 3
pages: 317--322
month: mar
monthnumber: 3
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224214
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 10:48:43 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:48:43 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. L. Davis
rawtitle: Uniform Shift Networks
entry:
@Article{Davis:1974:USN,
  author =       "R. L. Davis",
  title =        "Uniform Shift Networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "317--322",
  month =        mar,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224214",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 10:48:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Fateman:1974:PMP
author: Richard J. Fateman
title: Polynomial Multiplication, Powers, and asymptotic Analysis: Some Comments
journal: j-SIAM-J-COMPUT
volume: 3
number: 3
pages: 196--213
year: 1974
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
bibdate: Mon Nov 29 10:57:57 MST 2010
bibtimestamp: 2010.11.29 10:57:57 MST
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: Richard J. Fateman
rawtitle: Polynomial Multiplication, Powers, and asymptotic Analysis: {Some} Comments
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/3/3; https://www.math.utah.edu/pub/tex/bib/fparith.bib; Theory/auto.diff.bib; Theory/Comp.Alg.1.bib

entry:
@Article{Fateman:1974:PMP,
  author =       "Richard J. Fateman",
  title =        "Polynomial Multiplication, Powers, and asymptotic
                 Analysis: {Some} Comments",
  journal =      j-SIAM-J-COMPUT,
  volume =       "3",
  number =       "3",
  pages =        "196--213",
  month =        "????",
  year =         "1974",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Mon Nov 29 10:57:57 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/3/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Theory/auto.diff.bib; Theory/Comp.Alg.1.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  referred =     "[Bren78a].",
}


bibtype: article
filename: fparith.bib
label: Fettweis:1974:PFP
author: A. Fettweis
title: On properties of floating-point roundoff noise
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 22
number: 2
pages: 149--151
month: apr
monthnumber: 4
year: 1974
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 08:40:53 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:53 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: A. Fettweis
rawtitle: On properties of floating-point roundoff noise
entry:
@Article{Fettweis:1974:PFP,
  author =       "A. Fettweis",
  title =        "On properties of floating-point roundoff noise",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "22",
  number =       "2",
  pages =        "149--151",
  month =        apr,
  year =         "1974",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "The probability density and related properties of the
                 relative error due to rounding after floating-point
                 arithmetic operations can be computed from the
                 distributions of the mantissa and its absolute error.
                 Various results obtained, in particular, \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Fischer:1974:FLI
author: Michael J. Fischer and Larry J. Stockmeyer
title: Fast on-line integer multiplication
journal: j-J-COMP-SYS-SCI
volume: 9
number: 3
pages: 317--331
month: dec
monthnumber: 12
year: 1974
CODEN: JCSSBM
DOI: https://doi.org/10.1016/S0022-0000(74)80047-4
ISSN: 0022-0000 (print), 1090-2724 (electronic) OR 00220000 (print), 10902724 (electronic)
ISSNL: 0022-0000 OR 00220000
bibdate: Tue Jan 29 15:25:28 MST 2019
bibtimestamp: 2019.01.29 15:25:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0022000074800474
fjournal: Journal of Computer and System Sciences
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00220000
rawauthor: Michael J. Fischer and Larry J. Stockmeyer
rawtitle: Fast on-line integer multiplication
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib

entry:
@Article{Fischer:1974:FLI,
  author =       "Michael J. Fischer and Larry J. Stockmeyer",
  title =        "Fast on-line integer multiplication",
  journal =      j-J-COMP-SYS-SCI,
  volume =       "9",
  number =       "3",
  pages =        "317--331",
  month =        dec,
  year =         "1974",
  CODEN =        "JCSSBM",
  DOI =          "https://doi.org/10.1016/S0022-0000(74)80047-4",
  ISSN =         "0022-0000 (print), 1090-2724 (electronic)",
  ISSN-L =       "0022-0000",
  bibdate =      "Tue Jan 29 15:25:28 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022000074800474",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computer and System Sciences",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00220000",
}


bibtype: mastersthesis
filename: fparith.bib
label: Fischer:1974:FPP
author: David Michael Fischer
title: Floating point processor for teleoperator studies
type: Thesis (M.S.)
school: Massachusetts Institute of Technology. Dept. of Mechanical Engineering
address: Cambridge, MA, USA
pages: 35 + 14
year: 1974
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: David Michael Fischer
rawtitle: Floating point processor for teleoperator studies
entry:
@MastersThesis{Fischer:1974:FPP,
  author =       "David Michael Fischer",
  title =        "Floating point processor for teleoperator studies",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Mechanical Engineering",
  address =      "Cambridge, MA, USA",
  pages =        "35 + 14",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Gardiner:1974:CAI
author: A. B. Gardiner
title: Comments on ``An Augmented Iterative Array for High Speed Division''
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 3
pages: 326--327
month: mar
monthnumber: 3
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.223931
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:31 MDT 2011
bibtimestamp: 2011.07.12 11:27:31 MDT
note: See cite Cappa:1973:AIA.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672524
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. B. Gardiner
rawnote: See \cite{Cappa:1973:AIA}.
rawtitle: Comments on {``An Augmented Iterative Array for High Speed Division''}
entry:
@Article{Gardiner:1974:CAI,
  author =       "A. B. Gardiner",
  title =        "Comments on {``An Augmented Iterative Array for High
                 Speed Division''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "3",
  pages =        "326--327",
  month =        mar,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223931",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Cappa:1973:AIA}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672524",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Gentleman:1974:MAR
author: W. Morven Gentleman and Scott B. Marovich
title: More on Algorithms that Reveal Properties of Floating Point Arithmetic Units
journal: j-CACM
volume: 17
number: 5
pages: 276--277
month: may
monthnumber: 5
year: 1974
CODEN: CACMA2
DOI: https://doi.org/10.1145/360980.361003
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:43:47 MST 2001
bibtimestamp: 2001.01.22 06:43:47 MST
note: See cite Malcolm:1972:ARP.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Univ. Waterloo, Ont., Canada
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: W. Morven Gentleman and Scott B. Marovich
rawnote: See \cite{Malcolm:1972:ARP}.
rawtitle: More on Algorithms that Reveal Properties of Floating Point Arithmetic Units
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#GentlemanM74; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
algorithms; base of the arithmetic; digital arithmetic; floating point arithmetic units; high level; languages; trailing digits

entry:
@Article{Gentleman:1974:MAR,
  author =       "W. Morven Gentleman and Scott B. Marovich",
  title =        "More on Algorithms that Reveal Properties of Floating
                 Point Arithmetic Units",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "276--277",
  month =        may,
  year =         "1974",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/360980.361003",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:43:47 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#GentlemanM74;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Malcolm:1972:ARP}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Waterloo, Ont., Canada",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithms; base of the arithmetic; digital
                 arithmetic; floating point arithmetic units; high
                 level; languages; trailing digits",
  oldlabel =     "GentlemanM74",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GentlemanM74",
}


bibtype: book
filename: fparith.bib
label: Hildebrand:1974:INA
author: Francis Begnaud Hildebrand
title: Introduction to numerical analysis
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
edition: Second
pages: xiii + 669
year: 1974
ISBN: 0-07-028761-9 OR 0070287619
ISBN13: 978-0-07-028761-7 OR 9780070287617
LCCN: QA297 .H54 1974
bibdate: Fri Aug 20 09:19:58 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:19:58 MDT
series: International series in pure and applied mathematics
remark: Reprinted in cite Hildebrand:1987:INA.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Francis Begnaud Hildebrand
rawtitle: Introduction to numerical analysis
entry:
@Book{Hildebrand:1974:INA,
  author =       "Francis Begnaud Hildebrand",
  title =        "Introduction to numerical analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "xiii + 669",
  year =         "1974",
  ISBN =         "0-07-028761-9",
  ISBN-13 =      "978-0-07-028761-7",
  LCCN =         "QA297 .H54 1974",
  bibdate =      "Fri Aug 20 09:19:58 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted in \cite{Hildebrand:1987:INA}.",
  subject =      "Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Hill:1974:RFF
author: Bruce M. Hill
title: The rank-frequency form of Zipf's law
journal: j-J-AM-STAT-ASSOC
volume: 69
number: 348
pages: 1017--1026
month: dec
monthnumber: 12
year: 1974
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
MRclass: 62E15
MRnumber: 0426242 (54 \#14188)
MRreviewer: S. M. Samuels
bibdate: Sat Nov 12 09:13:23 2011
bibtimestamp: 2011.11.12 09:13:23 ???
fjournal: Journal of the American Statistical Association
ZMnumber: Zbl 0301.60011
acknowledgement: ack-nhfb
corpsource: Department of Statistics, University of Michigan, Ann Arbor, MI, USA
journalURL: http://www.tandfonline.com/loi/uasa20
treatment: T Theoretical or Mathematical
rawauthor: Bruce M. Hill
rawtitle: The rank-frequency form of {Zipf}'s law
bibsource:
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib

keywords:
Bose--Einstein allocation; distribution; random processes; rank frequency form; statistics; Zipf's law

entry:
@Article{Hill:1974:RFF,
  author =       "Bruce M. Hill",
  title =        "The rank-frequency form of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "69",
  number =       "348",
  pages =        "1017--1026",
  month =        dec,
  year =         "1974",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15",
  MRnumber =     "0426242 (54 \#14188)",
  MRreviewer =   "S. M. Samuels",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  ZMnumber =     "Zbl 0301.60011",
  acknowledgement = ack-nhfb,
  classification = "B0240 (Probability and statistics); C1140
                 (Probability and statistics)",
  corpsource =   "Department of Statistics, University of Michigan, Ann
                 Arbor, MI, USA",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Bose--Einstein allocation; distribution; random
                 processes; rank frequency form; statistics; Zipf's
                 law",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: fparith.bib
label: Hull:1974:LFM
author: T. E. Hull and J. J. Hofbauer
type: Technical report
number: 63
institution: University of Toronto, Department of Computer Science
address: Toronto, ON, Canada
pages: vi + 84
year: 1974
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: decimal floating-point arithmetic; Electronic digital computers --- Programming
acknowledgement: ack-nhfb
rawauthor: T. E. Hull and J. J. Hofbauer
title:
Language facilities for multiple precision floating point computation, with examples, and the description of a preprocessor

rawtitle:
Language facilities for multiple precision floating point computation, with examples, and the description of a preprocessor

entry:
@TechReport{Hull:1974:LFM,
  author =       "T. E. Hull and J. J. Hofbauer",
  title =        "Language facilities for multiple precision floating
                 point computation, with examples, and the description
                 of a preprocessor",
  type =         "Technical report",
  number =       "63",
  institution =  "University of Toronto, Department of Computer
                 Science",
  address =      "Toronto, ON, Canada",
  pages =        "vi + 84",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; Electronic digital
                 computers --- Programming",
}


bibtype: article
filename: fparith.bib
label: Kinoshita:1974:FPA
author: Eisuke Kinoshita and Hideo Kosako and Yoshiaki Kojima
title: Floating-Point Arithmetic Algorithms in the Symmetric Residue Number System
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 1
pages: 9--20
month: jan
monthnumber: 1
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1974.223772
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68A10
MRnumber: 50 9042
bibdate: Tue Jul 12 11:27:29 MDT 2011
bibtimestamp: 2011.07.12 11:27:29 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
reviewer: M. S. Cheema
rawauthor: Eisuke Kinoshita and Hideo Kosako and Yoshiaki Kojima
rawtitle: Floating-Point Arithmetic Algorithms in the Symmetric Residue Number System
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672365; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077

entry:
@Article{Kinoshita:1974:FPA,
  author =       "Eisuke Kinoshita and Hideo Kosako and Yoshiaki
                 Kojima",
  title =        "Floating-Point Arithmetic Algorithms in the Symmetric
                 Residue Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "1",
  pages =        "9--20",
  month =        jan,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1974.223772",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68A10",
  MRnumber =     "50 9042",
  bibdate =      "Tue Jul 12 11:27:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672365;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  reviewer =     "M. S. Cheema",
  summary =      "The residue number system is an integer number system
                 and is inconvenient to represent numbers with
                 fractional parts. In the symmetric residue system, a
                 new representation of floating-point numbers and
                 arithmetic algorithms for its addition, \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Kroft:1974:CTC
author: D. Kroft
title: Comments on ``A Two's Complement Parallel Array Multiplication Algorithm''
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 12
pages: 1327--1328
month: dec
monthnumber: 12
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.223863
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:38 MDT 2011
bibtimestamp: 2011.07.12 11:27:38 MDT
note: See cite Baugh:1973:TCP,Blankenship:1974:CTC.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672456
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Kroft
rawnote: See \cite{Baugh:1973:TCP,Blankenship:1974:CTC}.
rawtitle: Comments on {``A Two's Complement Parallel Array Multiplication Algorithm''}
entry:
@Article{Kroft:1974:CTC,
  author =       "D. Kroft",
  title =        "Comments on {``A Two's Complement Parallel Array
                 Multiplication Algorithm''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1327--1328",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223863",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Baugh:1973:TCP,Blankenship:1974:CTC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672456",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Kulisch:1974:PCC
author: U. Kulisch
title: Formalization and implementation of floating-point arithmetics
crossref: Panagiotopoulos:1974:PCC
pages: 328--369
year: 1974
MRclass: 65G05
MRnumber: 57 14392
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
acknowledgement: ack-nhfb
reviewer: R. H. Bartels
rawauthor: U. Kulisch
rawtitle: Formalization and implementation of floating-point arithmetics
entry:
@InProceedings{Kulisch:1974:PCC,
  author =       "U. Kulisch",
  title =        "Formalization and implementation of floating-point
                 arithmetics",
  crossref =     "Panagiotopoulos:1974:PCC",
  pages =        "328--369",
  year =         "1974",
  MRclass =      "65G05",
  MRnumber =     "57 14392",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "R. H. Bartels",
}


bibtype: article
filename: fparith.bib
label: Ling:1974:CSA
author: Robert F. Ling
title: Comparison of several algorithms for computing sample means and variances
journal: j-J-AM-STAT-ASSOC
volume: 69
number: 348
pages: 859--866
month: dec
monthnumber: 12
year: 1974
CODEN: JSTNAL
DOI: https://doi.org/10.1080/01621459.1974.10480219
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Jan 25 08:05:46 MST 2012
bibtimestamp: 2012.01.25 08:05:46 MST
fjournal: Journal of the American Statistical Association
keywords: mean; standard deviation; stat; updating; variance
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: Robert F. Ling
rawtitle: Comparison of several algorithms for computing sample means and variances
bibsource:
Distributed/QLD.bib; Distributed/QLD/1974.bib; http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314230; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib; Theory/Matrix.bib

URL:
http://www.jstor.org/stable/2286154; https://www.tandfonline.com/doi/abs/10.1080/01621459.1974.10480219; https://www.tandfonline.com/doi/pdf/10.1080/01621459.1974.10480219

remark:
This is an early paper on the numerical difficulties associated with two important statistical algorithms. See also entry cite McCullough:2019:WTS in fparith.bib that shows that even after 45 years, some statistics code in database software remains poor.

entry:
@Article{Ling:1974:CSA,
  author =       "Robert F. Ling",
  title =        "Comparison of several algorithms for computing sample
                 means and variances",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "69",
  number =       "348",
  pages =        "859--866",
  month =        dec,
  year =         "1974",
  CODEN =        "JSTNAL",
  DOI =          "https://doi.org/10.1080/01621459.1974.10480219",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:46 MST 2012",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1974.bib;
                 http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314230;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib;
                 Theory/Matrix.bib",
  URL =          "http://www.jstor.org/stable/2286154;
                 https://www.tandfonline.com/doi/abs/10.1080/01621459.1974.10480219;
                 https://www.tandfonline.com/doi/pdf/10.1080/01621459.1974.10480219",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "Simulation; statistics; numeric calculation",
  enum =         "7605",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "mean; standard deviation; stat; updating; variance",
  location =     "SEL: Wi",
  remark =       "This is an early paper on the numerical difficulties
                 associated with two important statistical algorithms.
                 See also entry \cite{McCullough:2019:WTS} in
                 fparith.bib that shows that even after 45 years, some
                 statistics code in database software remains poor.",
  revision =     "16/01/94",
  xxtitle =      "Comparison of Several Algorithms for Computing Means
                 and Variances",
}


bibtype: article
filename: fparith.bib
label: Linnainmaa:1974:ASK
author: Seppo Linnainmaa
title: Analysis of Some Known Methods of Improving the Accuracy of Floating-Point Sums
journal: j-BIT
volume: 14
number: 2
pages: 167--202
month: jun
monthnumber: 6
year: 1974
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01932946
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65G05
MRnumber: MR0483373 (58 \#3381)
bibdate: Fri Dec 08 13:05:19 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:05:19 ???
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=2&spage=167
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: accurate floating-point summation; floating-point arithmetic; rounding errors
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/10543
reviewer: H. Ratschek
rawauthor: Seppo Linnainmaa
rawtitle: Analysis of Some Known Methods of Improving the Accuracy of Floating-Point Sums
entry:
@Article{Linnainmaa:1974:ASK,
  author =       "Seppo Linnainmaa",
  title =        "Analysis of Some Known Methods of Improving the
                 Accuracy of Floating-Point Sums",
  journal =      j-BIT,
  volume =       "14",
  number =       "2",
  pages =        "167--202",
  month =        jun,
  year =         "1974",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932946",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "MR0483373 (58 \#3381)",
  bibdate =      "Fri Dec 08 13:05:19 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=2&spage=167",
  acknowledgement = ack-nj,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  reviewer =     "H. Ratschek",
}


bibtype: incollection
filename: fparith.bib
label: Metropolis:1974:SAA
author: N. Metropolis and Gian-Carlo Rota
title: Significance arithmetic---on the algebra of binary strings
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: 241--251
year: 1974
MRclass: 02F43 (68A15)
MRnumber: MR0354335 (50 \#6815)
MRreviewer: Stephen Tanny
bibdate: Wed Nov 14 19:04:40 2007
bibtimestamp: 2007.11.14 19:04:40 ???
ZMnumber: 0311.65031
acknowledgement: ack-nhfb
rawauthor: N. Metropolis and Gian-Carlo Rota
rawtitle: Significance arithmetic---on the algebra of binary strings
booktitle:
Studies in numerical analysis (papers in honour of Cornelius Lanczos on the occasion of his 80th birthday)

rawbooktitle:
Studies in numerical analysis (papers in honour of {Cornelius Lanczos} on the occasion of his 80th birthday)

entry:
@InCollection{Metropolis:1974:SAA,
  author =       "N. Metropolis and Gian-Carlo Rota",
  booktitle =    "Studies in numerical analysis (papers in honour of
                 {Cornelius Lanczos} on the occasion of his 80th
                 birthday)",
  title =        "Significance arithmetic---on the algebra of binary
                 strings",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "241--251",
  year =         "1974",
  MRclass =      "02F43 (68A15)",
  MRnumber =     "MR0354335 (50 \#6815)",
  MRreviewer =   "Stephen Tanny",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0311.65031",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Miller:1974:CCN
author: Webb Miller
title: Computational complexity and numerical stability
crossref: ACM:1974:CRS
pages: 317--322
year: 1974
bibdate: Wed Nov 24 12:46:29 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 12:46:29 ???
acknowledgement: ack-nhfb
rawauthor: Webb Miller
rawtitle: Computational complexity and numerical stability
entry:
@InProceedings{Miller:1974:CCN,
  author =       "Webb Miller",
  title =        "Computational complexity and numerical stability",
  crossref =     "ACM:1974:CRS",
  pages =        "317--322",
  year =         "1974",
  bibdate =      "Wed Nov 24 12:46:29 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: manual
filename: fparith.bib
label: Moon:1974:MRM
author: David A. Moon
title: MacLISP Reference Manual
organization: MIT Project MAC
address: Cambridge, MA, USA
pages: 317--322
month: apr
monthnumber: 4
year: 1974
bibdate: Wed Jan 29 16:47:55 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 16:47:55 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: David A. Moon
rawtitle: {MacLISP} Reference Manual
remark:
From cite Steele:2004:RHP: ``In early 1971, he [White] began to analyze the machine-language algorithm used in the implementation of MacLisp (described in this report) to convert PDP-10 floating-point numbers into decimal notation.''

entry:
@Manual{Moon:1974:MRM,
  author =       "David A. Moon",
  title =        "{MacLISP} Reference Manual",
  organization = "MIT Project MAC",
  address =      "Cambridge, MA, USA",
  month =        apr,
  year =         "1974",
  bibdate =      "Wed Jan 29 16:47:55 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``In early 1971, he
                 [White] began to analyze the machine-language algorithm
                 used in the implementation of MacLisp (described in
                 this report) to convert PDP-10 floating-point numbers
                 into decimal notation.''",
}


bibtype: article
filename: fparith.bib
label: Neumaier:1974:REV
author: A. Neumaier
journal: j-Z-ANGE-MATH-MECH
volume: 54
pages: 39--51
year: 1974
CODEN: ZAMMAX
ISSN: 0044-2267 (print), 1521-4001 (electronic) OR 00442267 (print), 15214001 (electronic)
ISSNL: 0044-2267 OR 00442267
bibdate: Fri Jan 12 11:37:56 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.01.12 11:37:56 ???
fjournal: Zeitschrift fur Angewandte Mathematik und Mechanik
keywords: accurate floating-point summation
language: German
acknowledgement: ack-jr
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001
rawauthor: A. Neumaier
title:
Rundungsfehleranalyse Einiger Verfahren Zur Summation Endlicher Summen. (German) [Rounding error analysis of a method for summation of finite sums]

rawtitle:
{Rundungsfehleranalyse Einiger Verfahren Zur Summation Endlicher Summen}. ({German}) [{Rounding} error analysis of a method for summation of finite sums]

entry:
@Article{Neumaier:1974:REV,
  author =       "A. Neumaier",
  title =        "{Rundungsfehleranalyse Einiger Verfahren Zur Summation
                 Endlicher Summen}. ({German}) [{Rounding} error
                 analysis of a method for summation of finite sums]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "54",
  pages =        "39--51",
  year =         "1974",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-jr,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  keywords =     "accurate floating-point summation",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Newbery:1974:EAP
author: A. C. R. Newbery
title: Error Analysis for Polynomial Evaluation
journal: j-MATH-COMPUT
volume: 28
number: 127
pages: 789--793
month: jul
monthnumber: 7
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
corpsource: Univ. Kentucky, Lexington, KY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: A. C. R. Newbery
rawtitle: Error Analysis for Polynomial Evaluation
keywords:
analysis; Chebyshev; computable error bound; error analysis; floating point error; function evaluation; Horner's scheme; polynomial evaluation; polynomials

classcodes:
B0290B (Error analysis in numerical methods); B0290D (Functional analysis); C4110 (Error analysis in numerical methods); C4120 (Functional analysis)

entry:
@Article{Newbery:1974:EAP,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for Polynomial Evaluation",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "789--793",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290B (Error analysis in numerical methods); B0290D
                 (Functional analysis); C4110 (Error analysis in
                 numerical methods); C4120 (Functional analysis)",
  corpsource =   "Univ. Kentucky, Lexington, KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analysis; Chebyshev; computable error bound; error
                 analysis; floating point error; function evaluation;
                 Horner's scheme; polynomial evaluation; polynomials",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: mastersthesis
filename: fparith.bib
label: Prezas:1974:FPA
author: Pericles Panos Prezas
title: Floating point arithmetic unit
type: Thesis (M.S.)
publisher: The author
school: Illinois Institute of Technology
address: Chicago, IL.
pages: ix + 77
year: 1974
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Pericles Panos Prezas
rawtitle: Floating point arithmetic unit
entry:
@MastersThesis{Prezas:1974:FPA,
  author =       "Pericles Panos Prezas",
  title =        "Floating point arithmetic unit",
  type =         "Thesis ({M.S.})",
  publisher =    "The author",
  school =       "Illinois Institute of Technology",
  address =      "Chicago, IL.",
  pages =        "ix + 77",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Rauscher:1974:MUX
author: Tomlinson G. Rauscher
journal: j-SIGMICRO
volume: 5
number: 2
pages: 29--63
month: apr
monthnumber: 4
year: 1974
CODEN: SIGMDJ
DOI: https://doi.org/10.1145/1217157.1217160
ISSN: 0163-5751, 1050-916X OR 01635751, 1050916X
ISSNL: 0163-5751 OR 01635751
bibdate: Fri Apr 16 10:27:17 MDT 2021
bibtimestamp: 2021.04.16 10:27:17 MDT
URL: https://dl.acm.org/doi/10.1145/1217157.1217160
fjournal: ACM SIGMICRO Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigmicro
rawauthor: Tomlinson G. Rauscher
title:
Microprogramming the AN / UYK-17(XB-1)(V) signal processing element signal processing arithmetic unit

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigmicro.bib

abstract:
The AN/UYK-17(XB-1)(V) Signal Processing Element (SPE) is a high performance computer system being developed at the Naval Research Laboratory for radar, sonar, and communication applications. To perform signal processing tasks efficiently, the SPE comprises multiple functional units that execute different processes in parallel. Due to the inherent parallelism in signal processing tasks, horizontal microprograms are used to control the functional units [references 5 and 6]. This report overviews the SPE, describes the Signal Processing Arithmetic Unit (SPAU) in detail, discusses ANIMIL --- the microprogramming language for representing SPAU microprograms, and illustrates the use of the ANIMIL translator with a simple microprogram. Companion documents describe the SPAU simulator program (reference 3) and the formal syntax and semantics of the ANIMIL language (reference 4).

rawabstract:
The AN/UYK-17(XB-1)(V) Signal Processing Element (SPE) is a high performance computer system being developed at the Naval Research Laboratory for radar, sonar, and communication applications. To perform signal processing tasks efficiently, the SPE comprises multiple functional units that execute different processes in parallel. Due to the inherent parallelism in signal processing tasks, horizontal microprograms are used to control the functional units [references 5 and 6]. This report overviews the SPE, describes the Signal Processing Arithmetic Unit (SPAU) in detail, discusses ANIMIL --- the microprogramming language for representing SPAU microprograms, and illustrates the use of the ANIMIL translator with a simple microprogram. Companion documents describe the SPAU simulator program (reference 3) and the formal syntax and semantics of the ANIMIL language (reference 4).

rawtitle:
Microprogramming the {AN\slash UYK-17(XB-1)(V)} signal processing element signal processing arithmetic unit

entry:
@Article{Rauscher:1974:MUX,
  author =       "Tomlinson G. Rauscher",
  title =        "Microprogramming the {AN\slash UYK-17(XB-1)(V)} signal
                 processing element signal processing arithmetic unit",
  journal =      j-SIGMICRO,
  volume =       "5",
  number =       "2",
  pages =        "29--63",
  month =        apr,
  year =         "1974",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1217157.1217160",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:17 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/1217157.1217160",
  abstract =     "The AN/UYK-17(XB-1)(V) Signal Processing Element (SPE)
                 is a high performance computer system being developed
                 at the Naval Research Laboratory for radar, sonar, and
                 communication applications. To perform signal
                 processing tasks efficiently, the SPE comprises
                 multiple functional units that execute different
                 processes in parallel. Due to the inherent parallelism
                 in signal processing tasks, horizontal microprograms
                 are used to control the functional units [references 5
                 and 6]. This report overviews the SPE, describes the
                 Signal Processing Arithmetic Unit (SPAU) in detail,
                 discusses ANIMIL --- the microprogramming language for
                 representing SPAU microprograms, and illustrates the
                 use of the ANIMIL translator with a simple
                 microprogram. Companion documents describe the SPAU
                 simulator program (reference 3) and the formal syntax
                 and semantics of the ANIMIL language (reference 4).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}


bibtype: article
filename: fparith.bib
label: Renner:1974:RRN
author: K. Renner and S. Gupta
title: Reduction of roundoff noise in wave digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 21
number: 2
pages: 305--310
month: mar
monthnumber: 3
year: 1974
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: K. Renner and S. Gupta
rawtitle: Reduction of roundoff noise in wave digital filters
entry:
@Article{Renner:1974:RRN,
  author =       "K. Renner and S. Gupta",
  title =        "Reduction of roundoff noise in wave digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "21",
  number =       "2",
  pages =        "305--310",
  month =        mar,
  year =         "1974",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Roundoff noise generated by arithmetic operations in a
                 digital-filter computational sequence is undesirable in
                 that it serves to distort the true signal at the
                 output. Furthermore, coefficient wordlength is directly
                 related to the generated noise. \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Scaife:1974:SNA
editor: B. K. P. Scaife
title: Studies in numerical analysis
publisher: The Royal Irish Academy
address: Dublin, Ireland
pages: xxii + 333
year: 1974
MRclass: 65-06
MRnumber: MR0347039 (49 \#11759)
bibdate: Thu Nov 8 19:02:54 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 19:02:54 ???
note: Papers in honour of Cornelius Lanczos on the occasion of his 80th birthday
acknowledgement: ack-nhfb
raweditor: B. K. P. Scaife
rawnote: Papers in honour of Cornelius Lanczos on the occasion of his 80th birthday
rawtitle: Studies in numerical analysis
entry:
@Book{Scaife:1974:SNA,
  editor =       "B. K. P. Scaife",
  title =        "Studies in numerical analysis",
  publisher =    "The Royal Irish Academy",
  address =      "Dublin, Ireland",
  pages =        "xxii + 333",
  year =         "1974",
  MRclass =      "65-06",
  MRnumber =     "MR0347039 (49 \#11759)",
  bibdate =      "Thu Nov 8 19:02:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Papers in honour of Cornelius Lanczos on the occasion
                 of his 80th birthday",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Schmid:1974:DC
author: Hermann Schmid
title: Decimal Computation
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xi + 266
year: 1974
ISBN: 0-471-76180-X OR 047176180X
ISBN13: 978-0-471-76180-8 OR 9780471761808
LCCN: QA75 .S34
bibdate: Thu Sep 1 10:14:05 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:05 ???
note: Reprinted cite Schmid:1983:DC.
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: Hermann Schmid
rawnote: Reprinted \cite{Schmid:1983:DC}.
rawtitle: Decimal Computation
entry:
@Book{Schmid:1974:DC,
  author =       "Hermann Schmid",
  title =        "Decimal Computation",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 266",
  year =         "1974",
  ISBN =         "0-471-76180-X",
  ISBN-13 =      "978-0-471-76180-8",
  LCCN =         "QA75 .S34",
  bibdate =      "Thu Sep 1 10:14:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted \cite{Schmid:1983:DC}.",
  acknowledgement = ack-nj,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Sites:1974:SBD
author: R. L. Sites
title: Serial Binary Division by Ten
journal: j-IEEE-TRANS-COMPUT
volume: 23
number: 12
pages: 1299--1301
month: dec
monthnumber: 12
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.223849
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Aug 07 18:02:35 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 18:02:35 ???
fjournal: IEEE Transactions on Computers
keywords: decimal arithmetic
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. L. Sites
rawtitle: Serial Binary Division by Ten
abstract:
A technique is presented for dividing a positive binary integer by ten, in which the bits of the input are presented serially, low-order bit first. A complete division by ten is performed in two word times (comparable to the time needed for two serial additions). The technique can be useful in serial conversions from binary to decimal, or in scaling binary numbers by powers of 10.

rawabstract:
A technique is presented for dividing a positive binary integer by ten, in which the bits of the input are presented serially, low-order bit first. A complete division by ten is performed in two word times (comparable to the time needed for two serial additions). The technique can be useful in serial conversions from binary to decimal, or in scaling binary numbers by powers of 10.

entry:
@Article{Sites:1974:SBD,
  author =       "R. L. Sites",
  title =        "Serial Binary Division by Ten",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "23",
  number =       "12",
  pages =        "1299--1301",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223849",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 07 18:02:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A technique is presented for dividing a positive
                 binary integer by ten, in which the bits of the input
                 are presented serially, low-order bit first. A complete
                 division by ten is performed in two word times
                 (comparable to the time needed for two serial
                 additions). The technique can be useful in serial
                 conversions from binary to decimal, or in scaling
                 binary numbers by powers of 10.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal arithmetic",
}


bibtype: book
filename: fparith.bib
label: Sterbenz:1974:FPC
author: Pat H. Sterbenz
title: Floating Point Computation
publisher: pub-PH
address: pub-PH:adr
pages: xiv + 316
year: 1974
ISBN: 0-13-322495-3 OR 0133224953
ISBN13: 978-0-13-322495-5 OR 9780133224955
LCCN: QA76.8.I12 S771 1974
MRclass: 68A05 (65G05)
MRnumber: 50 1556
bibdate: Sat May 29 08:01:36 1999
bibtimestamp: 1999.05.29 08:01:36 ???
series: Prentice-Hall Series in Automatic Computation.
acknowledgement: ack-nj
reviewer: F. J. Murray
rawauthor: Pat H. Sterbenz
rawtitle: Floating Point Computation
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib

keywords:
Compiling (Electronic computers); Computation by computer systems --- Floating point representation; Floating-point arithmetic; IBM 360 (Computer) --- Programming

remark:
From p. 116: ``There is general agreement that the mantissas of floating-point numbers are not uniformly distributed. [See Hamming (1962) [cite Hamming:1962:NMS], Pinkham (1961) [Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].] Instead, it is customary to assume that they are distributed logarithmically, that is, that the probability density function is $$ (3.12.9) f(m) = frac 1m ln r, qquad r^-1 leq m leq 1. $$ This assumption is based on the following observations: First, this distribution reproduces itself under multiplication, but a uniform distribution does not. [See Hamming (1962) [cite Hamming:1962:NMS] and Exercise 20.] A second justification is based on the fact that many of the numbers that arise in computation represent measurable quantities such as lengths, forces, etc., and it is reasonable to believe that the distribution of the mantissas of such quantities is independent of the units in which they are measured. Pinkham (1961) shows that this leads to the conclusion that the distribution of mantissas must be logarithmic.''

TOC:
Preface / ix 1. Floating-Point Number Systems / 1 1.1 Fixed-Point Calculation / 1 1.2 Floating-Decimal Representation of Numbers / 4 1.3 Floating-Decimal Arithmetic / 6 1.4 Floating-Point Number Systems / 9 1.5 FP(r, p, c) and FP(r, p, R) / 12 1.6 Laws of Algebra / 14 1.7 Inequalities in FP(r,p, c) / 21 1.8 FP(r, p, clq) / 22 1.9 The Solution of a * x = b in FP(r,p, c) / 29 1.10 Division / 33 Exercises / 35 2. Floating-Point Overflow and Underflow / 39 2.1 Bounds for Exponents / 39 2.2 $Omega $-Zero Fixup / 41 2.3 Interrupt / 44 2.4 Messages and Tests / 46 2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 2.6 Example / 50 2.7 Counting Mode / 57 2.8 Gradual Underflow / 59 2.9 Imprecise Interrupt / 61 2.10 Changing the Treatment of Spill / 62 2.11 Virtual Overflow and Underflow / 64 2.12 Division by Zero and Indeterminant Forms / 66 Exercises / 67 3. Error Analysis / 71 3.1 Significant Digits / 71 3.2 Relative Error / 73 3.3 Relative Error in FP(r,p, clq) / 75 3.4 Approximate Laws of Algebra / 80 3.5 Propagation of Rounding Error / 87 3.6 X**N / 92 3.7 Condition / 98 3.8 Error Analysis of a Program / 103 3.9 Backward Error Analysis / 105 3.10 Examples / 107 3.11 Changing the Problem / 109 3.12 Statistical Error Analysis / 113 Exercises / 117 4. Example / 123 4.1 Quadrature / 123 4.2 Power Series / 130 4.3 Exact Sums and Differences in FP(r, p, clq) / 137 4.4 Dismantling Floating-Point Numbers / 143 Exercises / 146 5. Double-Precision Calculation / 154 5.1 Programs Using Double-Precision Arithmetic / 155 5.2 Implicit Typing of Names / 162 5.3 Routines to Perform Double-Precision Arithmetic / 163 5.4 Double-Precision Multiplication / 165 5.5 Double-Precision Addition and Subtraction / 168 5.6 Double-Precision Division / 171 5.7 Writing Double-Precision Programs Without Language Support / 178 5.8 Uses of Double-Precision / 180 5.9 Higher-Precision Arithmetic / 185 Exercises / 186 6. Rounding / 189 6.1 General Considerations / 189 6.2 Uses of Rounding / 191 6.3 Implementation of Rounding / 192 6.4 Bias Removal / 194 6.5 Other ``Rounding'' Procedures / 197 Exercises / 198 7. Automatic Analysis of Error / 201 7.1 Introduction / 201 7.2 Significance Arithmetic / 202 7.3 Noisy Mode / 205 7.4 Interval Arithmetic / 207 7.5 Rerunning the Program in Higher-Precision / 213 Exercises / 222 8. Radix Conversion / 224 8.1 Equivalent Number of Digits / 224 8.2 Properties of Conversion Transformations / 228 8.3 Conversion Techniques / 232 Exercises / 238 9/ Carefully Written Programs / 240 9.1 Introduction / 240 9.2 Average Problem / 240 9.3 Quadratic Equation / 246 Exercises / 252 10. Checking and Testing / 255 10.1 Range Checking / 255 10.2 Mathematical Checks / 256 10.3 Testing / 259 Exercises / 261 11. Language Features for Floating-Point Computation / 263 11.1 Introduction / 263 11.2 Predictability, Controllability, Observability / 264 11.3 Ease of Programming / 265 11.4 Machine Independence / 267 Exercises / 269 12. Floating-Point Hardware / 271 12.1 Choice of Radix / 271 12.2 The Representation of Floating-Point Numbers / 273 12.3 FP(r, p, c) and FP(r, p, R) / 277 12.4 Unnormalized Numbers and Unnormalized Arithmetic / 278 Exercises / 282 13. Complex Numbers / 285 13.1 Programs Using Complex Numbers / 285 13.2 Relative Error / 286 13.3 Complex Arithmetic / 287 Exercises / 297 Bibliography / 301 Glossary of Symbols / 309 Index / 311

rawTOC:
Preface / ix \\ 1. Floating-Point Number Systems / 1 \\ 1.1 Fixed-Point Calculation / 1 \\ 1.2 Floating-Decimal Representation of Numbers / 4 \\ 1.3 Floating-Decimal Arithmetic / 6 \\ 1.4 Floating-Point Number Systems / 9 \\ 1.5 FP(r, p, c) and FP(r, p, R) / 12 \\ 1.6 Laws of Algebra / 14 \\ 1.7 Inequalities in FP(r,p, c) / 21 \\ 1.8 FP(r, p, clq) / 22 \\ 1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\ 1.10 Division / 33 \\ Exercises / 35 \\ 2. Floating-Point Overflow and Underflow / 39 \\ 2.1 Bounds for Exponents / 39 \\ 2.2 $\Omega$-Zero Fixup / 41 \\ 2.3 Interrupt / 44 \\ 2.4 Messages and Tests / 46 \\ 2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\ 2.6 Example / 50 \\ 2.7 Counting Mode / 57 \\ 2.8 Gradual Underflow / 59 \\ 2.9 Imprecise Interrupt / 61 \\ 2.10 Changing the Treatment of Spill / 62 \\ 2.11 Virtual Overflow and Underflow / 64 \\ 2.12 Division by Zero and Indeterminant Forms / 66 \\ Exercises / 67 \\ 3. Error Analysis / 71 \\ 3.1 Significant Digits / 71 \\ 3.2 Relative Error / 73 \\ 3.3 Relative Error in FP(r,p, clq) / 75 \\ 3.4 Approximate Laws of Algebra / 80 \\ 3.5 Propagation of Rounding Error / 87 \\ 3.6 X**N / 92 \\ 3.7 Condition / 98 \\ 3.8 Error Analysis of a Program / 103 \\ 3.9 Backward Error Analysis / 105 \\ 3.10 Examples / 107 \\ 3.11 Changing the Problem / 109 \\ 3.12 Statistical Error Analysis / 113 \\ Exercises / 117 \\ 4. Example / 123 \\ 4.1 Quadrature / 123 \\ 4.2 Power Series / 130 \\ 4.3 Exact Sums and Differences in FP(r, p, clq) / 137 \\ 4.4 Dismantling Floating-Point Numbers / 143 \\ Exercises / 146 \\ 5. Double-Precision Calculation / 154 \\ 5.1 Programs Using Double-Precision Arithmetic / 155 \\ 5.2 Implicit Typing of Names / 162 \\ 5.3 Routines to Perform Double-Precision Arithmetic / 163 \\ 5.4 Double-Precision Multiplication / 165 \\ 5.5 Double-Precision Addition and Subtraction / 168 \\ 5.6 Double-Precision Division / 171 \\ 5.7 Writing Double-Precision Programs Without Language Support / 178 \\ 5.8 Uses of Double-Precision / 180 \\ 5.9 Higher-Precision Arithmetic / 185 \\ Exercises / 186 \\ 6. Rounding / 189 \\ 6.1 General Considerations / 189 \\ 6.2 Uses of Rounding / 191 \\ 6.3 Implementation of Rounding / 192 \\ 6.4 Bias Removal / 194 \\ 6.5 Other ``Rounding'' Procedures / 197 \\ Exercises / 198 \\ 7. Automatic Analysis of Error / 201 \\ 7.1 Introduction / 201 \\ 7.2 Significance Arithmetic / 202 \\ 7.3 Noisy Mode / 205 \\ 7.4 Interval Arithmetic / 207 \\ 7.5 Rerunning the Program in Higher-Precision / 213 \\ Exercises / 222 \\ 8. Radix Conversion / 224 \\ 8.1 Equivalent Number of Digits / 224 \\ 8.2 Properties of Conversion Transformations / 228 \\ 8.3 Conversion Techniques / 232 \\ Exercises / 238 \\ 9/ Carefully Written Programs / 240 \\ 9.1 Introduction / 240 \\ 9.2 Average Problem / 240 \\ 9.3 Quadratic Equation / 246 \\ Exercises / 252 \\ 10. Checking and Testing / 255 \\ 10.1 Range Checking / 255 \\ 10.2 Mathematical Checks / 256 \\ 10.3 Testing / 259 \\ Exercises / 261 \\ 11. Language Features for Floating-Point Computation / 263 \\ 11.1 Introduction / 263 \\ 11.2 Predictability, Controllability, Observability / 264 \\ 11.3 Ease of Programming / 265 \\ 11.4 Machine Independence / 267 \\ Exercises / 269 \\ 12. Floating-Point Hardware / 271 \\ 12.1 Choice of Radix / 271 \\ 12.2 The Representation of Floating-Point Numbers / 273 \\ 12.3 FP(r, p, c) and FP(r, p, R) / 277 \\ 12.4 Unnormalized Numbers and Unnormalized Arithmetic / 278 \\ Exercises / 282 \\ 13. Complex Numbers / 285 \\ 13.1 Programs Using Complex Numbers / 285 \\ 13.2 Relative Error / 286 \\ 13.3 Complex Arithmetic / 287 \\ Exercises / 297 \\ Bibliography / 301 \\ Glossary of Symbols / 309 \\ Index / 311

entry:
@Book{Sterbenz:1974:FPC,
  author =       "Pat H. Sterbenz",
  title =        "Floating Point Computation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 316",
  year =         "1974",
  ISBN =         "0-13-322495-3",
  ISBN-13 =      "978-0-13-322495-5",
  LCCN =         "QA76.8.I12 S771 1974",
  MRclass =      "68A05 (65G05)",
  MRnumber =     "50 1556",
  bibdate =      "Sat May 29 08:01:36 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  series =       "Prentice-Hall Series in Automatic Computation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Compiling (Electronic computers); Computation by
                 computer systems --- Floating point representation;
                 Floating-point arithmetic; IBM 360 (Computer) ---
                 Programming",
  remark =       "From p. 116: ``There is general agreement that the
                 mantissas of floating-point numbers are not uniformly
                 distributed. [See Hamming (1962)
                 [\cite{Hamming:1962:NMS}], Pinkham (1961)
                 [Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
                 Instead, it is customary to assume that they are
                 distributed logarithmically, that is, that the
                 probability density function is

                  $$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
                 \leq m \leq 1. $$

                 This assumption is based on the following observations:
                 First, this distribution reproduces itself under
                 multiplication, but a uniform distribution does not.
                 [See Hamming (1962) [\cite{Hamming:1962:NMS}] and
                 Exercise 20.] A second justification is based on the
                 fact that many of the numbers that arise in computation
                 represent measurable quantities such as lengths,
                 forces, etc., and it is reasonable to believe that the
                 distribution of the mantissas of such quantities is
                 independent of the units in which they are measured.
                 Pinkham (1961) shows that this leads to the conclusion
                 that the distribution of mantissas must be
                 logarithmic.''",
  reviewer =     "F. J. Murray",
  tableofcontents = "Preface / ix \\
                 1. Floating-Point Number Systems / 1 \\
                 1.1 Fixed-Point Calculation / 1 \\
                 1.2 Floating-Decimal Representation of Numbers / 4 \\
                 1.3 Floating-Decimal Arithmetic / 6 \\
                 1.4 Floating-Point Number Systems / 9 \\
                 1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
                 1.6 Laws of Algebra / 14 \\
                 1.7 Inequalities in FP(r,p, c) / 21 \\
                 1.8 FP(r, p, clq) / 22 \\
                 1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
                 1.10 Division / 33 \\
                 Exercises / 35 \\
                 2. Floating-Point Overflow and Underflow / 39 \\
                 2.1 Bounds for Exponents / 39 \\
                 2.2 $\Omega$-Zero Fixup / 41 \\
                 2.3 Interrupt / 44 \\
                 2.4 Messages and Tests / 46 \\
                 2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
                 2.6 Example / 50 \\
                 2.7 Counting Mode / 57 \\
                 2.8 Gradual Underflow / 59 \\
                 2.9 Imprecise Interrupt / 61 \\
                 2.10 Changing the Treatment of Spill / 62 \\
                 2.11 Virtual Overflow and Underflow / 64 \\
                 2.12 Division by Zero and Indeterminant Forms / 66 \\
                 Exercises / 67 \\
                 3. Error Analysis / 71 \\
                 3.1 Significant Digits / 71 \\
                 3.2 Relative Error / 73 \\
                 3.3 Relative Error in FP(r,p, clq) / 75 \\
                 3.4 Approximate Laws of Algebra / 80 \\
                 3.5 Propagation of Rounding Error / 87 \\
                 3.6 X**N / 92 \\
                 3.7 Condition / 98 \\
                 3.8 Error Analysis of a Program / 103 \\
                 3.9 Backward Error Analysis / 105 \\
                 3.10 Examples / 107 \\
                 3.11 Changing the Problem / 109 \\
                 3.12 Statistical Error Analysis / 113 \\
                 Exercises / 117 \\
                 4. Example / 123 \\
                 4.1 Quadrature / 123 \\
                 4.2 Power Series / 130 \\
                 4.3 Exact Sums and Differences in FP(r, p, clq) / 137
                 \\
                 4.4 Dismantling Floating-Point Numbers / 143 \\
                 Exercises / 146 \\
                 5. Double-Precision Calculation / 154 \\
                 5.1 Programs Using Double-Precision Arithmetic / 155
                 \\
                 5.2 Implicit Typing of Names / 162 \\
                 5.3 Routines to Perform Double-Precision Arithmetic /
                 163 \\
                 5.4 Double-Precision Multiplication / 165 \\
                 5.5 Double-Precision Addition and Subtraction / 168 \\
                 5.6 Double-Precision Division / 171 \\
                 5.7 Writing Double-Precision Programs Without Language
                 Support / 178 \\
                 5.8 Uses of Double-Precision / 180 \\
                 5.9 Higher-Precision Arithmetic / 185 \\
                 Exercises / 186 \\
                 6. Rounding / 189 \\
                 6.1 General Considerations / 189 \\
                 6.2 Uses of Rounding / 191 \\
                 6.3 Implementation of Rounding / 192 \\
                 6.4 Bias Removal / 194 \\
                 6.5 Other ``Rounding'' Procedures / 197 \\
                 Exercises / 198 \\
                 7. Automatic Analysis of Error / 201 \\
                 7.1 Introduction / 201 \\
                 7.2 Significance Arithmetic / 202 \\
                 7.3 Noisy Mode / 205 \\
                 7.4 Interval Arithmetic / 207 \\
                 7.5 Rerunning the Program in Higher-Precision / 213 \\
                 Exercises / 222 \\
                 8. Radix Conversion / 224 \\
                 8.1 Equivalent Number of Digits / 224 \\
                 8.2 Properties of Conversion Transformations / 228 \\
                 8.3 Conversion Techniques / 232 \\
                 Exercises / 238 \\
                 9/ Carefully Written Programs / 240 \\
                 9.1 Introduction / 240 \\
                 9.2 Average Problem / 240 \\
                 9.3 Quadratic Equation / 246 \\
                 Exercises / 252 \\
                 10. Checking and Testing / 255 \\
                 10.1 Range Checking / 255 \\
                 10.2 Mathematical Checks / 256 \\
                 10.3 Testing / 259 \\
                 Exercises / 261 \\
                 11. Language Features for Floating-Point Computation /
                 263 \\
                 11.1 Introduction / 263 \\
                 11.2 Predictability, Controllability, Observability /
                 264 \\
                 11.3 Ease of Programming / 265 \\
                 11.4 Machine Independence / 267 \\
                 Exercises / 269 \\
                 12. Floating-Point Hardware / 271 \\
                 12.1 Choice of Radix / 271 \\
                 12.2 The Representation of Floating-Point Numbers / 273
                 \\
                 12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
                 12.4 Unnormalized Numbers and Unnormalized Arithmetic /
                 278 \\
                 Exercises / 282 \\
                 13. Complex Numbers / 285 \\
                 13.1 Programs Using Complex Numbers / 285 \\
                 13.2 Relative Error / 286 \\
                 13.3 Complex Arithmetic / 287 \\
                 Exercises / 297 \\
                 Bibliography / 301 \\
                 Glossary of Symbols / 309 \\
                 Index / 311",
}


bibtype: article
filename: fparith.bib
label: Suter:1974:MAA
author: B. W. Suter
title: The Modular Arithmetic of Arbitrarily Long Sequences of Digits
journal: j-IEEE-TRANS-COMPUT
volume: C-23
number: 12
pages: 1301--1303
month: dec
monthnumber: 12
year: 1974
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1974.223850
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 11:27:38 MDT 2011
bibtimestamp: 2011.07.12 11:27:38 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672443
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. W. Suter
rawtitle: The Modular Arithmetic of Arbitrarily Long Sequences of Digits
entry:
@Article{Suter:1974:MAA,
  author =       "B. W. Suter",
  title =        "The Modular Arithmetic of Arbitrarily Long Sequences
                 of Digits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1301--1303",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223850",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672443",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Syslo:1974:RAP
author: M. M. Syslo
title: Remarks on addition processes of positive floating-point numbers
journal: j-ZASTOS-MAT
volume: 14
pages: 415--417
year: 1974
CODEN: ZAMTAK
MRclass: 65G05
MRnumber: 50 8953
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
fjournal: Zastosowania Matematyki
acknowledgement: ack-nhfb
reviewer: Sven-AA ke Gustafson
rawauthor: M. M. Syslo
rawtitle: Remarks on addition processes of positive floating-point numbers
entry:
@Article{Syslo:1974:RAP,
  author =       "M. M. Syslo",
  title =        "Remarks on addition processes of positive
                 floating-point numbers",
  journal =      j-ZASTOS-MAT,
  volume =       "14",
  pages =        "415--417",
  year =         "1974",
  CODEN =        "ZAMTAK",
  MRclass =      "65G05",
  MRnumber =     "50 8953",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zastosowania Matematyki",
  reviewer =     "Sven-{\AA}ke Gustafson",
}


bibtype: phdthesis
filename: fparith.bib
label: Thompson:1974:IUF
author: Jackie Lloyd Thompson
title: An implementation of user-oriented floating point arithmetic
type: Dissertation (Ph.D. in Computing Science)
school: Texas A&M University
address: College Station, TX, USA
pages: 150
year: 1974
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Jackie Lloyd Thompson
rawtitle: An implementation of user-oriented floating point arithmetic
entry:
@PhdThesis{Thompson:1974:IUF,
  author =       "Jackie Lloyd Thompson",
  title =        "An implementation of user-oriented floating point
                 arithmetic",
  type =         "Dissertation ({Ph.D.} in {Computing Science})",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "150",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Tsao:1974:DSD
author: Nai Kuan Tsao
title: On the Distributions of Significant Digits and Roundoff Errors
journal: j-CACM
volume: 17
number: 5
pages: 269--271
month: may
monthnumber: 5
year: 1974
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65G05
MRnumber: 49 6595
MRreviewer: N. N. Abdelmalek
bibdate: Mon Jan 22 07:26:38 MST 2001
bibtimestamp: 2001.01.22 07:26:38 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Aerospace Res. Labs., Wright-Patterson AFB, OH, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
treatment: T Theoretical or Mathematical
rawauthor: Nai Kuan Tsao
rawtitle: On the Distributions of Significant Digits and Roundoff Errors
bibsource:
Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Generalized logarithmic law is derived for the distribution of the first $t$ significant digits of a random digital integer. This result is then used to determine the distribution of the roundoff errors in floating-point operations, which is a mixture of uniform and reciprocal distributions.

keywords:
Benford's Law; digital arithmetic; digital integer; distributions; error analysis; floating point operations; Law of Anomalous Numbers; logarithmic law; mathematical techniques; mean value; random; reciprocal; roundoff errors; significant digits; uniform distribution; variance; Zipf's Law

rawabstract:
Generalized logarithmic law is derived for the distribution of the first $t$ significant digits of a random digital integer. This result is then used to determine the distribution of the roundoff errors in floating-point operations, which is a mixture of uniform and reciprocal distributions.

entry:
@Article{Tsao:1974:DSD,
  author =       "Nai Kuan Tsao",
  title =        "On the Distributions of Significant Digits and
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "269--271",
  month =        may,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05",
  MRnumber =     "49 6595",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Mon Jan 22 07:26:38 MST 2001",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Generalized logarithmic law is derived for the
                 distribution of the first $t$ significant digits of a
                 random digital integer. This result is then used to
                 determine the distribution of the roundoff errors in
                 floating-point operations, which is a mixture of
                 uniform and reciprocal distributions.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "921",
  corpsource =   "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "Benford's Law; digital arithmetic; digital integer;
                 distributions; error analysis; floating point
                 operations; Law of Anomalous Numbers; logarithmic law;
                 mathematical techniques; mean value; random;
                 reciprocal; roundoff errors; significant digits;
                 uniform distribution; variance; Zipf's Law",
  oldlabel =     "Tsao74",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}


bibtype: article
filename: fparith.bib
label: Tsao:1974:SPE
author: Nai-Kuan Tsao
title: Some a Posteriori Error Bounds in Floating-Point Computations
journal: j-J-ACM
volume: 21
number: 1
pages: 6--17
month: jan
monthnumber: 1
year: 1974
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65G05
MRnumber: 49 8319
bibdate: Fri Dec 08 13:06:33 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:06:33 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
reviewer: N. N. Abdelmalek
rawauthor: Nai-Kuan Tsao
rawtitle: Some a Posteriori Error Bounds in Floating-Point Computations
entry:
@Article{Tsao:1974:SPE,
  author =       "Nai-Kuan Tsao",
  title =        "Some a Posteriori Error Bounds in Floating-Point
                 Computations",
  journal =      j-J-ACM,
  volume =       "21",
  number =       "1",
  pages =        "6--17",
  month =        jan,
  year =         "1974",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "49 8319",
  bibdate =      "Fri Dec 08 13:06:33 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  reviewer =     "N. N. Abdelmalek",
}


bibtype: article
filename: fparith.bib
label: Walker:1974:FGU
author: A. J. Walker
title: Fast generation of uniformly distributed pseudorandom numbers with floating-point representation
journal: j-ELECT-LETTERS
volume: 10
number: 25--26
pages: 533--534
day: 12
month: dec
monthnumber: 12
year: 1974
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19740423
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Dec 30 16:39:46 MST 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib
bibtimestamp: 2011.12.30 16:39:46 MST
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245313
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: A. J. Walker
rawtitle: Fast generation of uniformly distributed pseudorandom numbers with floating-point representation
entry:
@Article{Walker:1974:FGU,
  author =       "A. J. Walker",
  title =        "Fast generation of uniformly distributed pseudorandom
                 numbers with floating-point representation",
  journal =      j-ELECT-LETTERS,
  volume =       "10",
  number =       "25--26",
  pages =        "533--534",
  day =          "12",
  month =        dec,
  year =         "1974",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19740423",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Dec 30 16:39:46 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245313",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}


bibtype: article
filename: fparith.bib
label: Agrawal:1975:AAN
author: D. P. Agrawal
title: Arithmetic Algorithms in a Negative Base
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 10
pages: 998--1000
month: oct
monthnumber: 10
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224109
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:57 MDT 2011
bibtimestamp: 2011.07.12 07:57:57 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. P. Agrawal
rawtitle: Arithmetic Algorithms in a Negative Base
entry:
@Article{Agrawal:1975:AAN,
  author =       "D. P. Agrawal",
  title =        "Arithmetic Algorithms in a Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "998--1000",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224109",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Agrawal:1975:OAL
author: Dharma P. Agrawal
title: Optimum Array-Like Structures for High-Speed Arithmetic
crossref: IEEE:1975:SCA
pages: 208--219
year: 1975
bibdate: Wed Nov 14 17:44:11 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:44:11 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Agrawal.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Dharma P. Agrawal
rawtitle: Optimum Array-Like Structures for High-Speed Arithmetic
abstract:
Array-like structures for high-speed multiplication, division, square and square-root operations have been described in this paper. In these designs the division and square-rooting time have been made to approach to that of multiplication operation. These structures are optimum from speed and versatility point of view. Most of the cellular arrays described in the literature are adequately slow. The time delay is particularly significant in the division and square-rooting operations due to the ripple effect of the carries. Though the carry-save technique has been widely utilized for multiplication operation, it has been only recently employed by Cappa et al. in the design of a nonrestoring divider array. This requires sign-bit detection that makes the array non-uniform. Such an array has been named as an array-like structure. The carry-save method has been extended here for restoring division operation. Due to sign-detection and overflow correction requirements, the restoring method is slightly complex. But the main advantage of such restoring array is in its simple extension for multiplication operation. The array for the two operations, when pipelined, will have more computing power than all other multiplier-divider arrays. Suggestions have also been included for further speed improvement.par The technique applied for division operation is as well applicable for the square-rooting and an array-like structure for square-square-rooting operations has also been given. For performing any one of the four operations, the only manipulation to be done is to combine the two arrays; one for multiplication-division and another for square-square-rooting. Possible. methods of combining the two arrays have been indicated and their relative advantages and disadvantages have been mentioned. Finally, a generalized pipeline array-like structure with complete internal details and for 4-bit operation, has been shown. Due consideration has also been given to the possibility of large-scale-integration of different arrays presented in this paper.

rawabstract:
Array-like structures for high-speed multiplication, division, square and square-root operations have been described in this paper. In these designs the division and square-rooting time have been made to approach to that of multiplication operation. These structures are optimum from speed and versatility point of view. Most of the cellular arrays described in the literature are adequately slow. The time delay is particularly significant in the division and square-rooting operations due to the ripple effect of the carries. Though the carry-save technique has been widely utilized for multiplication operation, it has been only recently employed by Cappa et al. in the design of a nonrestoring divider array. This requires sign-bit detection that makes the array non-uniform. Such an array has been named as an array-like structure. The carry-save method has been extended here for restoring division operation. Due to sign-detection and overflow correction requirements, the restoring method is slightly complex. But the main advantage of such restoring array is in its simple extension for multiplication operation. The array for the two operations, when pipelined, will have more computing power than all other multiplier-divider arrays. Suggestions have also been included for further speed improvement.\par The technique applied for division operation is as well applicable for the square-rooting and an array-like structure for square-square-rooting operations has also been given. For performing any one of the four operations, the only manipulation to be done is to combine the two arrays; one for multiplication-division and another for square-square-rooting. Possible. methods of combining the two arrays have been indicated and their relative advantages and disadvantages have been mentioned. Finally, a generalized pipeline array-like structure with complete internal details and for 4-bit operation, has been shown. Due consideration has also been given to the possibility of large-scale-integration of different arrays presented in this paper.

entry:
@InProceedings{Agrawal:1975:OAL,
  author =       "Dharma P. Agrawal",
  title =        "Optimum Array-Like Structures for High-Speed
                 Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "208--219",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Agrawal.pdf",
  abstract =     "Array-like structures for high-speed multiplication,
                 division, square and square-root operations have been
                 described in this paper. In these designs the division
                 and square-rooting time have been made to approach to
                 that of multiplication operation. These structures are
                 optimum from speed and versatility point of view. Most
                 of the cellular arrays described in the literature are
                 adequately slow. The time delay is particularly
                 significant in the division and square-rooting
                 operations due to the ripple effect of the carries.
                 Though the carry-save technique has been widely
                 utilized for multiplication operation, it has been only
                 recently employed by Cappa et al. in the design of a
                 nonrestoring divider array. This requires sign-bit
                 detection that makes the array non-uniform. Such an
                 array has been named as an array-like structure. The
                 carry-save method has been extended here for restoring
                 division operation. Due to sign-detection and overflow
                 correction requirements, the restoring method is
                 slightly complex. But the main advantage of such
                 restoring array is in its simple extension for
                 multiplication operation. The array for the two
                 operations, when pipelined, will have more computing
                 power than all other multiplier-divider arrays.
                 Suggestions have also been included for further speed
                 improvement.\par

                 The technique applied for division operation is as well
                 applicable for the square-rooting and an array-like
                 structure for square-square-rooting operations has also
                 been given. For performing any one of the four
                 operations, the only manipulation to be done is to
                 combine the two arrays; one for multiplication-division
                 and another for square-square-rooting. Possible.
                 methods of combining the two arrays have been indicated
                 and their relative advantages and disadvantages have
                 been mentioned. Finally, a generalized pipeline
                 array-like structure with complete internal details and
                 for 4-bit operation, has been shown. Due consideration
                 has also been given to the possibility of
                 large-scale-integration of different arrays presented
                 in this paper.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: inproceedings
filename: fparith.bib
label: Atkins:1975:HRN
author: Daniel E. Atkins
title: Higher Radix, Non-restoring Division: History and recent Developments
crossref: IEEE:1975:SCA
pages: 158--167
year: 1975
bibdate: Wed Nov 14 17:43:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:43:08 ???
URL: http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Atkins.pdf
keywords: ARITH-3
acknowledgement: ack-nhfb
rawauthor: Daniel E. Atkins
rawtitle: Higher Radix, Non-restoring Division: History and recent Developments
abstract:
This paper reviews work related to the theory and application of higher-radix. non-restoring division as originally defined by Robertson in 1958.

rawabstract:
This paper reviews work related to the theory and application of higher-radix. non-restoring division as originally defined by Robertson in 1958.

entry:
@InProceedings{Atkins:1975:HRN,
  author =       "Daniel E. Atkins",
  title =        "Higher Radix, Non-restoring Division: History and
                 recent Developments",
  crossref =     "IEEE:1975:SCA",
  pages =        "158--167",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:43:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Atkins.pdf",
  abstract =     "This paper reviews work related to the theory and
                 application of higher-radix. non-restoring division as
                 originally defined by Robertson in 1958.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}


bibtype: article
filename: fparith.bib
label: Atkins:1975:IRR
author: D. E. Atkins
title: Introduction to the Role of Redundancy in Computer Arithmetic
journal: j-COMPUTER
volume: 8
number: 6
pages: 74--77
month: jun
monthnumber: 6
year: 1975
CODEN: CPTRB4
DOI: https://doi.org/10.1109/C-M.1975.219001
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Sat May 7 16:08:43 2022
bibtimestamp: 2022.05.07 16:08:43 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: D. E. Atkins
rawtitle: Introduction to the Role of Redundancy in Computer Arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/computer1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Atkins:1975:IRR,
  author =       "D. E. Atkins",
  title =        "Introduction to the Role of Redundancy in Computer
                 Arithmetic",
  journal =      j-COMPUTER,
  volume =       "8",
  number =       "6",
  pages =        "74--77",
  month =        jun,
  year =         "1975",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1975.219001",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat May 7 16:08:43 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


