# bibtab

bibtype: article
filename: fparith.bib
label: Zohar:1976:RTR
author: S. Zohar
title: Rounding and Truncation in Radix (-2) Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 5
pages: 464--469
month: may
monthnumber: 5
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674634
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:51 MDT 2011
bibtimestamp: 2011.07.12 06:24:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674634
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Zohar
rawtitle: Rounding and Truncation in Radix (-2) Systems
entry:
@Article{Zohar:1976:RTR,
  author =       "S. Zohar",
  title =        "Rounding and Truncation in Radix (-2) Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "5",
  pages =        "464--469",
  month =        may,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674634",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:51 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=1674634",
  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: Agrawal:1977:CNB
author: D. P. Agrawal
title: Comments on ``A Note on Base-$2$ Arithmetic Logic''
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 5
pages: 511--511
month: may
monthnumber: 5
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674869
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:54 MDT 2011
bibtimestamp: 2011.07.11 21:56:54 MDT
note: See cite Yuen:1975:NBA.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674869
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
rawnote: See \cite{Yuen:1975:NBA}.
rawtitle: Comments on {``A Note on Base-$2$ Arithmetic Logic''}
entry:
@Article{Agrawal:1977:CNB,
  author =       "D. P. Agrawal",
  title =        "Comments on {``A Note on Base-$2$ Arithmetic
                 Logic''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "5",
  pages =        "511--511",
  month =        may,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674869",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:54 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{Yuen:1975:NBA}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674869",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Albrecht:1977:GC
author: Rudolf Albrecht and Ulrich Kulisch
title: Grundlagen der Computer-Arithmetik
publisher: Springer-Verlag
address: Wien, Austria
pages: viii + 150
year: 1977
ISBN: 0-387-81410-8 OR 0387814108
ISBN13: 978-0-387-81410-0 OR 9780387814100
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
series: Computing: Supplementum; 1 Computing (Springer-Verlag). Supplementum; 1.
keywords: Algebra, Abstract.; Floating-point arithmetic.; Mathematics --- Data processing.
acknowledgement: ack-nhfb
rawauthor: Rudolf Albrecht and Ulrich Kulisch
rawtitle: {Grundlagen der Computer-Arithmetik}
remark:
``Diese Artikel stellen eine Auswahl von Vortragen dar, die auf einer vom 4. bis 8. August 1975 im `Mathematischen Forschungsinstitut Oberwolfach' stattgefundenen Tagung gehalten wurden.''

entry:
@Book{Albrecht:1977:GC,
  author =       "Rudolf Albrecht and Ulrich Kulisch",
  title =        "{Grundlagen der Computer-Arithmetik}",
  publisher =    "Springer-Verlag",
  address =      "Wien, Austria",
  pages =        "viii + 150",
  year =         "1977",
  ISBN =         "0-387-81410-8",
  ISBN-13 =      "978-0-387-81410-0",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Computing: Supplementum; 1 Computing
                 (Springer-Verlag). Supplementum; 1.",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra, Abstract.; Floating-point arithmetic.;
                 Mathematics --- Data processing.",
  remark =       "``Diese Artikel stellen eine Auswahl von Vortragen
                 dar, die auf einer vom 4. bis 8. August 1975 im
                 `Mathematischen Forschungsinstitut Oberwolfach'
                 stattgefundenen Tagung gehalten wurden.''",
}


bibtype: book
filename: fparith.bib
label: Albrecht:1977:GCA
editor: R. Albrecht and U. Kulisch
title: Grundlagen der Computer-Arithmetik toenglish Foundations of Computer Arithmetic endtoenglish
publisher: pub-SV
address: pub-SV:adr
pages: viii + 150
year: 1977
ISBN: 0-387-81410-8 OR 0387814108
ISBN13: 978-0-387-81410-0 OR 9780387814100
LCCN: QA162 .G78
bibdate: Fri Sep 16 16:30:41 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
acknowledgement: ack-nhfb
raweditor: R. Albrecht and U. Kulisch
rawtitle: {Grundlagen der Computer-Arithmetik} \toenglish {Foundations of Computer Arithmetic} \endtoenglish
note:
Diese Artikel stellen eine Auswahl von Vortragen dar, die auf einer vom 4. bis 8. August 1975 im `Mathematischen Forschungsinstitut Oberwolfach' stattgefundenen Tagung gehalten wurden.

rawnote:
Diese Artikel stellen eine Auswahl von Vortragen dar, die auf einer vom 4. bis 8. August 1975 im `Mathematischen Forschungsinstitut Oberwolfach' stattgefundenen Tagung gehalten wurden.

entry:
@Book{Albrecht:1977:GCA,
  editor =       "R. Albrecht and U. Kulisch",
  title =        "{Grundlagen der Computer-Arithmetik} \toenglish
                 {Foundations of Computer Arithmetic} \endtoenglish",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 150",
  year =         "1977",
  ISBN =         "0-387-81410-8",
  ISBN-13 =      "978-0-387-81410-0",
  LCCN =         "QA162 .G78",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Diese Artikel stellen eine Auswahl von Vortragen dar,
                 die auf einer vom 4. bis 8. August 1975 im
                 `Mathematischen Forschungsinstitut Oberwolfach'
                 stattgefundenen Tagung gehalten wurden.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Alexander:1977:SRR
author: V. L. Alexander
title: Square Root Routine
journal: j-IBM-TDB
volume: 20
number: 3
pages: 1222
month: aug
monthnumber: 8
year: 1977
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:15:41 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 10:15:41 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: V. L. Alexander
rawtitle: Square Root Routine
entry:
@Article{Alexander:1977:SRR,
  author =       "V. L. Alexander",
  title =        "Square Root Routine",
  journal =      j-IBM-TDB,
  volume =       "20",
  number =       "3",
  pages =        "1222",
  month =        aug,
  year =         "1977",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 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 =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1977:CAF
author: Anonymous
title: Computer Arithmetic: Foreword and Survey
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 609--609
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674892
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:55 MDT 2011
bibtimestamp: 2011.07.11 21:56:55 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674892
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Anonymous
rawtitle: Computer Arithmetic: Foreword and Survey
entry:
@Article{Anonymous:1977:CAF,
  author =       "Anonymous",
  title =        "Computer Arithmetic: Foreword and Survey",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "609--609",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674892",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:55 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=1674892",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: manual
filename: fparith.bib
label: AppleComputer:1977:ARM
author: Apple Computer, Inc
title: APPLESOFT reference manual: extended precision floating point BASIC language
organization: Apple Computer, Inc.
address: Cupertino, CA, USA
pages: 75
year: 1977
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: {Apple Computer, Inc}
rawtitle: {APPLESOFT} reference manual: extended precision floating point {BASIC} language
keywords:
Apple computer --- Programming.; BASIC (Computer program language) --- Programming.; Microcomputers --- Programming.

entry:
@Manual{AppleComputer:1977:ARM,
  author =       "{Apple Computer, Inc}",
  title =        "{APPLESOFT} reference manual: extended precision
                 floating point {BASIC} language",
  organization = "Apple Computer, Inc.",
  address =      "Cupertino, CA, USA",
  pages =        "75",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple computer --- Programming.; BASIC (Computer
                 program language) --- Programming.; Microcomputers ---
                 Programming.",
}


bibtype: article
filename: fparith.bib
label: Barak:1977:MAT
author: A. B. Barak
title: Multiplicative Algorithms for Ternary Arithmetic Using Binary Logic
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 8
pages: 823--826
month: aug
monthnumber: 8
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674922
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:56 MDT 2011
bibtimestamp: 2011.07.11 21:56:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674922
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. Barak
rawtitle: Multiplicative Algorithms for Ternary Arithmetic Using Binary Logic
entry:
@Article{Barak:1977:MAT,
  author =       "A. B. Barak",
  title =        "Multiplicative Algorithms for Ternary Arithmetic Using
                 Binary Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "8",
  pages =        "823--826",
  month =        aug,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674922",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 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=1674922",
  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: Bauer:1977:CFP
author: Henry R. Bauer
title: Comments on ``On the Floating Point Representation of Complex Numbers''
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 2
pages: 191--191
month: feb
monthnumber: 2
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.5009301
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:52 MDT 2011
bibtimestamp: 2011.07.11 21:56:52 MDT
note: See cite Yuen:1975:FPR.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009301
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Henry R. Bauer
rawnote: See \cite{Yuen:1975:FPR}.
rawtitle: Comments on {``On the Floating Point Representation of Complex Numbers''}
abstract:
A recent paper [Burroughs B7700 Information Processing Systems Reference Manual, p. 2-9, 1973, Burroughs Corporation] discussed an integrated notation for complex numbers. A second choice of the radix point position will increase the number of values near the origin. An argument is also made for unnormalized notation of both parts of a complex number.

rawabstract:
A recent paper [Burroughs B7700 Information Processing Systems Reference Manual, p. 2-9, 1973, Burroughs Corporation] discussed an integrated notation for complex numbers. A second choice of the radix point position will increase the number of values near the origin. An argument is also made for unnormalized notation of both parts of a complex number.

entry:
@Article{Bauer:1977:CFP,
  author =       "Henry R. Bauer",
  title =        "Comments on {``On the Floating Point Representation of
                 Complex Numbers''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "2",
  pages =        "191--191",
  month =        feb,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.5009301",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:52 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{Yuen:1975:FPR}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009301",
  abstract =     "A recent paper [Burroughs B7700 Information Processing
                 Systems Reference Manual, p. 2-9, 1973, Burroughs
                 Corporation] discussed an integrated notation for
                 complex numbers. A second choice of the radix point
                 position will increase the number of values near the
                 origin. An argument is also made for unnormalized
                 notation of both parts of a complex number.",
  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: Bivins:1977:SAA
author: Robert L. Bivins and Nicholas C. Metropolis
title: Significance Arithmetic: Application to a Partial Differential Equation
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 639--642
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674896
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Jan 12 11:37:56 1996
bibtimestamp: 1996.01.12 11:37:56 ???
fjournal: IEEE Transactions on Computers
ZMnumber: 0405.65056
acknowledgement: ack-jr
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Robert L. Bivins and Nicholas C. Metropolis
rawtitle: Significance Arithmetic: Application to a Partial Differential Equation
bibsource:
http://dblp.uni-trier.de/db/journals/tc/tc26.html#BivinsM77; 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/iel5/12/35159/01674896.pdf?tp=&isnumber=35159&arnumber=1674896&punumber=12

abstract:
The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial-differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference-equation approximation to Burgers' equation.

rawabstract:
The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial-differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference-equation approximation to Burgers' equation.

entry:
@Article{Bivins:1977:SAA,
  author =       "Robert L. Bivins and Nicholas C. Metropolis",
  title =        "Significance Arithmetic: Application to a Partial
                 Differential Equation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "639--642",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674896",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://dblp.uni-trier.de/db/journals/tc/tc26.html#BivinsM77;
                 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/iel5/12/35159/01674896.pdf?tp=&isnumber=35159&arnumber=1674896&punumber=12",
  ZMnumber =     "0405.65056",
  abstract =     "The methods of significance arithmetic are applied to
                 the numerical solution of a nonlinear
                 partial-differential equation. Our approach permits the
                 use of initial values having imprecision considerably
                 greater than that of rounding error; moreover, the
                 intermediate and final quantities are monitored so that
                 at any stage the precision of such quantities is
                 available. An algorithm is found that represents
                 faithfully the solution to a difference-equation
                 approximation to Burgers' equation.",
  acknowledgement = ack-jr,
  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: Bohlender:1977:FPC
author: Gerd Bohlender
title: Floating-Point Computation of Functions with Maximum Accuracy
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 621--632
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674894
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65D15 (68A99)
MRnumber: 56 9908
bibdate: Fri Dec 8 08:24:14 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
fjournal: IEEE Transactions on Computers
keywords: accurate floating-point summation
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
reviewer: Bernard H. Rosman
rawauthor: Gerd Bohlender
rawtitle: Floating-Point Computation of Functions with Maximum Accuracy
entry:
@Article{Bohlender:1977:FPC,
  author =       "Gerd Bohlender",
  title =        "Floating-Point Computation of Functions with Maximum
                 Accuracy",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "621--632",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674894",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D15 (68A99)",
  MRnumber =     "56 9908",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  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",
  keywords =     "accurate floating-point summation",
  reviewer =     "Bernard H. Rosman",
}


bibtype: mastersthesis
filename: fparith.bib
label: Brinkmann:1977:FPT
author: Hubert Eldie Brinkmann
title: A floating-point processor for the Texas Instruments model 980A computer
type: Electrical Engineering Thesis (M.S.)
publisher: Brinkmann
school: Texas A&M University
address: College Station, TX, USA
pages: x + 68
year: 1977
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: Microprocessors.; Microprogramming.; Miniature computers --- Programming.
acknowledgement: ack-nhfb
rawauthor: Hubert Eldie Brinkmann
rawtitle: A floating-point processor for the {Texas Instruments} model {980A} computer
entry:
@MastersThesis{Brinkmann:1977:FPT,
  author =       "Hubert Eldie Brinkmann",
  title =        "A floating-point processor for the {Texas Instruments}
                 model {980A} computer",
  type =         "Electrical Engineering Thesis ({M.S.})",
  publisher =    "Brinkmann",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "x + 68",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microprocessors.; Microprogramming.; Miniature
                 computers --- Programming.",
}


bibtype: inproceedings
filename: fparith.bib
label: Brown:1977:MSI
author: W. S. Brown
title: A realistic model of floating-point computation
crossref: Rice:1977:MSI
number: 39
pages: 343--360
year: 1977
DOI: https://doi.org/10.1016/B978-0-12-587260-7.50017-0
MRclass: 68A05
MRnumber: 58 3605
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib
bibtimestamp: 1995.12.08 08:24:14 ???
URL: https://www.sciencedirect.com/science/article/abs/pii/B9780125872607500170
acknowledgement: ack-nhfb
reviewer: Costica Cazacu
rawauthor: W. S. Brown
rawtitle: A realistic model of floating-point computation
entry:
@InProceedings{Brown:1977:MSI,
  author =       "W. S. Brown",
  title =        "A realistic model of floating-point computation",
  crossref =     "Rice:1977:MSI",
  number =       "39",
  pages =        "343--360",
  year =         "1977",
  DOI =          "https://doi.org/10.1016/B978-0-12-587260-7.50017-0",
  MRclass =      "68A05",
  MRnumber =     "58 3605",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "https://www.sciencedirect.com/science/article/abs/pii/B9780125872607500170",
  acknowledgement = ack-nhfb,
  reviewer =     "Costica Cazacu",
}


bibtype: article
filename: fparith.bib
label: Collins:1977:APS
author: George E. Collins and David R. Musser
title: Analysis of the Pope--Stein Division Algorithm
journal: j-INFO-PROC-LETT
volume: 6
number: 5
pages: 151--155
month: oct
monthnumber: 10
year: 1977
CODEN: IFPLAT
DOI: https://doi.org/10.1016/0020-0190(77)90012-6
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
bibdate: Tue Nov 17 10:49:43 MST 1998
bibtimestamp: 1998.11.17 10:49:43 MST
fjournal: Information Processing Letters
acknowledgement: ack-nj
corpsource: Computer Sci. Dept., University of Wisconsin, Madison, WI, USA
journalURL: http://www.sciencedirect.com/science/journal/00200190/
treatment: T Theoretical or Mathematical
rawauthor: George E. Collins and David R. Musser
rawtitle: Analysis of the {Pope--Stein} Division Algorithm
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/infoproc1970.bib

keywords:
algorithm; algorithm theory; digital arithmetic; integer division; multiple precision integer division; trial quotient digits

entry:
@Article{Collins:1977:APS,
  author =       "George E. Collins and David R. Musser",
  title =        "Analysis of the {Pope--Stein} Division Algorithm",
  journal =      j-INFO-PROC-LETT,
  volume =       "6",
  number =       "5",
  pages =        "151--155",
  day =          "??",
  month =        oct,
  year =         "1977",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/0020-0190(77)90012-6",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Tue Nov 17 10:49:43 MST 1998",
  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/infoproc1970.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classification = "C4240 (Programming and algorithm theory)",
  corpsource =   "Computer Sci. Dept., University of Wisconsin, Madison,
                 WI, USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190/",
  keywords =     "algorithm; algorithm theory; digital arithmetic;
                 integer division; multiple precision integer division;
                 trial quotient digits",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Colquhoun:1977:FAS
author: D. G. Colquhoun
title: A Fast Approximation to the Sine Function
journal: j-SPE
volume: 7
number: 2
pages: 227--229
month: mar
monthnumber: 3
year: 1977
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Fri Dec 08 13:06:08 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:06:08 ???
fjournal: Software---Practice and Experience
acknowledgement: ack-nj
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: D. G. Colquhoun
rawtitle: A Fast Approximation to the Sine Function
entry:
@Article{Colquhoun:1977:FAS,
  author =       "D. G. Colquhoun",
  title =        "A Fast Approximation to the Sine Function",
  journal =      j-SPE,
  volume =       "7",
  number =       "2",
  pages =        "227--229",
  month =        mar # "--" # apr,
  year =         "1977",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Fri Dec 08 13:06:08 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}


bibtype: book
filename: fparith.bib
label: DEC:1977:VAH
author: Digital Equipment Corporation
title: VAX-11 / 780 Architecture Handbook
publisher: pub-DP
address: pub-DP:adr
pages: 328
year: 1977
LCCN: QA76.8 .V12D5 B 2 829 348
bibdate: Thu Sep 15 18:50:55 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:50:55 ???
acknowledgement: ack-nhfb
rawauthor: {Digital Equipment Corporation}
rawtitle: {VAX-11}\slash 780 Architecture Handbook
entry:
@Book{DEC:1977:VAH,
  author =       "{Digital Equipment Corporation}",
  title =        "{VAX-11}\slash 780 Architecture Handbook",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  pages =        "328",
  year =         "1977",
  LCCN =         "QA76.8 .V12D5 B 2 829 348",
  bibdate =      "Thu Sep 15 18:50:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}


bibtype: inproceedings
filename: fparith.bib
label: Dekker:1977:MRR
author: T. J. Dekker
title: Machine Requirements for Reliable Portable Software
crossref: Cowell:1977:PMS
pages: 22--36
year: 1977
bibdate: Wed Nov 07 08:38:01 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.07 08:38:01 ???
acknowledgement: ack-nhfb
rawauthor: T. J. Dekker
rawtitle: Machine Requirements for Reliable Portable Software
entry:
@InProceedings{Dekker:1977:MRR,
  author =       "T. J. Dekker",
  title =        "Machine Requirements for Reliable Portable Software",
  crossref =     "Cowell:1977:PMS",
  pages =        "22--36",
  year =         "1977",
  bibdate =      "Wed Nov 07 08:38:01 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Derenzo:1977:AHC
author: Stephen E. Derenzo
title: Approximations for Hand Calculators Using Small Integer Coefficients
journal: j-MATH-COMPUT
volume: 31
number: 137
pages: 214--222
month: jan
monthnumber: 1
year: 1977
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
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Stephen E. Derenzo
rawtitle: Approximations for Hand Calculators Using Small Integer Coefficients
keywords:
approximations; function approximation; function evaluation; hand calculators; programmable calculators; small integer coefficients

classcodes:
B0290D (Functional analysis); B0290F (Interpolation and function approximation); C4120 (Functional analysis); C4130 (Interpolation and function approximation); C7310 (Mathematics computing)

entry:
@Article{Derenzo:1977:AHC,
  author =       "Stephen E. Derenzo",
  title =        "Approximations for Hand Calculators Using Small
                 Integer Coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "137",
  pages =        "214--222",
  month =        jan,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation); C7310 (Mathematics computing)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; function approximation; function
                 evaluation; hand calculators; programmable calculators;
                 small integer coefficients",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Egbert:1977:PCAa
author: W. E. Egbert
title: Personal Calculator Algorithms I: Square Roots
journal: j-HEWLETT-PACKARD-J
volume: 28
number: 9
pages: 22--24
month: may
monthnumber: 5
year: 1977
CODEN: HPJOAX
ISSN: 0018-1153 OR 00181153
bibdate: Thu Sep 1 10:15:41 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 10:15:41 ???
fjournal: Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company
keywords: electronic calculators; HP personal calculator; square root algorithm
acknowledgement: ack-nj
classcodes: C5420 (Mainframes and minicomputers); C7310 (Mathematics computing)
treatment: A Application; T Theoretical or Mathematical
rawauthor: W. E. Egbert
rawtitle: Personal Calculator Algorithms {I}: Square Roots
entry:
@Article{Egbert:1977:PCAa,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {I}: Square Roots",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "28",
  number =       "9",
  pages =        "22--24",
  month =        may,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5420 (Mainframes and minicomputers); C7310
                 (Mathematics computing)",
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
  keywords =     "electronic calculators; HP personal calculator; square
                 root algorithm",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Egbert:1977:PCAb
author: W. E. Egbert
title: Personal Calculator Algorithms II: Trigonometric Functions
journal: j-HEWLETT-PACKARD-J
volume: 28
number: 10
pages: 17--20
month: jun
monthnumber: 6
year: 1977
CODEN: HPJOAX
ISSN: 0018-1153 OR 00181153
bibdate: Thu Sep 1 10:15:56 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 10:15:56 ???
fjournal: Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company
acknowledgement: ack-nj
rawauthor: W. E. Egbert
rawtitle: Personal Calculator Algorithms {II}: Trigonometric Functions
entry:
@Article{Egbert:1977:PCAb,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {II}: Trigonometric
                 Functions",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "28",
  number =       "10",
  pages =        "17--20",
  month =        jun,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:15:56 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 =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
}


bibtype: article
filename: fparith.bib
label: Egbert:1977:PCAc
author: W. E. Egbert
title: Personal Calculator Algorithms III: Inverse Trigonometric Functions
journal: j-HEWLETT-PACKARD-J
volume: 29
number: 3
pages: 22--23
month: nov
monthnumber: 11
year: 1977
CODEN: HPJOAX
ISSN: 0018-1153 OR 00181153
bibdate: Thu Sep 1 10:16:10 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 10:16:10 ???
fjournal: Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company
acknowledgement: ack-nj
rawauthor: W. E. Egbert
rawtitle: Personal Calculator Algorithms {III}: Inverse Trigonometric Functions
entry:
@Article{Egbert:1977:PCAc,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {III}: Inverse
                 Trigonometric Functions",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "29",
  number =       "3",
  pages =        "22--23",
  month =        nov,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:16:10 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 =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1977:GHO
author: Milos D. Ercegovac
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 667--680
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674900
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:56 MDT 2011
bibtimestamp: 2011.07.11 21:56:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milo{\v{s}} D. Ercegovac
title:
A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

abstract:
A parallel computational method, amenable for efficient hardware-level implementation, is described. It provides a simple and fast algorithm for the evaluation of polynomials, certain rational functions and arithmetic expressions, solving a class of systems of linear equations, or performing the basic arithmetic operations in a fixed-point number representation system. The time required to perform the computation is of the order of $m$ carry-free addition operations, $m$ being the number of digits in the solution. In particular, the method is suitable for fast evaluation of mathematical functions in hardware.

keywords:
Arithmetic expressions; digital computer arithmetic; E-method; evaluation of real-valued functions; fixed-point representation; hardware-level implementation; integral powers; linear systems; on-line algorithms; parallel computation; polynomials; rational functions; redundant number systems

rawabstract:
A parallel computational method, amenable for efficient hardware-level implementation, is described. It provides a simple and fast algorithm for the evaluation of polynomials, certain rational functions and arithmetic expressions, solving a class of systems of linear equations, or performing the basic arithmetic operations in a fixed-point number representation system. The time required to perform the computation is of the order of $m$ carry-free addition operations, $m$ being the number of digits in the solution. In particular, the method is suitable for fast evaluation of mathematical functions in hardware.

rawtitle:
A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer

entry:
@Article{Ercegovac:1977:GHO,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A General Hardware-Oriented Method for Evaluation of
                 Functions and Computations in a Digital Computer",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "667--680",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 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=1674900",
  abstract =     "A parallel computational method, amenable for
                 efficient hardware-level implementation, is described.
                 It provides a simple and fast algorithm for the
                 evaluation of polynomials, certain rational functions
                 and arithmetic expressions, solving a class of systems
                 of linear equations, or performing the basic arithmetic
                 operations in a fixed-point number representation
                 system. The time required to perform the computation is
                 of the order of $m$ carry-free addition operations, $m$
                 being the number of digits in the solution. In
                 particular, the method is suitable for fast evaluation
                 of mathematical functions in hardware.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arithmetic expressions; digital computer arithmetic;
                 E-method; evaluation of real-valued functions;
                 fixed-point representation; hardware-level
                 implementation; integral powers; linear systems;
                 on-line algorithms; parallel computation; polynomials;
                 rational functions; redundant number systems",
}


bibtype: article
filename: fparith.bib
label: Evans:1977:AAT
author: Gillian R. Evans
title: From abacus to algorism: Theory and practice in medieval arithmetic
journal: j-BRITISH-J-HIST-SCI
volume: 10
number: 2
pages: 114--131
month: jul
monthnumber: 7
year: 1977
CODEN: BJHSAT
DOI: https://doi.org/10.1017/S0007087400015375
ISSN: 0007-0874 (print), 1474-001X (electronic) OR 00070874 (print), 1474001X (electronic)
ISSNL: 0007-0874 OR 00070874
MRclass: 01A35 (Mathematics in the medieval)
MRnumber: 522510 (80e:01006)
MRreviewer: M. Folkerts
bibdate: Thu Sep 23 07:34:43 MDT 2010
bibtimestamp: 2010.09.23 07:34:43 MDT
URL: http://www.jstor.org/stable/4025865
fjournal: British Journal for the History of Science
ZMnumber: 0358.01003
acknowledgement: ack-nhfb
journalURL: http://journals.cambridge.org/action/displayJournal?jid=BJH
rawauthor: Gillian R. Evans
rawtitle: From abacus to algorism: Theory and practice in medieval arithmetic
bibsource:
http://journals.cambridge.org/action/displayJournal?jid=BJH; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database

abstract:
This paper deals primarily with the change in practical procedures of calculation which took place during the course of the twelfth century in Western Europe. At the beginning of the period, the abacus was in relatively common use; towards the end, it was being superseded by the method of calculation which was known as the algorism. Certain differences of theory are apparent. Among the textbooks which were most influential in bringing about the change was Sacrobosco's Algorithmus Vulgaris. Authors of both abacus and algorism treatises give an account of number-symbols and discuss elementary number theory briefly, but the algorism treatise show how much more confident the authors were in using Arabic numerals. The algorisms employ a symbol for zero; although it has antecedents in some abacus treatises, its usefulness was clearly not fully perceived by the authors, because the columns of the abacus made it unnecessary to use a counter to indicate that the number under consideration was, for example, 306, not 36. The algorisms deal with a far wider range of operations; while the abacus treatises confine themselves to multiplication and division of whole numbers and fractions, the algorisms have addition, subtraction, doubling, halving, multiplication, division, the extraction of roots and progression, as well as numeration. Changes in technical terminology are discussed. There are two appendices, one dealing with the compilation of arithmetical texts in Bodleian Library Oxford, MS.~Laud.~Misc.~644, and the other on the arithmetical sense of the term equipollentia, which was a technical term of dialectic.

rawabstract:
This paper deals primarily with the change in practical procedures of calculation which took place during the course of the twelfth century in Western Europe. At the beginning of the period, the abacus was in relatively common use; towards the end, it was being superseded by the method of calculation which was known as the algorism. Certain differences of theory are apparent. Among the textbooks which were most influential in bringing about the change was Sacrobosco's Algorithmus Vulgaris. Authors of both abacus and algorism treatises give an account of number-symbols and discuss elementary number theory briefly, but the algorism treatise show how much more confident the authors were in using Arabic numerals. The algorisms employ a symbol for zero; although it has antecedents in some abacus treatises, its usefulness was clearly not fully perceived by the authors, because the columns of the abacus made it unnecessary to use a counter to indicate that the number under consideration was, for example, 306, not 36. The algorisms deal with a far wider range of operations; while the abacus treatises confine themselves to multiplication and division of whole numbers and fractions, the algorisms have addition, subtraction, doubling, halving, multiplication, division, the extraction of roots and progression, as well as numeration. Changes in technical terminology are discussed. There are two appendices, one dealing with the compilation of arithmetical texts in Bodleian Library Oxford, MS.~Laud.~Misc.~644, and the other on the arithmetical sense of the term equipollentia, which was a technical term of dialectic.

entry:
@Article{Evans:1977:AAT,
  author =       "Gillian R. Evans",
  title =        "From abacus to algorism: Theory and practice in
                 medieval arithmetic",
  journal =      j-BRITISH-J-HIST-SCI,
  volume =       "10",
  number =       "2",
  pages =        "114--131",
  month =        jul,
  year =         "1977",
  CODEN =        "BJHSAT",
  DOI =          "https://doi.org/10.1017/S0007087400015375",
  ISSN =         "0007-0874 (print), 1474-001X (electronic)",
  ISSN-L =       "0007-0874",
  MRclass =      "01A35 (Mathematics in the medieval)",
  MRnumber =     "522510 (80e:01006)",
  MRreviewer =   "M. Folkerts",
  bibdate =      "Thu Sep 23 07:34:43 MDT 2010",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=BJH;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  URL =          "http://www.jstor.org/stable/4025865",
  ZMnumber =     "0358.01003",
  abstract =     "This paper deals primarily with the change in
                 practical procedures of calculation which took place
                 during the course of the twelfth century in Western
                 Europe. At the beginning of the period, the abacus was
                 in relatively common use; towards the end, it was being
                 superseded by the method of calculation which was known
                 as the algorism. Certain differences of theory are
                 apparent. Among the textbooks which were most
                 influential in bringing about the change was
                 Sacrobosco's Algorithmus Vulgaris. Authors of both
                 abacus and algorism treatises give an account of
                 number-symbols and discuss elementary number theory
                 briefly, but the algorism treatise show how much more
                 confident the authors were in using Arabic numerals.
                 The algorisms employ a symbol for zero; although it has
                 antecedents in some abacus treatises, its usefulness
                 was clearly not fully perceived by the authors, because
                 the columns of the abacus made it unnecessary to use a
                 counter to indicate that the number under consideration
                 was, for example, 306, not 36. The algorisms deal with
                 a far wider range of operations; while the abacus
                 treatises confine themselves to multiplication and
                 division of whole numbers and fractions, the algorisms
                 have addition, subtraction, doubling, halving,
                 multiplication, division, the extraction of roots and
                 progression, as well as numeration. Changes in
                 technical terminology are discussed. There are two
                 appendices, one dealing with the compilation of
                 arithmetical texts in Bodleian Library Oxford,
                 MS.~Laud.~Misc.~644, and the other on the arithmetical
                 sense of the term equipollentia, which was a technical
                 term of dialectic.",
  acknowledgement = ack-nhfb,
  fjournal =     "British Journal for the History of Science",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BJH",
  ZMreviewer =   "Gillian R. Evans",
}


bibtype: article
filename: fparith.bib
label: Feldman:1977:EEA
author: Michael B. Feldman
title: Embedding extended arithmetic in SNOBOL4
journal: j-SIGPLAN
volume: 12
number: 1
pages: 67--72
month: jan
monthnumber: 1
year: 1977
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:13:59 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:13:59 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
corpsource: George Washington University, Washington, DC, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
treatment: P Practical
rawauthor: Michael B. Feldman
rawtitle: Embedding extended arithmetic in {SNOBOL4}
keywords:
complex numbers; data structure; data structures; digital arithmetic; embedded; extended arithmetic; procedure oriented languages; rotational numbers; SNOBOL4

entry:
@Article{Feldman:1977:EEA,
  author =       "Michael B. Feldman",
  title =        "Embedding extended arithmetic in {SNOBOL4}",
  journal =      j-SIGPLAN,
  volume =       "12",
  number =       "1",
  pages =        "67--72",
  month =        jan,
  year =         "1977",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:13:59 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages)",
  corpsource =   "George Washington University, Washington, DC, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "complex numbers; data structure; data structures;
                 digital arithmetic; embedded; extended arithmetic;
                 procedure oriented languages; rotational numbers;
                 SNOBOL4",
  treatment =    "P Practical",
}


bibtype: book
filename: fparith.bib
label: Forsythe:1977:CMM
author: George E. (George Elmer) Forsythe and Michael A. Malcolm and Cleve B. Moler
title: Computer Methods for Mathematical Computations
publisher: pub-PH
address: pub-PH:adr
pages: xi + 259
year: 1977
ISBN: 0-13-165332-6 OR 0131653326
ISBN13: 978-0-13-165332-0 OR 9780131653320
LCCN: QA297 .F5681
MRclass: 65-01
MRnumber: MR0458783 (56 \#16983)
MRreviewer: Sven-{\AA}ke Gustafson
bibdate: Tue May 25 09:01:08 2010
bibtimestamp: 2010.05.25 09:01:08 ???
series: Prentice-Hall series in automatic computation
keywords: Fortran (computer program language); numerical analysis -- data processing
ZMnumber: 0361.65002
acknowledgement: ack-nhfb
rawauthor: George E. (George Elmer) Forsythe and Michael A. Malcolm and Cleve B. Moler
rawtitle: Computer Methods for Mathematical Computations
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.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/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

note:
Cited in AA ke Bjorck's bibliography on least squares, which is available by anonymous ftp from path =math.liu.se= in path =pub/references=

remark:
Subroutines and exercises for the computer solution of problems involving matrices, integrals, differential equations, spline functions, zeros and extrema of functions, least squares, and Monte Carlo techniques.

subject:
Numerical analysis; Data processing; Computer programs; Problems, exercises, etc; FORTRAN (Computer program language)

TOC:
Introduction Floating-point computation Linear systems of equations Interpolation Numerical integration Initial value problems in ordinary differential equations Solution of nonlinear equations Optimization Least squares and the singular value decomposition Random number generation and Monte Carlo methods

rawnote:
Cited in {\AA}ke Bj{\"o}rck's bibliography on least squares, which is available by anonymous ftp from \path=math.liu.se= in \path=pub/references=

rawTOC:
Introduction \\ Floating-point computation \\ Linear systems of equations \\ Interpolation \\ Numerical integration \\ Initial value problems in ordinary differential equations \\ Solution of nonlinear equations \\ Optimization \\ Least squares and the singular value decomposition \\ Random number generation and Monte Carlo methods

entry:
@Book{Forsythe:1977:CMM,
  author =       "George E. (George Elmer) Forsythe and Michael A.
                 Malcolm and Cleve B. Moler",
  title =        "Computer Methods for Mathematical Computations",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 259",
  year =         "1977",
  ISBN =         "0-13-165332-6",
  ISBN-13 =      "978-0-13-165332-0",
  LCCN =         "QA297 .F5681",
  MRclass =      "65-01",
  MRnumber =     "MR0458783 (56 \#16983)",
  MRreviewer =   "Sven-{\AA}ke Gustafson",
  bibdate =      "Tue May 25 09:01:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.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/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
                 squares, which is available by anonymous ftp from
                 \path=math.liu.se= in \path=pub/references=",
  price =        "US\$16.95",
  series =       "Prentice-Hall series in automatic computation",
  ZMnumber =     "0361.65002",
  acknowledgement = ack-nhfb,
  classmath =    "*65-01 Textbooks (numerical analysis) 68-01 Textbooks
                 (computer science)",
  keywords =     "Fortran (computer program language); numerical
                 analysis -- data processing",
  remark =       "Subroutines and exercises for the computer solution of
                 problems involving matrices, integrals, differential
                 equations, spline functions, zeros and extrema of
                 functions, least squares, and Monte Carlo techniques.",
  subject =      "Numerical analysis; Data processing; Computer
                 programs; Problems, exercises, etc; FORTRAN (Computer
                 program language)",
  tableofcontents = "Introduction \\
                 Floating-point computation \\
                 Linear systems of equations \\
                 Interpolation \\
                 Numerical integration \\
                 Initial value problems in ordinary differential
                 equations \\
                 Solution of nonlinear equations \\
                 Optimization \\
                 Least squares and the singular value decomposition \\
                 Random number generation and Monte Carlo methods",
}


bibtype: techreport
filename: fparith.bib
label: Frenckner:1977:MFP
author: K. Frenckner and M. Persson and S. Romberger and Y. Sundblad
title: Microprogrammed floating-point arithmetic for the Varian-73 computer
type: Technical report
number: TRITA-NA-7702
institution: Kungl. Tekniska Hogskolan
address: Stockholm, Sweden
pages: 37
month: jun
monthnumber: 6
year: 1977
bibdate: Fri May 25 05:52:09 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.05.25 05:52:09 ???
URL: http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0028467
acknowledgement: ack-nhfb
rawauthor: K. Frenckner and M. Persson and S. Romberger and Y. Sundblad
rawtitle: Microprogrammed floating-point arithmetic for the {Varian-73} computer
entry:
@TechReport{Frenckner:1977:MFP,
  author =       "K. Frenckner and M. Persson and S. Romberger and Y.
                 Sundblad",
  title =        "Microprogrammed floating-point arithmetic for the
                 {Varian-73} computer",
  type =         "Technical report",
  number =       "TRITA-NA-7702",
  institution =  "Kungl. Tekniska H{\"o}gskolan",
  address =      "Stockholm, Sweden",
  pages =        "37",
  month =        jun,
  year =         "1977",
  bibdate =      "Fri May 25 05:52:09 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0028467",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Ginsberg:1977:NID
author: Myron Ginsberg
title: Numerical influences on the design of floating-point arithmetic for microcomputers
type: Technical report
number: CS 7708
institution: Department of Computer Science, Southern Methodist University
address: Dallas, TX, USA
pages: 72
year: 1977
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: Floating-point arithmetic --- Data processing.
acknowledgement: ack-nhfb
rawauthor: Myron Ginsberg
rawtitle: Numerical influences on the design of floating-point arithmetic for microcomputers
entry:
@TechReport{Ginsberg:1977:NID,
  author =       "Myron Ginsberg",
  title =        "Numerical influences on the design of floating-point
                 arithmetic for microcomputers",
  type =         "Technical report",
  number =       "CS 7708",
  institution =  "Department of Computer Science, Southern Methodist
                 University",
  address =      "Dallas, TX, USA",
  pages =        "72",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic --- Data processing.",
}


bibtype: techreport
filename: fparith.bib
label: Goldsmith:1977:ICF
author: Theodore C. Goldsmith
title: An integrated circuit floating point accumulator
type: NASA technical note
number: NASA TN D-8509 NASA
address: Washington, DC, USA
pages: 26
year: 1977
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
remark: Issued June 1977.
acknowledgement: ack-nhfb
rawauthor: Theodore C. Goldsmith
rawtitle: An integrated circuit floating point accumulator
institution:
National Aeronautics and Space Administration; for sale by the National Technical Information Service

entry:
@TechReport{Goldsmith:1977:ICF,
  author =       "Theodore C. Goldsmith",
  title =        "An integrated circuit floating point accumulator",
  type =         "{NASA} technical note",
  number =       "NASA TN D-8509 NASA",
  institution =  "National Aeronautics and Space Administration; for
                 sale by the National Technical Information Service",
  address =      "Washington, DC, USA",
  pages =        "26",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  govtdocnumber = "NAS 1.14:D-8509",
  remark =       "Issued June 1977.",
}


bibtype: article
filename: fparith.bib
label: Goodman:1977:EGD
author: R. Goodman and A. Feldstein
title: Effect of Guard Digits and Normalization Options on Floating Point Multiplication
journal: j-COMPUTING
volume: 18
number: 2
pages: 93--106
year: 1977
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G05
MRnumber: 55 11596
bibdate: Fri Dec 08 12:02:42 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 12:02:42 ???
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/607
reviewer: N. N. Abdelmalek
rawauthor: R. Goodman and A. Feldstein
rawtitle: Effect of Guard Digits and Normalization Options on Floating Point Multiplication
entry:
@Article{Goodman:1977:EGD,
  author =       "R. Goodman and A. Feldstein",
  title =        "Effect of Guard Digits and Normalization Options on
                 Floating Point Multiplication",
  journal =      j-COMPUTING,
  volume =       "18",
  number =       "2",
  pages =        "93--106",
  month =        "????",
  year =         "1977",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "55 11596",
  bibdate =      "Fri Dec 08 12:02:42 1995",
  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",
  reviewer =     "N. N. Abdelmalek",
}


bibtype: article
filename: fparith.bib
label: Goodwin:1977:CUO
author: D. T. Goodwin
title: Conditions for Underflow and Overflow of an Arithmetic Stack
journal: j-COMP-J
volume: 20
number: 1
pages: 56--62
month: feb
monthnumber: 2
year: 1977
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/20.1.56
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:59 MST 2012
bibtimestamp: 2012.12.04 14:47:59 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C4210 (Formal logic)
corpsource: Department of Computer Sci., University of Keele, Keele, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: D. T. Goodwin
rawtitle: Conditions for Underflow and Overflow of an Arithmetic Stack
bibsource:
Compendex database; http://comjnl.oxfordjournals.org/content/20/1.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/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/20/1/56.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/56.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/57.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/58.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/59.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/60.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/61.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/62.tif

keywords:
arbitrary string; arithmetic stack; automata theory --- Context Free Languages; behaviour; computer metatheory; computer operating systems --- Program Compilers; context free language; context-free languages; loading; overflow; underflow

entry:
@Article{Goodwin:1977:CUO,
  author =       "D. T. Goodwin",
  title =        "Conditions for Underflow and Overflow of an Arithmetic
                 Stack",
  journal =      j-COMP-J,
  volume =       "20",
  number =       "1",
  pages =        "56--62",
  month =        feb,
  year =         "1977",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/20.1.56",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:59 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/20/1.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/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/20/1/56.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/56.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/57.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/58.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/59.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/60.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/61.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/62.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4210 (Formal logic)",
  classification = "721; 723",
  corpsource =   "Department of Computer Sci., University of Keele,
                 Keele, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arbitrary string; arithmetic stack; automata theory
                 --- Context Free Languages; behaviour; computer
                 metatheory; computer operating systems --- Program
                 Compilers; context free language; context-free
                 languages; loading; overflow; underflow",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Gregory:1977:BCR
author: Robert Todd Gregory and David W. Matula
title: Base conversion in residue number systems
journal: j-BIT
volume: 17
number: 3
pages: 286--302
month: sep
monthnumber: 9
year: 1977
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01932149
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 10A30 (68A10)
MRnumber: MR0476627 (57 \#16186)
MRreviewer: L. Carlitz
bibdate: Wed Jan 4 18:52:15 MST 2006
bibtimestamp: 2006.01.04 18:52:15 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=17&issue=3&spage=286
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: Interval arithmetic; residue arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Robert Todd Gregory and David W. Matula
rawtitle: Base conversion in residue number systems
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=17&issue=3; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Gregory:1977:BCR,
  author =       "Robert Todd Gregory and David W. Matula",
  title =        "Base conversion in residue number systems",
  journal =      j-BIT,
  volume =       "17",
  number =       "3",
  pages =        "286--302",
  month =        sep,
  year =         "1977",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932149",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "10A30 (68A10)",
  MRnumber =     "MR0476627 (57 \#16186)",
  MRreviewer =   "L. Carlitz",
  bibdate =      "Wed Jan 4 18:52:15 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=17&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=17&issue=3&spage=286",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Interval arithmetic; residue arithmetic",
}


bibtype: article
filename: fparith.bib
label: Hashizume:1977:FPA
author: B. Hashizume
title: Floating Point Arithmetic
journal: j-BYTE
volume: 2
number: 11
pages: 76--78, 180--188
month: nov
monthnumber: 11
year: 1977
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
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: BYTE Magazine
acknowledgement: ack-nj
rawauthor: B. Hashizume
rawtitle: Floating Point Arithmetic
entry:
@Article{Hashizume:1977:FPA,
  author =       "B. Hashizume",
  title =        "Floating Point Arithmetic",
  journal =      j-BYTE,
  volume =       "2",
  number =       "11",
  pages =        "76--78, 180--188",
  month =        nov,
  year =         "1977",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  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 =     "BYTE Magazine",
}


bibtype: article
filename: fparith.bib
label: Hastings:1977:FPH
author: Jordan Towner Hastings
title: Floating point half-word packing for Control Data Corporation 6000/7000 series hardware
journal: j-SPE
volume: 7
number: 1
pages: 146--147
month: jan
monthnumber: 1
year: 1977
CODEN: SPEXBL
DOI: https://doi.org/10.1002/spe.4380070111
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Wed Sep 10 12:36:39 MDT 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/spe.bib
bibtimestamp: 2014.09.10 12:36:39 MDT
fjournal: Software --- Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
onlinedate: 27 Oct 2006
rawauthor: Jordan Towner Hastings
rawtitle: Floating point half-word packing for {Control Data Corporation 6000/7000 series} hardware
entry:
@Article{Hastings:1977:FPH,
  author =       "Jordan Towner Hastings",
  title =        "Floating point half-word packing for {Control Data
                 Corporation 6000/7000 series} hardware",
  journal =      j-SPE,
  volume =       "7",
  number =       "1",
  pages =        "146--147",
  month =        jan,
  year =         "1977",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380070111",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Sep 10 12:36:39 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "27 Oct 2006",
}


bibtype: phdthesis
filename: fparith.bib
label: Hough:1977:EAI
author: David Granville Hough
title: Explaining and ameliorating the ill-condition of zeros of polynomials
type: Ph.D. Thesis
school: Electronics Research Lab., University of California, Berkeley
address: Berkeley, CA, USA
pages: 303
month: feb
monthnumber: 2
year: 1977
bibdate: Thu Jan 12 09:05:57 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.01.12 09:05:57 ???
URL: http://wwwlib.umi.com/dissertations/fullcit/7731401
acknowledgement: ack-nhfb
rawauthor: David Granville Hough
rawtitle: Explaining and ameliorating the ill-condition of zeros of polynomials
entry:
@PhdThesis{Hough:1977:EAI,
  author =       "David Granville Hough",
  title =        "Explaining and ameliorating the ill-condition of zeros
                 of polynomials",
  type =         "{Ph.D.} Thesis",
  school =       "Electronics Research Lab., University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "303",
  month =        feb,
  year =         "1977",
  bibdate =      "Thu Jan 12 09:05:57 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/7731401",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Jenkins:1977:URN
author: W. Jenkins and B. Leon
title: The use of residue number systems in the design of finite impulse response digital filters
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 24
number: 4
pages: 191--201
month: apr
monthnumber: 4
year: 1977
CODEN: ICSYBT
DOI: https://doi.org/10.1109/PGEC.1967.264810
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23467
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: W. Jenkins and B. Leon
rawtitle: The use of residue number systems in the design of finite impulse response digital filters
entry:
@Article{Jenkins:1977:URN,
  author =       "W. Jenkins and B. Leon",
  title =        "The use of residue number systems in the design of
                 finite impulse response digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "24",
  number =       "4",
  pages =        "191--201",
  month =        apr,
  year =         "1977",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23467",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A technique is presented for implementing a finite
                 impulse response (FIR) digital filter in a residue
                 number system (RNS). For many years residue number
                 coding has been recognized as a system which provides a
                 capability for the implementation of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Jullien:1977:HRD
author: G. Jullien and W. Miller and J. Soltis and A. Baraniecka and B. Tseng
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '77
title: Hardware realization of digital signal processing elements using the residue number system
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 506--510
year: 1977
DOI: https://doi.org/10.1049/el:19770117
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: G. Jullien and W. Miller and J. Soltis and A. Baraniecka and B. Tseng
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing, {ICASSP '77}
rawtitle: Hardware realization of digital signal processing elements using the residue number system
entry:
@InProceedings{Jullien:1977:HRD,
  author =       "G. Jullien and W. Miller and J. Soltis and A.
                 Baraniecka and B. Tseng",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '77}",
  title =        "Hardware realization of digital signal processing
                 elements using the residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "506--510",
  year =         "1977",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19770117",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In the past, hardware realization of digital signal
                 processing elements have been based upon binary
                 arithmetic concepts. Because of the dependence between
                 digits in binary arithmetic operations, the hardware
                 required to construct arithmetic elements \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1977:CYC
author: W. M. Kahan and B. N. Parlett
title: Can You Count on Your Calculator?
type: Memorandum
number: UCB/ERL M77/21
institution: Electronics Research Laboratory, College of Engineering, University of California, Berkeley
address: Berkeley, CA, USA
pages: ii + 28
day: 6
month: apr
monthnumber: 4
year: 1977
bibdate: Fri Jan 12 11:37:56 1996
bibtimestamp: 1996.01.12 11:37:56 ???
acknowledgement: ack-jr
rawauthor: W. M. Kahan and B. N. Parlett
rawtitle: Can You Count on Your Calculator?
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

note:
German Transl. Published In: Jahrbuch Uberblicke Mathematik 1978, Ed. by B. Fuchssteiner and others, Bibliographisches Institut, Mannheim-Wien-Zurich, 199--216, 1978

URL:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib

rawnote:
German Transl. Published In: Jahrbuch {\"U}berblicke Mathematik 1978, Ed. by B. Fuchssteiner and others, Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich, 199--216, 1978

entry:
@TechReport{Kahan:1977:CYC,
  author =       "W. M. Kahan and B. N. Parlett",
  title =        "Can You Count on Your Calculator?",
  type =         "Memorandum",
  number =       "UCB/ERL M77/21",
  institution =  "Electronics Research Laboratory, College of
                 Engineering, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "ii + 28",
  day =          "6",
  month =        apr,
  year =         "1977",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "German Transl. Published In: Jahrbuch {\"U}berblicke
                 Mathematik 1978, Ed. by B. Fuchssteiner and others,
                 Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich,
                 199--216, 1978",
  URL =          "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-jr,
}


bibtype: article
filename: fparith.bib
label: Kent:1977:HSF
author: J. G. Kent
title: Highlights of a Study of Floating-Point Instructions
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 660--666
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674899
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 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. G. Kent
rawtitle: Highlights of a Study of Floating-Point Instructions
abstract:
The research work that this paper is based on resulted in the development of tools for the theoretical definition, analysis and comparison of floating-point instructions as mathematical mappings. These tools can be used to study the properties of most floating-point instructions and their operands.

rawabstract:
The research work that this paper is based on resulted in the development of tools for the theoretical definition, analysis and comparison of floating-point instructions as mathematical mappings. These tools can be used to study the properties of most floating-point instructions and their operands.

entry:
@Article{Kent:1977:HSF,
  author =       "J. G. Kent",
  title =        "Highlights of a Study of Floating-Point Instructions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "660--666",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674899",
  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",
  abstract =     "The research work that this paper is based on resulted
                 in the development of tools for the theoretical
                 definition, analysis and comparison of floating-point
                 instructions as mathematical mappings. These tools can
                 be used to study the properties of most floating-point
                 instructions and their operands.",
  acknowledgement = ack-nj,
  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: Kent:1977:HST
author: S. A. Kent
title: A High-Speed Threshold Gate Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 12
pages: 1279--1283
month: dec
monthnumber: 12
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674790
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:59 MDT 2011
bibtimestamp: 2011.07.11 21:56:59 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674790
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. A. Kent
rawtitle: A High-Speed Threshold Gate Multiplier
entry:
@Article{Kent:1977:HST,
  author =       "S. A. Kent",
  title =        "A High-Speed Threshold Gate Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "12",
  pages =        "1279--1283",
  month =        dec,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674790",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674790",
  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: Kornerup:1977:UNR
author: P. Kornerup and B. D. Shriver
title: A Unified Numeric Representation Arithmetic Unit and Its Language Support
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 651--659
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674898
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:55 MDT 2011
bibtimestamp: 2011.07.11 21:56:55 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674898
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Kornerup and B. D. Shriver
rawtitle: A Unified Numeric Representation Arithmetic Unit and Its Language Support
entry:
@Article{Kornerup:1977:UNR,
  author =       "P. Kornerup and B. D. Shriver",
  title =        "A Unified Numeric Representation Arithmetic Unit and
                 Its Language Support",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "651--659",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674898",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:55 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=1674898",
  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: Krishnamurthy:1977:MPU
author: E. V. Krishnamurthy
title: Matrix Processors Using $p$-adic Arithmetic for Exact Linear Computations
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 633--639
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674895
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:55 MDT 2011
bibtimestamp: 2011.07.11 21:56:55 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674895
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. V. Krishnamurthy
rawtitle: Matrix Processors Using $p$-adic Arithmetic for Exact Linear Computations
entry:
@Article{Krishnamurthy:1977:MPU,
  author =       "E. V. Krishnamurthy",
  title =        "Matrix Processors Using $p$-adic Arithmetic for Exact
                 Linear Computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "633--639",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674895",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:55 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=1674895",
  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: Kuck:1977:ARM
author: David J. Kuck and Douglass S. Parker Jr. and Ahmed H. Sameh
title: Analysis of Rounding Methods in Floating-Point Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 643--650
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674897
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65G05
MRnumber: 57 7979
bibdate: Fri Dec 08 12:00:49 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 12:00:49 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
reviewer: V. V. Ivanov
rawauthor: David J. Kuck and Douglass S. {Parker Jr.} and Ahmed H. Sameh
rawtitle: Analysis of Rounding Methods in Floating-Point Arithmetic
entry:
@Article{Kuck:1977:ARM,
  author =       "David J. Kuck and Douglass S. {Parker Jr.} and Ahmed
                 H. Sameh",
  title =        "Analysis of Rounding Methods in Floating-Point
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "643--650",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674897",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G05",
  MRnumber =     "57 7979",
  bibdate =      "Fri Dec 08 12:00:49 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "V. V. Ivanov",
}


bibtype: article
filename: fparith.bib
label: Kulisch:1977:MFC
author: Ulrich Kulisch
title: Mathematical foundations of computer arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 610--620
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674893
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat May 18 14:33:16 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:33:16 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Ulrich Kulisch
rawtitle: Mathematical foundations of computer arithmetic
entry:
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  author =       "Ulrich Kulisch",
  title =        "Mathematical foundations of computer arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "610--620",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674893",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat May 18 14:33:16 2002",
  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: Lee:1977:FNS
author: S. C. Lee and A. D. Edgar
title: The Focus Number System
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 11
pages: 1167--1170
month: nov
monthnumber: 11
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674770
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:57 MDT 2011
bibtimestamp: 2011.07.11 21:56:57 MDT
note: See comments cite Lee:1979:AFN,Swartzlander:1979:CFN.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674770
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. C. Lee and A. D. Edgar
rawnote: See comments \cite{Lee:1979:AFN,Swartzlander:1979:CFN}.
rawtitle: The {Focus} Number System
entry:
@Article{Lee:1977:FNS,
  author =       "S. C. Lee and A. D. Edgar",
  title =        "The {Focus} Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "11",
  pages =        "1167--1170",
  month =        nov,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674770",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:57 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{Lee:1979:AFN,Swartzlander:1979:CFN}.",
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  acknowledgement = ack-nhfb,
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}


bibtype: article
filename: fparith.bib
label: Ligomenides:1977:SSF
author: P. A. Ligomenides
title: The Skip-and-Set Fast-Division Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 10
pages: 1030--1032
month: oct
monthnumber: 10
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674740
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 10:17:27 MDT 2011
bibtimestamp: 2011.07.13 10:17:27 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674740
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. A. Ligomenides
rawtitle: The Skip-and-Set Fast-Division Algorithm
entry:
@Article{Ligomenides:1977:SSF,
  author =       "P. A. Ligomenides",
  title =        "The Skip-and-Set Fast-Division Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "10",
  pages =        "1030--1032",
  month =        oct,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674740",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 10:17:27 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=1674740",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
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}


bibtype: book
filename: fparith.bib
label: Luke:1977:ACM
author: Yudell L. Luke
title: Algorithms for the Computation of Mathematical Functions
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xiii + 284
year: 1977
ISBN: 0-12-459940-0 OR 0124599400
ISBN13: 978-0-12-459940-6 OR 9780124599406
LCCN: QA351 .L7961
bibdate: Wed Dec 15 10:38:19 1993
bibtimestamp: 1993.12.15 10:38:19 ???
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: Algorithms for the Computation of Mathematical Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.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/mathcw.bib

TOC:
Preface / xi 1: Basic Formulas / 1 1.1 Introduction / 1 1.2 The Generalized Hypergeometric Function and the $G$-Function / 1 1.3 Expansion of $_pF_q(z)$ and $G^q - r, 1_p + 1, q(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev Polynomials of the First Kind / 4 1.4 Efficient Evaluation of Series of Chebyshev Polynomials / 17 1.5 Rational Approximations for Generalized Hypergeometric Functions / 20 1.6 The Pade Table / 27 1.7 Computations of and Checks on Coefficients and Tables / 29 1.8 Tables of the Functions $e^-zeta $, and $e^-xi $ / 35 2: Identification of Functions / 41 2.1 Introduction / 41 2.2 The Generalized Hypergeometric Function $_pF_q(z)$ / 41 2.3 The G-Function / 47 2.4 Miscellaneous Functions / 48 3: General Remarks on the Algorithms and Programs / 49 3.1 Introduction / 49 3.2 Precision and Complex Arithmetic / 49 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 5: Coefficients for the Expansion of the Confluent Hypergeometric Function $_1F_1(a;c;z)$ in Ascending Series of Chebyshev Polynomials / 70 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$ in Ascending Series of Chebyshev Polynomials / 82 8: Coefficients for the Expansion of the Confluent Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$ in Descending Series of Chebyshev Polynomials / 88 9: Coefficients for the Expansion of the Functions $G^m,1_1,3(z^2/4|^1_a,b,c)$, $m = 3$ or $m = 2$, in Descending Series of Chebyshev Polynomials / 101 10: Differential and Integral Properties of Expansions in Series of Chebyshev Polynomials of the First Kind / 116 11: Expansion of Exponential Type Integrals in Series of Chebyshev Polynomials of the First Kind / 126 11.1 Introduction / 126 11.2 The Representation for $g(x)$ / 127 11.3 The Representation for $G(x)$ / 129 11.4 Exponential Type Integrals Involving Logarithms / 133 11.5 Numerical Examples / 135 11.6 Errata / 139 12: Conversion of a Power Series into a Series of Chebyshev Polynomials of the First Kind / 154 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159 14: Pade Approximations for $_2F_1(1,b;c;-z)$ / 174 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182 16: Pade Approximations for $_1F_1(1;c;-z)$ / 192 17: Rational Approximations for Bessel Functions of the First Kind / 203 18: Pade Approximations for $I_nu + 1(z)/I_nu (z)$ / 220 19: Evaluation of Bessel Functions of the First Kind by Use of the Backward Recurrence Formula 19.1 Introduction / 230 19.2 Backward Recurrence Schemata for $I_nu (z)$ and $J_nu (z)$ / 230 19.3 Numerical Examples / 240 19.4 Mathematical Description of Programs / 243 19.4.1 Evaluation of Functions Related to $I_m + nu (z)$ and $J_m + nu (z)$ / 243 19.4.2 Evaluation of Functions Related to $e^-lI_m + nu (z)$ / 245 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ / 252 21: Pade Approximations for $z U(1;2-b;z)$ / 265 Appendices Bibliography / 280 Notation Index / 281 Subject Index / 283

rawTOC:
Preface / xi \\ 1: Basic Formulas / 1 \\ 1.1 Introduction / 1 \\ 1.2 The Generalized Hypergeometric Function and the $G$-Function / 1 \\ 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1, q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev Polynomials of the First Kind / 4 \\ 1.4 Efficient Evaluation of Series of Chebyshev Polynomials / 17 \\ 1.5 Rational Approximations for Generalized Hypergeometric Functions / 20 \\ 1.6 The Pad{\'e} Table / 27 \\ 1.7 Computations of and Checks on Coefficients and Tables / 29 \\ 1.8 Tables of the Functions $e^{-\zeta}$, and $e^{-\xi}$ / 35 \\ 2: Identification of Functions / 41 \\ 2.1 Introduction / 41 \\ 2.2 The Generalized Hypergeometric Function $_pF_q(z)$ / 41 \\ 2.3 The G-Function / 47 \\ 2.4 Miscellaneous Functions / 48 \\ 3: General Remarks on the Algorithms and Programs / 49 \\ 3.1 Introduction / 49 \\ 3.2 Precision and Complex Arithmetic / 49 \\ 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\ 5: Coefficients for the Expansion of the Confluent Hypergeometric Function $_1F_1(a;c;z)$ in Ascending Series of Chebyshev Polynomials / 70 \\ 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\ 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$ in Ascending Series of Chebyshev Polynomials / 82 \\ 8: Coefficients for the Expansion of the Confluent Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$ in Descending Series of Chebyshev Polynomials / 88 \\ 9: Coefficients for the Expansion of the Functions $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$, in Descending Series of Chebyshev Polynomials / 101 \\ 10: Differential and Integral Properties of Expansions in Series of Chebyshev Polynomials of the First Kind / 116 \\ 11: Expansion of Exponential Type Integrals in Series of Chebyshev Polynomials of the First Kind / 126 \\ 11.1 Introduction / 126 \\ 11.2 The Representation for $g(x)$ / 127 \\ 11.3 The Representation for $G(x)$ / 129 \\ 11.4 Exponential Type Integrals Involving Logarithms / 133 \\ 11.5 Numerical Examples / 135 \\ 11.6 Errata / 139 \\ 12: Conversion of a Power Series into a Series of Chebyshev Polynomials of the First Kind / 154 \\ 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159 \\ 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174 \\ 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182 \\ 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192 \\ 17: Rational Approximations for Bessel Functions of the First Kind / 203 \\ 18: Pad{\'e} Approximations for $I_{\nu + 1}(z)/I_\nu(z)$ / 220 \\ 19: Evaluation of Bessel Functions of the First Kind by Use of the Backward Recurrence Formula \\ 19.1 Introduction / 230 \\ 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and $J_\nu(z)$ / 230 \\ 19.3 Numerical Examples / 240 \\ 19.4 Mathematical Description of Programs / 243 \\ 19.4.1 Evaluation of Functions Related to $I_{m + \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\ 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m + \nu}(z)$ / 245 \\ 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ / 252 \\ 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265 \\ Appendices \\ Bibliography / 280 \\ Notation Index / 281 \\ Subject Index / 283

entry:
@Book{Luke:1977:ACM,
  author =       "Yudell L. Luke",
  title =        "Algorithms for the Computation of Mathematical
                 Functions",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 284",
  year =         "1977",
  ISBN =         "0-12-459940-0",
  ISBN-13 =      "978-0-12-459940-6",
  LCCN =         "QA351 .L7961",
  bibdate =      "Wed Dec 15 10:38:19 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.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/mathcw.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / xi \\
                 1: Basic Formulas / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 The Generalized Hypergeometric Function and the
                 $G$-Function / 1 \\
                 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
                 q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
                 Polynomials of the First Kind / 4 \\
                 1.4 Efficient Evaluation of Series of Chebyshev
                 Polynomials / 17 \\
                 1.5 Rational Approximations for Generalized
                 Hypergeometric Functions / 20 \\
                 1.6 The Pad{\'e} Table / 27 \\
                 1.7 Computations of and Checks on Coefficients and
                 Tables / 29 \\
                 1.8 Tables of the Functions $e^{-\zeta}$, and
                 $e^{-\xi}$ / 35 \\
                 2: Identification of Functions / 41 \\
                 2.1 Introduction / 41 \\
                 2.2 The Generalized Hypergeometric Function $_pF_q(z)$
                 / 41 \\
                 2.3 The G-Function / 47 \\
                 2.4 Miscellaneous Functions / 48 \\
                 3: General Remarks on the Algorithms and Programs / 49
                 \\
                 3.1 Introduction / 49 \\
                 3.2 Precision and Complex Arithmetic / 49 \\
                 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
                 5: Coefficients for the Expansion of the Confluent
                 Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
                 Series of Chebyshev Polynomials / 70 \\
                 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
                 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
                 in Ascending Series of Chebyshev Polynomials / 82 \\
                 8: Coefficients for the Expansion of the Confluent
                 Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
                 in Descending Series of Chebyshev Polynomials / 88 \\
                 9: Coefficients for the Expansion of the Functions
                 $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
                 in Descending Series of Chebyshev Polynomials / 101 \\
                 10: Differential and Integral Properties of Expansions
                 in Series of Chebyshev Polynomials of the First Kind /
                 116 \\
                 11: Expansion of Exponential Type Integrals in Series
                 of Chebyshev Polynomials of the First Kind / 126 \\
                 11.1 Introduction / 126 \\
                 11.2 The Representation for $g(x)$ / 127 \\
                 11.3 The Representation for $G(x)$ / 129 \\
                 11.4 Exponential Type Integrals Involving Logarithms /
                 133 \\
                 11.5 Numerical Examples / 135 \\
                 11.6 Errata / 139 \\
                 12: Conversion of a Power Series into a Series of
                 Chebyshev Polynomials of the First Kind / 154 \\
                 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
                 \\
                 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
                 \\
                 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
                 \\
                 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
                 \\
                 17: Rational Approximations for Bessel Functions of the
                 First Kind / 203 \\
                 18: Pad{\'e} Approximations for $I_{\nu +
                 1}(z)/I_\nu(z)$ / 220 \\
                 19: Evaluation of Bessel Functions of the First Kind by
                 Use of the Backward Recurrence Formula \\
                 19.1 Introduction / 230 \\
                 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
                 $J_\nu(z)$ / 230 \\
                 19.3 Numerical Examples / 240 \\
                 19.4 Mathematical Description of Programs / 243 \\
                 19.4.1 Evaluation of Functions Related to $I_{m +
                 \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
                 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
                 \nu}(z)$ / 245 \\
                 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
                 252 \\
                 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
                 \\
                 Appendices \\
                 Bibliography / 280 \\
                 Notation Index / 281 \\
                 Subject Index / 283",
  wrongisbn =    "0-12-459940-6",
}


bibtype: techreport
filename: fparith.bib
label: Maag:1977:SRE
author: Werner Maag and Rudolf Wehrli
title: Survey on rounding effects in floating-point arithmetic
type: Report
institution: CM Schanis AG
address: Schanis, Switzerland
pages: 73
year: 1977
bibdate: Thu May 09 09:10:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:10:32 ???
acknowledgement: ack-nhfb
rawauthor: Werner Maag and Rudolf Wehrli
rawtitle: Survey on rounding effects in floating-point arithmetic
entry:
@TechReport{Maag:1977:SRE,
  author =       "Werner Maag and Rudolf Wehrli",
  title =        "Survey on rounding effects in floating-point
                 arithmetic",
  type =         "Report",
  institution =  "CM Sch{\"a}nis AG",
  address =      "Sch{\"a}nis, Switzerland",
  pages =        "73",
  year =         "1977",
  bibdate =      "Thu May 09 09:10:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Merzbach:1977:GSF
author: Uta C. Merzbach
title: Georg Scheutz and the first printing calculator
volume: 36
publisher: Smithsonian Institution Press
address: Washington, DC, USA
pages: iii + 74
year: 1977
LCCN: QA75 .M46
bibdate: Mon Jan 21 21:21:54 MST 2013
bibtimestamp: 2013.01.21 21:21:54 MST
series: Smithsonian studies in history and technology
subject: Calculators; History; Scheutz, George
acknowledgement: ack-nhfb
subjectdates: 1785--1873
rawauthor: Uta C. Merzbach
rawtitle: {Georg Scheutz} and the first printing calculator
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager

entry:
@Book{Merzbach:1977:GSF,
  author =       "Uta C. Merzbach",
  title =        "{Georg Scheutz} and the first printing calculator",
  volume =       "36",
  publisher =    "Smithsonian Institution Press",
  address =      "Washington, DC, USA",
  pages =        "iii + 74",
  year =         "1977",
  LCCN =         "QA75 .M46",
  bibdate =      "Mon Jan 21 21:21:54 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Smithsonian studies in history and technology",
  acknowledgement = ack-nhfb,
  subject =      "Calculators; History; Scheutz, George",
  subject-dates = "1785--1873",
}


bibtype: incollection
filename: fparith.bib
label: Metropolis:1977:MSA
author: N. Metropolis
title: Methods of significance arithmetic
crossref: Jacobs:1977:SAN
pages: 179--192
year: 1977
MRclass: 65G05 (68A99)
MRnumber: MR0451673 (56 \#9955)
MRreviewer: N. N. Abdelmalek
bibdate: Thu Nov 8 14:50:25 2007
bibtimestamp: 2007.11.08 14:50:25 ???
acknowledgement: ack-nhfb
rawauthor: N. Metropolis
rawtitle: Methods of significance arithmetic
entry:
@InCollection{Metropolis:1977:MSA,
  author =       "N. Metropolis",
  title =        "Methods of significance arithmetic",
  crossref =     "Jacobs:1977:SAN",
  pages =        "179--192",
  year =         "1977",
  MRclass =      "65G05 (68A99)",
  MRnumber =     "MR0451673 (56 \#9955)",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Thu Nov 8 14:50:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Metropolis:1977:SAP
author: N. Metropolis and Stephen M. Tanny
title: Significance arithmetic: the probability of carrying
journal: j-COMPUT-MATH-APPL
volume: 3
number: 1
pages: 77--81
year: 1977
CODEN: CMAPDK
ISSN: 0886-9561 OR 08869561
ISSNL: 0898-1221 OR 08981221
MRclass: 65G05 (10A30 65C10)
MRnumber: MR0458846 (56 \#17046)
MRreviewer: Artenio De Matteis
bibdate: Thu Nov 8 14:50:26 2007
bibtimestamp: 2007.11.08 14:50:26 ???
fjournal: Computers & Mathematics with Applications. An International Journal. Part B
ZMnumber: 0371.60015
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: N. Metropolis and Stephen M. Tanny
rawtitle: Significance arithmetic: the probability of carrying
abstract:
This article develops a number of probabilistic results related to a combinatorial representation of the real number system. This representation employs an algorithmic definition of the arithmetic operations analogous to that used by a computer. A carry function for each place is defined and the distribution of these functions is characterized in terms of classical combinatorial polynomials

rawabstract:
This article develops a number of probabilistic results related to a combinatorial representation of the real number system. This representation employs an algorithmic definition of the arithmetic operations analogous to that used by a computer. A carry function for each place is defined and the distribution of these functions is characterized in terms of classical combinatorial polynomials

entry:
@Article{Metropolis:1977:SAP,
  author =       "N. Metropolis and Stephen M. Tanny",
  title =        "Significance arithmetic: the probability of carrying",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "1",
  pages =        "77--81",
  year =         "1977",
  CODEN =        "CMAPDK",
  ISSN =         "0886-9561",
  ISSN-L =       "0898-1221",
  MRclass =      "65G05 (10A30 65C10)",
  MRnumber =     "MR0458846 (56 \#17046)",
  MRreviewer =   "Artenio De Matteis",
  bibdate =      "Thu Nov 8 14:50:26 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 =     "0371.60015",
  abstract =     "This article develops a number of probabilistic
                 results related to a combinatorial representation of
                 the real number system. This representation employs an
                 algorithmic definition of the arithmetic operations
                 analogous to that used by a computer. A carry function
                 for each place is defined and the distribution of these
                 functions is characterized in terms of classical
                 combinatorial polynomials",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers \& Mathematics with Applications. An
                 International Journal. Part B",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: fparith.bib
label: Mitra:1977:CDI
author: Debasis Mitra
journal: j-BELL-SYST-TECH-J
volume: 56
number: 9
pages: 1679--1699
month: nov
monthnumber: 11
year: 1977
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:56 MST 2010
bibtimestamp: 2010.11.09 11:15:56 MST
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: Debasis Mitra
title:
Criteria for Determining if a High-Order Digital Filter Using Saturation Arithmetic is Free of Overflow Oscillations

bibsource:
http://bstj.bell-labs.com/oldfiles/year.1977/BSTJ.1977.5609.html; http://www.alcatel-lucent.com/bstj/vol56-1977/bstj-vol56-issue09.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://bstj.bell-labs.com/BSTJ/images/Vol56/bstj56-9-1679.pdf; http://www.alcatel-lucent.com/bstj/vol56-1977/articles/bstj56-9-1679.pdf

rawtitle:
Criteria for Determining if a High-Order Digital Filter Using Saturation Arithmetic is Free of Overflow Oscillations

entry:
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  author =       "Debasis Mitra",
  title =        "Criteria for Determining if a High-Order Digital
                 Filter Using Saturation Arithmetic is Free of Overflow
                 Oscillations",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "56",
  number =       "9",
  pages =        "1679--1699",
  month =        nov,
  year =         "1977",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:56 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1977/BSTJ.1977.5609.html;
                 http://www.alcatel-lucent.com/bstj/vol56-1977/bstj-vol56-issue09.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol56/bstj56-9-1679.pdf;
                 http://www.alcatel-lucent.com/bstj/vol56-1977/articles/bstj56-9-1679.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: fparith.bib
label: Ninke:1977:SRB
author: W. H. Ninke and G. R. Ritchie
title: Shift Register Binary Rate Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 3
pages: 276--278
month: mar
monthnumber: 3
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674819
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:53 MDT 2011
bibtimestamp: 2011.07.11 21:56:53 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674819
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: W. H. Ninke and G. R. Ritchie
rawtitle: Shift Register Binary Rate Multipliers
entry:
@Article{Ninke:1977:SRB,
  author =       "W. H. Ninke and G. R. Ritchie",
  title =        "Shift Register Binary Rate Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "3",
  pages =        "276--278",
  month =        mar,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674819",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:53 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=1674819",
  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: Oliver:1977:EAM
author: J. Oliver
title: An Error Analysis of the Modified Clenshaw Method for Evaluating Chebyshev and Fourier Series
journal: j-J-INST-MATH-APPL
volume: 20
number: 3
pages: 379--391
year: 1977
CODEN: JMTAA8
ISSN: 0020-2932 OR 00202932
ISSNL: 0020-2932 OR 00202932
MRclass: 65G05 (41A50)
MRnumber: 57 #4508
MRreviewer: David L. Elliott
bibdate: Fri Apr 5 07:38:01 MST 2002
bibtimestamp: 2002.04.05 07:38:01 MST
fjournal: Journal of the Institute of Mathematics and its Applications
ZMnumber: 0397.65013
acknowledgement: ack-nhfb
journalURL: http://imamat.oxfordjournals.org/content/by/year
rawauthor: J. Oliver
rawtitle: An Error Analysis of the Modified {Clenshaw} Method for Evaluating {Chebyshev} and {Fourier} Series
bibsource:
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib

entry:
@Article{Oliver:1977:EAM,
  author =       "J. Oliver",
  title =        "An Error Analysis of the Modified {Clenshaw} Method
                 for Evaluating {Chebyshev} and {Fourier} Series",
  journal =      j-J-INST-MATH-APPL,
  volume =       "20",
  number =       "3",
  pages =        "379--391",
  year =         "1977",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  ISSN-L =       "0020-2932",
  MRclass =      "65G05 (41A50)",
  MRnumber =     "57 #4508",
  MRreviewer =   "David L. Elliott",
  bibdate =      "Fri Apr 5 07:38:01 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
  ZMnumber =     "0397.65013",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
  xxtitle =      "An error analysis of the modified {Clenshaw} methods
                 for evaluating {Chebyshev} and {Fourier} series",
}


bibtype: article
filename: fparith.bib
label: Oliver:1977:SRE
author: J. Oliver
title: On the sensitivity to rounding errors of Chebyshev series approximations
journal: j-J-COMPUT-APPL-MATH
volume: 3
number: 2
pages: 89--98
month: jun
monthnumber: 6
year: 1977
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:16 MST 2017
bibtimestamp: 2017.02.25 11:59:16 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X77900031
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: J. Oliver
rawtitle: On the sensitivity to rounding errors of {Chebyshev} series approximations
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib

entry:
@Article{Oliver:1977:SRE,
  author =       "J. Oliver",
  title =        "On the sensitivity to rounding errors of {Chebyshev}
                 series approximations",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "3",
  number =       "2",
  pages =        "89--98",
  month =        jun,
  year =         "1977",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X77900031",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: fparith.bib
label: Palmer:1977:ISF
author: J. Palmer
title: The Intel Standard for Floating Point Arithmetic
crossref: IEEE:1977:ICS
pages: 107--112
year: 1977
bibdate: Fri Nov 09 19:09:10 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:09:10 ???
acknowledgement: ack-nhfb
rawauthor: J. Palmer
rawtitle: The {Intel} Standard for Floating Point Arithmetic
entry:
@InProceedings{Palmer:1977:ISF,
  author =       "J. Palmer",
  title =        "The {Intel} Standard for Floating Point Arithmetic",
  crossref =     "IEEE:1977:ICS",
  pages =        "107--112",
  year =         "1977",
  bibdate =      "Fri Nov 09 19:09:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Papantoni-Kazakos:1977:CRE
author: P. Papantoni-Kazakos
title: Consideration of round off errors in the design of mean square estimators
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 22
number: 2
pages: 276--279
month: apr
monthnumber: 4
year: 1977
CODEN: IETAA9
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
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 Automatic Control
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: P. Papantoni-Kazakos
rawtitle: Consideration of round off errors in the design of mean square estimators
entry:
@Article{Papantoni-Kazakos:1977:CRE,
  author =       "P. Papantoni-Kazakos",
  title =        "Consideration of round off errors in the design of
                 mean square estimators",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "22",
  number =       "2",
  pages =        "276--279",
  month =        apr,
  year =         "1977",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  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 Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "In this correspondence, a search for the optimal
                 polynomial mean-square (ms) estimator is undertaken;
                 when the input is a vector with fixed dimensionality
                 and at the calculation of the estimator characteristics
                 the round off errors are considered. \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Randell:1977:CGC
author: B. Randell
title: Colossus: Godfather of the Computer
journal: j-NEW-SCIENTIST
volume: 73
number: 1038
pages: 346--348
day: 10
month: feb
monthnumber: 2
year: 1977
CODEN: NWSCAL
ISSN: 0262-4079, 0028-6664 OR 02624079, 00286664
ISSNL: 0262-4079 OR 02624079
bibdate: Wed Oct 13 11:51:16 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:51:16 ???
note: Reprinted in cite [ 7.5]Randell:1982:ODC.
fjournal: New Scientist
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/02624079
rawauthor: B. Randell
rawnote: Reprinted in \cite[\S 7.5]{Randell:1982:ODC}.
rawtitle: {Colossus}: Godfather of the Computer
entry:
@Article{Randell:1977:CGC,
  author =       "B. Randell",
  title =        "{Colossus}: Godfather of the Computer",
  journal =      j-NEW-SCIENTIST,
  volume =       "73",
  number =       "1038",
  pages =        "346--348",
  day =          "10",
  month =        feb,
  year =         "1977",
  CODEN =        "NWSCAL",
  ISSN =         "0262-4079, 0028-6664",
  ISSN-L =       "0262-4079",
  bibdate =      "Wed Oct 13 11:51:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.5]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
}


bibtype: article
filename: fparith.bib
label: Reimer:1977:AFO
author: M. Reimer
journal: j-COMPUTING
volume: 17
number: 4
pages: 289--296
year: 1977
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Fri Sep 16 16:30:40 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 16:30:40 ???
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/607
rawauthor: M. Reimer
title:
Auswertungsalgorithmen fast-optimaler numerischer Stabilitat fur Polynome toenglish Algorithms of Near-optimal Numerical Stability for the Evaluation of Polynomials endtoenglish 

rawtitle:
{Auswertungsalgorithmen fast-optimaler numerischer Stabilit{\"a}t f{\"u}r Polynome} \toenglish {Algorithms of Near-optimal Numerical Stability for the Evaluation of Polynomials} \endtoenglish

entry:
@Article{Reimer:1977:AFO,
  author =       "M. Reimer",
  title =        "{Auswertungsalgorithmen fast-optimaler numerischer
                 Stabilit{\"a}t f{\"u}r Polynome} \toenglish {Algorithms
                 of Near-optimal Numerical Stability for the Evaluation
                 of Polynomials} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "17",
  number =       "4",
  pages =        "289--296",
  month =        "????",
  year =         "1977",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:40 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: Ris:1977:UDF
author: Frederic N. Ris
title: A unified decimal floating-point architecture for the support of high-level languages
journal: j-SIGPLAN
volume: 12
number: 9
pages: 60--70
month: sep
monthnumber: 9
year: 1977
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:14:09 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:14:09 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
corpsource: IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
treatment: P Practical
rawauthor: Frederic N. Ris
rawtitle: A unified decimal floating-point architecture for the support of high-level languages
keywords:
architecture; decimal floating-point arithmetic; digital arithmetic; high level languages; procedure oriented languages; unified

entry:
@Article{Ris:1977:UDF,
  author =       "Frederic N. Ris",
  title =        "A unified decimal floating-point architecture for the
                 support of high-level languages",
  journal =      j-SIGPLAN,
  volume =       "12",
  number =       "9",
  pages =        "60--70",
  month =        sep,
  year =         "1977",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:14:09 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "architecture; decimal floating-point arithmetic;
                 digital arithmetic; high level languages; procedure
                 oriented languages; unified",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Rjabko:1977:AHM
author: B. Ja. Rjabko
title: An analogue of Haffmen's method for the optimal summation of floating point numbers. (Russian)
journal: Diskret. Analiz
volume: 30
pages: 38--45, 77
year: 1977
MRclass: 68C05 (68E99)
MRnumber: 80c:68023
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 ???
language: Russian
acknowledgement: ack-nhfb
reviewer: Vladimir Sleinikov
rawauthor: B. Ja. Rjabko
rawtitle: An analogue of {Haffmen}'s method for the optimal summation of floating point numbers. ({Russian})
entry:
@Article{Rjabko:1977:AHM,
  author =       "B. Ja. Rjabko",
  title =        "An analogue of {Haffmen}'s method for the optimal
                 summation of floating point numbers. ({Russian})",
  journal =      "Diskret. Analiz",
  volume =       "30",
  pages =        "38--45, 77",
  year =         "1977",
  MRclass =      "68C05 (68E99)",
  MRnumber =     "80c:68023",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  reviewer =     "Vladimir Sleinikov",
  xxjournal =    "Metody Diskret. Anal. v Reshenii Kombinatornykh
                 Zadach",
}


bibtype: article
filename: fparith.bib
label: Sanyal:1977:AND
author: S. Sanyal
title: An algorithm for nonrestoring division
journal: j-COMP-DESIGN
volume: 16
number: 5
pages: 124--127
month: may
monthnumber: 5
year: 1977
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
bibdate: Thu Sep 1 10:15:08 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 10:15:08 ???
fjournal: Computer Design
acknowledgement: ack-nj
rawauthor: S. Sanyal
rawtitle: An algorithm for nonrestoring division
entry:
@Article{Sanyal:1977:AND,
  author =       "S. Sanyal",
  title =        "An algorithm for nonrestoring division",
  journal =      j-COMP-DESIGN,
  volume =       "16",
  number =       "5",
  pages =        "124--127",
  month =        may,
  year =         "1977",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Thu Sep 1 10:15:08 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 =     "Computer Design",
}


bibtype: mastersthesis
filename: fparith.bib
label: Simmons:1977:SRA
author: David Michael Simmons
title: Signal-to-noise ration analysis of block floating point FFTS
type: Electrical Engineering Thesis (M.S.)
school: University of Missouri--Rolla
address: Rolla, MO, USA
pages: 114
year: 1977
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 Simmons
rawtitle: Signal-to-noise ration analysis of block floating point {FFTS}
entry:
@MastersThesis{Simmons:1977:SRA,
  author =       "David Michael Simmons",
  title =        "Signal-to-noise ration analysis of block floating
                 point {FFTS}",
  type =         "Electrical Engineering Thesis ({M.S.})",
  school =       "University of Missouri--Rolla",
  address =      "Rolla, MO, USA",
  pages =        "114",
  year =         "1977",
  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: Soderstrand:1977:HSL
author: M. A. Soderstrand
title: A high-speed low-cost recursive digital filter using residue number arithmetic
journal: j-PROC-IEEE
volume: 65
number: 7
pages: 1065--1067
month: jul
monthnumber: 7
year: 1977
CODEN: IEEPAD
DOI: https://doi.org/10.1109/PGEC.1967.264810
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31255
fjournal: Proceedings of the IEEE
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: M. A. Soderstrand
rawtitle: A high-speed low-cost recursive digital filter using residue number arithmetic
entry:
@Article{Soderstrand:1977:HSL,
  author =       "M. A. Soderstrand",
  title =        "A high-speed low-cost recursive digital filter using
                 residue number arithmetic",
  journal =      j-PROC-IEEE,
  volume =       "65",
  number =       "7",
  pages =        "1065--1067",
  month =        jul,
  year =         "1977",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31255",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Use of table look-up multiplication by fractional
                 coefficients allows implementation of high-speed,
                 low-cost recursive digital filters using residue number
                 arithmetic. An 8-bit equivalent filter based on the
                 lossless discrete integrator (LDI) \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Soderstrand:1977:MRN
author: M. A. Soderstrand and E. L. Fields
title: Multipliers for residue-number-arithmetic digital filters
journal: j-ELECT-LETTERS
volume: 13
number: 6
pages: 164--166
day: 17
month: mar
monthnumber: 3
year: 1977
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19770117
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4249252
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: M. A. Soderstrand and E. L. Fields
rawtitle: Multipliers for residue-number-arithmetic digital filters
entry:
@Article{Soderstrand:1977:MRN,
  author =       "M. A. Soderstrand and E. L. Fields",
  title =        "Multipliers for residue-number-arithmetic digital
                 filters",
  journal =      j-ELECT-LETTERS,
  volume =       "13",
  number =       "6",
  pages =        "164--166",
  day =          "17",
  month =        mar,
  year =         "1977",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19770117",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4249252",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A recently proposed residue-number-arithmetic digital
                 filter offers major cost and speed advantages over
                 binary-arithmetic digital filters, but suffers one
                 major drawback. The filter coefficients must be
                 constant, since the lack of a fast method of \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Steer:1977:DHS
author: D. G. Steer and S. R. Penstone
title: Digital Hardware for Sine-Cosine Functions
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 12
pages: 1283--1286
month: dec
monthnumber: 12
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674791
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:56 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 10:15:56 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. G. Steer and S. R. Penstone
rawtitle: Digital Hardware for Sine-Cosine Functions
entry:
@Article{Steer:1977:DHS,
  author =       "D. G. Steer and S. R. Penstone",
  title =        "Digital Hardware for Sine-Cosine Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "12",
  pages =        "1283--1286",
  month =        dec,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674791",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  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: Stenzel:1977:CHS
author: W. J. Stenzel
title: A Compact High-Spped Multiplication Scheme
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 10
pages: 948--957
month: oct
monthnumber: 10
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674730
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 09 19:20:56 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:20:56 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: W. J. Stenzel
rawtitle: A Compact High-Spped Multiplication Scheme
entry:
@Article{Stenzel:1977:CHS,
  author =       "W. J. Stenzel",
  title =        "A Compact High-Spped Multiplication Scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "10",
  pages =        "948--957",
  month =        oct,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674730",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:20:56 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: Stoutemyer:1977:AEA
author: David R. Stoutemyer
title: Automatic Error Analysis Using Computer Algebraic Manipulation
journal: j-TOMS
volume: 3
number: 1
pages: 26--43
month: mar
monthnumber: 3
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355719.355721
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Sep 02 22:30:11 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.02 22:30:11 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David R. Stoutemyer
rawtitle: Automatic Error Analysis Using Computer Algebraic Manipulation
abstract:
This paper shows how the inherent error and the fixed-point or floating-point roundoff of chopoff error of an expression can be determined automatically using a computer algebra language such as REDUCE.

rawabstract:
This paper shows how the inherent error and the fixed-point or floating-point roundoff of chopoff error of an expression can be determined automatically using a computer algebra language such as {REDUCE}.

entry:
@Article{Stoutemyer:1977:AEA,
  author =       "David R. Stoutemyer",
  title =        "Automatic Error Analysis Using Computer Algebraic
                 Manipulation",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "26--43",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355721",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 02 22:30:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper shows how the inherent error and the
                 fixed-point or floating-point roundoff of chopoff error
                 of an expression can be determined automatically using
                 a computer algebra language such as {REDUCE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Thong:1977:ARE
author: Tran Thong and Bede Liu
title: Accumulation of roundoff errors in floating point FFT
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 24
number: 3
pages: 132--143
month: mar
monthnumber: 3
year: 1977
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
MRclass: 65G05
MRnumber: 55 1722
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 Circuits and Systems
acknowledgement: ack-nhfb
reviewer: Sven-AA ke Gustafson
rawauthor: Tran Thong and Bede Liu
rawtitle: Accumulation of roundoff errors in floating point {FFT}
entry:
@Article{Thong:1977:ARE,
  author =       "Tran Thong and Bede Liu",
  title =        "Accumulation of roundoff errors in floating point
                 {FFT}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "24",
  number =       "3",
  pages =        "132--143",
  month =        mar,
  year =         "1977",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  MRclass =      "65G05",
  MRnumber =     "55 1722",
  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 Circuits and Systems",
  reviewer =     "Sven-{\AA}ke Gustafson",
  summary =      "A statistical model for roundoff error is used to
                 predict the output noise to signal ratio of the two
                 common FFT algorithms, the decimation in time and the
                 decimation in frequency algorithms. A unified approach
                 is used to obtain the error in both algorithms
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Tran-Thong:1977:FPF
author: Tran-Thong and Bede Liu
journal: j-TOMS
volume: 3
number: 1
pages: 54--59
month: mar
monthnumber: 3
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355719.355723
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65T05
MRnumber: 55 \#11658
bibdate: Sat Aug 27 22:12:55 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1994.08.27 22:12:55 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: computer arithmetic; double-length summation; fast Fourier transform; roundoff error
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Tr{\^a}{\`n}-Th{\^o}{\'n}g and Bede Liu
title:
Floating Point Fast Fourier Transform Computation Using Double Precision Floating Point Accumulators

abstract:
Most commonly available fast Fourier transform (FFT) subroutines use single precision chopping arithmetic, and the resulting normalized roundoff error, in computing an $N$-point transform with $ N = prod _i = 1^M a_i $ is $ O(M^2) $. This paper proposes a modification of these subroutines for use on computers with a hardwired double precision arithmetic unit. The resulting normalized roundoff error is $ O(M) $ and is independent of the $ a_i $. The modification leads to a negligible increase in storage. For most computers, the increase in the execution time is small. For certain computers, such as IBM System/360 models 91 and 195, the modification can result in a decrease in the execution time.

rawabstract:
Most commonly available fast Fourier transform (FFT) subroutines use single precision chopping arithmetic, and the resulting normalized roundoff error, in computing an $N$-point transform with $ N = \prod_{i = 1}^M a_i $ is $ O(M^2) $. This paper proposes a modification of these subroutines for use on computers with a hardwired double precision arithmetic unit. The resulting normalized roundoff error is $ O(M) $ and is independent of the $ a_i $. The modification leads to a negligible increase in storage. For most computers, the increase in the execution time is small. For certain computers, such as IBM System/360 models 91 and 195, the modification can result in a decrease in the execution time.

rawtitle:
Floating Point Fast {Fourier} Transform Computation Using Double Precision Floating Point Accumulators

entry:
@Article{Tran-Thong:1977:FPF,
  author =       "Tr{\^a}{\`n}-Th{\^o}{\'n}g and Bede Liu",
  title =        "Floating Point Fast {Fourier} Transform Computation
                 Using Double Precision Floating Point Accumulators",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "54--59",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355723",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65T05",
  MRnumber =     "55 \#11658",
  bibdate =      "Sat Aug 27 22:12:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Most commonly available fast Fourier transform (FFT)
                 subroutines use single precision chopping arithmetic,
                 and the resulting normalized roundoff error, in
                 computing an $N$-point transform with $ N = \prod_{i =
                 1}^M a_i $ is $ O(M^2) $. This paper proposes a
                 modification of these subroutines for use on computers
                 with a hardwired double precision arithmetic unit. The
                 resulting normalized roundoff error is $ O(M) $ and is
                 independent of the $ a_i $. The modification leads to a
                 negligible increase in storage. For most computers, the
                 increase in the execution time is small. For certain
                 computers, such as IBM System/360 models 91 and 195,
                 the modification can result in a decrease in the
                 execution time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computer arithmetic; double-length summation; fast
                 Fourier transform; roundoff error",
}


bibtype: article
filename: fparith.bib
label: Trivedi:1977:LAD
author: Kishor S. Trivedi and Milos D. Ercegovac
title: On-line algorithms for division and multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 681--687
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674901
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 30 07:29:16 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.30 07:29:16 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac
rawtitle: On-line algorithms for division and multiplication
entry:
@Article{Trivedi:1977:LAD,
  author =       "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
  title =        "On-line algorithms for division and multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "681--687",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674901",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 30 07:29:16 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: Trivedi:1977:UCF
author: K. S. Trivedi
title: On the Use of Continued Fractions for Digital Computer Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 700--704
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674903
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:56 MDT 2011
bibtimestamp: 2011.07.11 21:56:56 MDT
note: See corrections cite Trivedi:1978:CUC.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674903
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. S. Trivedi
rawnote: See corrections \cite{Trivedi:1978:CUC}.
rawtitle: On the Use of Continued Fractions for Digital Computer Arithmetic
entry:
@Article{Trivedi:1977:UCF,
  author =       "K. S. Trivedi",
  title =        "On the Use of Continued Fractions for Digital Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "700--704",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674903",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 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 corrections \cite{Trivedi:1978:CUC}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674903",
  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: Ushijima:1977:SEP
author: Kazuo Ushijima
title: Step to an Efficient Program for Floating-point Summation
journal: j-SPE
volume: 7
number: 6
pages: 759--769
month: nov
monthnumber: 11
year: 1977
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Sat May 31 13:36:16 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.31 13:36:16 MDT
fjournal: Software---Practice and Experience
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: Kazuo Ushijima
rawtitle: Step to an Efficient Program for Floating-point Summation
entry:
@Article{Ushijima:1977:SEP,
  author =       "Kazuo Ushijima",
  title =        "Step to an Efficient Program for Floating-point
                 Summation",
  journal =      j-SPE,
  volume =       "7",
  number =       "6",
  pages =        "759--769",
  month =        nov # "\slash " # dec,
  year =         "1977",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}


bibtype: article
filename: fparith.bib
label: Williams:1977:SIA
author: R. P. Williams
title: Serial Integer Arithmetic with Magnetic Bubbles
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 3
pages: 260--264
month: mar
monthnumber: 3
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674814
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:52 MDT 2011
bibtimestamp: 2011.07.11 21:56:52 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674814
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. P. Williams
rawtitle: Serial Integer Arithmetic with Magnetic Bubbles
entry:
@Article{Williams:1977:SIA,
  author =       "R. P. Williams",
  title =        "Serial Integer Arithmetic with Magnetic Bubbles",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "3",
  pages =        "260--264",
  month =        mar,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674814",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:52 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=1674814",
  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: Wozniakowski:1977:NSC
author: H. Wozniakowski
title: Numerical Stability of the Chebyshev Method for the Solution of Large Linear Systems
journal: j-NUM-MATH
volume: 28
number: 2
pages: 191--209
year: 1977
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Department of Computer Sci., Carnegie-Mellon University, Pittsburgh, PA, USA
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: H. Wo{\'z}niakowski
rawtitle: Numerical Stability of the {Chebyshev} Method for the Solution of Large Linear Systems
keywords:
Chebyshev approximation; Chebyshev method; computed residuals; error analysis; floating point arithmetic; iterative methods; large linear systems; linear systems; numerical stability; rounding error analysis

entry:
@Article{Wozniakowski:1977:NSC,
  author =       "H. Wo{\'z}niakowski",
  title =        "Numerical Stability of the {Chebyshev} Method for the
                 Solution of Large Linear Systems",
  journal =      j-NUM-MATH,
  volume =       "28",
  number =       "2",
  pages =        "191--209",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4110 (Error analysis in numerical methods); C4140
                 (Linear algebra)",
  corpsource =   "Department of Computer Sci., Carnegie-Mellon
                 University, Pittsburgh, PA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "Chebyshev approximation; Chebyshev method; computed
                 residuals; error analysis; floating point arithmetic;
                 iterative methods; large linear systems; linear
                 systems; numerical stability; rounding error analysis",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Yuen:1977:NRD
author: C. K. Yuen
title: A New Representation for Decimal Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 12
pages: 1286--1288
month: dec
monthnumber: 12
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674792
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Aug 07 18:00:38 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 18:00:38 ???
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: C. K. Yuen
rawtitle: A New Representation for Decimal Numbers
abstract:
A new representation for decimal numbers is proposed. It uses a mixture of positive and negative radixes to ensure that the maximum value of a four bit decimal digit is 9. This eliminates the more complex carry generation process required in BCD addition.

rawabstract:
A new representation for decimal numbers is proposed. It uses a mixture of positive and negative radixes to ensure that the maximum value of a four bit decimal digit is 9. This eliminates the more complex carry generation process required in BCD addition.

entry:
@Article{Yuen:1977:NRD,
  author =       "C. K. Yuen",
  title =        "A New Representation for Decimal Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "12",
  pages =        "1286--1288",
  month =        dec,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674792",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 07 18:00:38 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A new representation for decimal numbers is proposed.
                 It uses a mixture of positive and negative radixes to
                 ensure that the maximum value of a four bit decimal
                 digit is 9. This eliminates the more complex carry
                 generation process required in BCD addition.",
  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: inproceedings
filename: fparith.bib
label: Abu-El-Haija:1978:AER
author: A. Abu-El-Haija and A. Peterson
booktitle: IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '78
title: An approach to eliminate roundoff errors in digital filters
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 75--78
year: 1978
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: A. Abu-El-Haija and A. Peterson
rawbooktitle: {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '78}
rawtitle: An approach to eliminate roundoff errors in digital filters
entry:
@InProceedings{Abu-El-Haija:1978:AER,
  author =       "A. Abu-El-Haija and A. Peterson",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '78}",
  title =        "An approach to eliminate roundoff errors in digital
                 filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "75--78",
  year =         "1978",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Roundoff noise and limit cycle oscillations due to
                 postmultiplication rounding can seriously limit the
                 application of recursive digital filters in practice,
                 particularly for poles near the unit circle or near z =
                 +1. Rounding is usually performed by \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Agrawal:1978:AIR
author: Dharma P. Agrawal
title: On Arithmetic Inter-relationships and Hardware Interchangeability of Negabinary and Binary Systems
crossref: IEEE:1978:PSC
pages: 88--96
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal.pdf
acknowledgement: ack-nhfb
rawauthor: Dharma P. Agrawal
rawtitle: On Arithmetic Inter-relationships and Hardware Interchangeability of Negabinary and Binary Systems
abstract:
Recent use of the negabinary system in the application oriented digital hardware, has encouraged the search for suitable arithmetic algorithms in $ - 2 $ base. These algorithms have been directly utilized in designing logic circuits and several logic implementations have been reported in the literature. The main objective of this paper is to show the close relationship between $ + 2 $ base addition and $ - 2 $ base negative addition. Two possible ways of utilizing binary adders for performing negabinary addition and their underlying theories are presented. Two similar techniques of using negabinary adders for binary addition are also considered in detail. An interesting aspect of this investigation about negabinary base is that negative addition (rather than just addition) seems to be the primitive operation from logic complexity and interchangeability of $ + 2 $ and $ - 2 $ adders point of view.par The technique of adding two numbers in one system by the adders of the other system is extended here for multiple operand addition. This requires inclusion of an additional correction factor. Further, the additive algorithms of this work lead to four simple conversion processes of number from one system to another. This paper seems to be a realistic step towards the use of similar hardware for $ + 2 $ and $ - 2 $ bases and hence this allows an instantaneous flexibility on the selection of number system. It is believed that this paper will attract more attention on the use of $ - 2 $ base system for the design of special purpose digital machines and process controllers.

keywords:
Addition; ARITH-4; base conversion; binary numbers; even positioned bits; multiple addition; negabinary system; negative addition; negative radix; odd positioned bits.

rawabstract:
Recent use of the negabinary system in the application oriented digital hardware, has encouraged the search for suitable arithmetic algorithms in $ - 2 $ base. These algorithms have been directly utilized in designing logic circuits and several logic implementations have been reported in the literature. The main objective of this paper is to show the close relationship between $ + 2 $ base addition and $ - 2 $ base negative addition. Two possible ways of utilizing binary adders for performing negabinary addition and their underlying theories are presented. Two similar techniques of using negabinary adders for binary addition are also considered in detail. An interesting aspect of this investigation about negabinary base is that negative addition (rather than just addition) seems to be the primitive operation from logic complexity and interchangeability of $ + 2 $ and $ - 2 $ adders point of view.\par The technique of adding two numbers in one system by the adders of the other system is extended here for multiple operand addition. This requires inclusion of an additional correction factor. Further, the additive algorithms of this work lead to four simple conversion processes of number from one system to another. This paper seems to be a realistic step towards the use of similar hardware for $ + 2 $ and $ - 2 $ bases and hence this allows an instantaneous flexibility on the selection of number system. It is believed that this paper will attract more attention on the use of $ - 2 $ base system for the design of special purpose digital machines and process controllers.

entry:
@InProceedings{Agrawal:1978:AIR,
  author =       "Dharma P. Agrawal",
  title =        "On Arithmetic Inter-relationships and Hardware
                 Interchangeability of Negabinary and Binary Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "88--96",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal.pdf",
  abstract =     "Recent use of the negabinary system in the application
                 oriented digital hardware, has encouraged the search
                 for suitable arithmetic algorithms in $ - 2 $ base.
                 These algorithms have been directly utilized in
                 designing logic circuits and several logic
                 implementations have been reported in the literature.
                 The main objective of this paper is to show the close
                 relationship between $ + 2 $ base addition and $ - 2 $
                 base negative addition. Two possible ways of utilizing
                 binary adders for performing negabinary addition and
                 their underlying theories are presented. Two similar
                 techniques of using negabinary adders for binary
                 addition are also considered in detail. An interesting
                 aspect of this investigation about negabinary base is
                 that negative addition (rather than just addition)
                 seems to be the primitive operation from logic
                 complexity and interchangeability of $ + 2 $ and $ - 2
                 $ adders point of view.\par

                 The technique of adding two numbers in one system by
                 the adders of the other system is extended here for
                 multiple operand addition. This requires inclusion of
                 an additional correction factor. Further, the additive
                 algorithms of this work lead to four simple conversion
                 processes of number from one system to another. This
                 paper seems to be a realistic step towards the use of
                 similar hardware for $ + 2 $ and $ - 2 $ bases and
                 hence this allows an instantaneous flexibility on the
                 selection of number system. It is believed that this
                 paper will attract more attention on the use of $ - 2 $
                 base system for the design of special purpose digital
                 machines and process controllers.",
  acknowledgement = ack-nhfb,
  keywords =     "Addition; ARITH-4; base conversion; binary numbers;
                 even positioned bits; multiple addition; negabinary
                 system; negative addition; negative radix; odd
                 positioned bits.",
}


bibtype: inproceedings
filename: fparith.bib
label: Agrawal:1978:MAL
author: Dharma P. Agrawal and T. R. N. Rao
title: On Modular $ (2^n + 1) $ Arithmetic Logic
crossref: IEEE:1978:PSC
pages: 104--108
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal_Rao.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Dharma P. Agrawal and T. R. N. Rao
rawtitle: On Modular $ (2^n + 1) $ Arithmetic Logic
abstract:
A novel format for representing modulo $ (2^n + 1) $ numbers, is shown to be helpful in achieving modular addition and complementation. Logic for fast addition using carry-look-ahead and modular complementation is also presented.

rawabstract:
A novel format for representing modulo $ (2^n + 1) $ numbers, is shown to be helpful in achieving modular addition and complementation. Logic for fast addition using carry-look-ahead and modular complementation is also presented.

entry:
@InProceedings{Agrawal:1978:MAL,
  author =       "Dharma P. Agrawal and T. R. N. Rao",
  title =        "On Modular $ (2^n + 1) $ Arithmetic Logic",
  crossref =     "IEEE:1978:PSC",
  pages =        "104--108",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal_Rao.pdf",
  abstract =     "A novel format for representing modulo $ (2^n + 1) $
                 numbers, is shown to be helpful in achieving modular
                 addition and complementation. Logic for fast addition
                 using carry-look-ahead and modular complementation is
                 also presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: article
filename: fparith.bib
label: Andrews:1978:EFM
author: M. Andrews and S. F. McCormick and G. D. Taylor
title: Evaluation of Functions on Microcomputers: Square Root
journal: j-COMPUT-MATH-APPL
volume: 4
number: 4
pages: 359--367
year: 1978
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Sep 15 18:40:29 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:40:29 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: M. Andrews and S. F. McCormick and G. D. Taylor
rawtitle: Evaluation of Functions on Microcomputers: Square Root
entry:
@Article{Andrews:1978:EFM,
  author =       "M. Andrews and S. F. McCormick and G. D. Taylor",
  title =        "Evaluation of Functions on Microcomputers: Square
                 Root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "4",
  number =       "4",
  pages =        "359--367",
  year =         "1978",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:40:29 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 =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}


bibtype: article
filename: fparith.bib
label: Andrews:1978:IAN
author: M. Andrews
title: Influence of architecture on numerical algorithms
journal: j-MICROPROC-MICROSYS
volume: 2
number: 3
pages: 130--137
month: jun
monthnumber: 6
year: 1978
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
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: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: M. Andrews
rawtitle: Influence of architecture on numerical algorithms
entry:
@Article{Andrews:1978:IAN,
  author =       "M. Andrews",
  title =        "Influence of architecture on numerical algorithms",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "3",
  pages =        "130--137",
  month =        jun,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  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 =     "Microprocessors and Microsystems",
}


bibtype: article
filename: fparith.bib
label: Andrews:1978:UEF
author: M. Andrews and T. Mraz
title: Unified elementary function generator
journal: j-MICROPROC-MICROSYS
volume: 2
number: 5
pages: 270--273
month: oct
monthnumber: 10
year: 1978
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
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 ???
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: M. Andrews and T. Mraz
rawtitle: Unified elementary function generator
entry:
@Article{Andrews:1978:UEF,
  author =       "M. Andrews and T. Mraz",
  title =        "Unified elementary function generator",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "5",
  pages =        "270--273",
  month =        oct,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  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",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: manual
filename: fparith.bib
label: Apple:1978:AIR
title: Applesoft II reference manual: extended floating-point BASIC
organization: Apple Computer, Inc.
address: Cupertino, CA, USA
pages: 63
year: 1978
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: Apple II (Computer) --- Programming; BASIC (Computer program language)
acknowledgement: ack-nhfb
key: Apple
rawtitle: {Applesoft II} reference manual: extended floating-point {BASIC}
entry:
@Manual{Apple:1978:AIR,
  key =          "Apple",
  title =        "{Applesoft II} reference manual: extended
                 floating-point {BASIC}",
  organization = "Apple Computer, Inc.",
  address =      "Cupertino, CA, USA",
  pages =        "63",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming; BASIC (Computer
                 program language)",
}


bibtype: inproceedings
filename: fparith.bib
label: Atkins:1978:CTA
author: D. E. Atkins and S. C. Ong
title: A Comparison of Two Approaches to Multi-Operand Binary Addition
crossref: IEEE:1978:PSC
pages: 125--139
year: 1978
bibdate: Wed Nov 14 17:47:38 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:47:38 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Atkins.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: D. E. Atkins and S. C. Ong
rawtitle: A Comparison of Two Approaches to Multi-Operand Binary Addition
abstract:
This paper presents the results of one phase of a study concerning methods for addition of $ P > 2 $ numbers, each encoded as a vector of digits (digit vector) of length $N$. Such multi-operand addition has been studied most often in the context of reducing a set of partial products to a single result in the implementation of multiplication. More generalized multi-operand addition, most notably in the form of inner product calculations is, however, central to numerous scientific applications of digital computers. Although multioperand addition is trivially accomplished by accumulation (iteration in time) in any general purpose machine, demands for very high-speed computation, typified by 2- and 3-D signal processing prompt implementation of dedicated, hardware-intensive structures for multi-operand addition. This study, for example, is motivated in part by requirements for rapid simultaneous addition of up to 100, 16-bit operands in the design of a dedicated processor for real-time reconstruction of 3-D images of the beating heart and breathing lungs.

rawabstract:
This paper presents the results of one phase of a study concerning methods for addition of $ P > 2 $ numbers, each encoded as a vector of digits (digit vector) of length $N$. Such multi-operand addition has been studied most often in the context of reducing a set of partial products to a single result in the implementation of multiplication. More generalized multi-operand addition, most notably in the form of inner product calculations is, however, central to numerous scientific applications of digital computers. Although multioperand addition is trivially accomplished by accumulation (iteration in time) in any general purpose machine, demands for very high-speed computation, typified by 2- and 3-D signal processing prompt implementation of dedicated, hardware-intensive structures for multi-operand addition. This study, for example, is motivated in part by requirements for rapid simultaneous addition of up to 100, 16-bit operands in the design of a dedicated processor for real-time reconstruction of 3-D images of the beating heart and breathing lungs.

entry:
@InProceedings{Atkins:1978:CTA,
  author =       "D. E. Atkins and S. C. Ong",
  title =        "A Comparison of Two Approaches to Multi-Operand Binary
                 Addition",
  crossref =     "IEEE:1978:PSC",
  pages =        "125--139",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:47:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Atkins.pdf",
  abstract =     "This paper presents the results of one phase of a
                 study concerning methods for addition of $ P > 2 $
                 numbers, each encoded as a vector of digits (digit
                 vector) of length $N$. Such multi-operand addition has
                 been studied most often in the context of reducing a
                 set of partial products to a single result in the
                 implementation of multiplication. More generalized
                 multi-operand addition, most notably in the form of
                 inner product calculations is, however, central to
                 numerous scientific applications of digital computers.
                 Although multioperand addition is trivially
                 accomplished by accumulation (iteration in time) in any
                 general purpose machine, demands for very high-speed
                 computation, typified by 2- and 3-D signal processing
                 prompt implementation of dedicated, hardware-intensive
                 structures for multi-operand addition. This study, for
                 example, is motivated in part by requirements for rapid
                 simultaneous addition of up to 100, 16-bit operands in
                 the design of a dedicated processor for real-time
                 reconstruction of 3-D images of the beating heart and
                 breathing lungs.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: techreport
filename: fparith.bib
label: Banerji:1978:HSD
author: Dilip K. Banerji and To-Yat Cheung and V. Ganesan
title: A high speed division method in residue arithmetic
institution: Department of Computer Science, University of Ottawa
address: Ottawa, ON, Canada K1N 6N5
pages: 7
year: 1978
bibdate: Thu Nov 18 09:44:27 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:44:27 ???
URL: http://books.google.com/books?id=q8fBIwAACAAJ
remark: Credited to CH1630-3/81/0000/0158 IEEE 1981; where did this appear?
acknowledgement: ack-nhfb
rawauthor: Dilip K. Banerji and To-Yat Cheung and V. Ganesan
rawtitle: A high speed division method in residue arithmetic
entry:
@TechReport{Banerji:1978:HSD,
  author =       "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
  title =        "A high speed division method in residue arithmetic",
  institution =  "Department of Computer Science, University of Ottawa",
  address =      "Ottawa, ON, Canada K1N 6N5",
  pages =        "7",
  year =         "1978",
  bibdate =      "Thu Nov 18 09:44:27 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://books.google.com/books?id=q8fBIwAACAAJ",
  acknowledgement = ack-nhfb,
  remark =       "Credited to CH1630-3/81/0000/0158 IEEE 1981; where did
                 this appear?",
}


bibtype: article
filename: fparith.bib
label: Baraniecka:1978:DTR
author: A. Baraniecka and G. Jullien
title: On decoding techniques for residue number system realizations of digital signal processing hardware
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 25
number: 11
pages: 935--936
month: nov
monthnumber: 11
year: 1978
CODEN: ICSYBT
DOI: https://doi.org/10.1049/el:19770117
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23475
fjournal: IEEE Transactions on Circuits and Systems
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Baraniecka and G. Jullien
rawtitle: On decoding techniques for residue number system realizations of digital signal processing hardware
entry:
@Article{Baraniecka:1978:DTR,
  author =       "A. Baraniecka and G. Jullien",
  title =        "On decoding techniques for residue number system
                 realizations of digital signal processing hardware",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "25",
  number =       "11",
  pages =        "935--936",
  month =        nov,
  year =         "1978",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19770117",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23475",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "In a recent issue of this journal, a hardware
                 implementation of the Chinese Remainder Theorem was
                 proposed for the translation of residue coded outputs
                 into natural integer for an FIR filter realization. The
                 method requires a modulo M adder- \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Bareiss:1978:PEA
author: Erwin H. Bareiss and Jesse L. Barlow
title: Probabilistic error analysis of computer arithmetics
publisher: Department of Electrical Engineering and Computer Science, Northwestern University
address: Evanston, IL, USA
pages: 97
year: 1978
bibdate: Sat Nov 29 12:09:29 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.29 12:09:29 ???
acknowledgement: ack-nhfb
rawauthor: Erwin H. Bareiss and Jesse L. Barlow
rawtitle: Probabilistic error analysis of computer arithmetics
entry:
@Book{Bareiss:1978:PEA,
  author =       "Erwin H. Bareiss and Jesse L. Barlow",
  title =        "Probabilistic error analysis of computer arithmetics",
  publisher =    "Department of Electrical Engineering and Computer
                 Science, Northwestern University",
  address =      "Evanston, IL, USA",
  pages =        "97",
  year =         "1978",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 12:09:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Barsi:1978:ACR
author: F. Barsi and P. Maestrini
title: Arithmetic Codes in Residue Number Systems with Magnitude Index
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 12
pages: 1185--1188
month: dec
monthnumber: 12
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675023
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:33 MDT 2011
bibtimestamp: 2011.07.11 08:13:33 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: Arithmetic Codes in Residue Number Systems with Magnitude Index
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675023; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35165

entry:
@Article{Barsi:1978:ACR,
  author =       "F. Barsi and P. Maestrini",
  title =        "Arithmetic Codes in Residue Number Systems with
                 Magnitude Index",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "12",
  pages =        "1185--1188",
  month =        dec,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675023",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:33 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=1675023;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35165",
  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 idea of adding a magnitude index to the residue
                 representation of numbers is reconsidered. The range of
                 a given residue number system is supposed to be divided
                 into intervals of equal width, and the magnitude index
                 of a number X is defined as an \ldots{}",
}


bibtype: manual
filename: fparith.bib
label: BellHowellCo:1978:BHF
author: Bell and Howell Co and Apple Computer, Inc
title: [Bell and Howell floating point Basic programming reference manual]
organization: Bell and Howell, Audio-Visual Products Division
address: Chicago, IL, USA
pages: xiii + 168
year: 1978
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: Apple II (Computer) --- Programming.; BASIC (Computer program language)
acknowledgement: ack-nhfb
rawauthor: {Bell and Howell Co} and {Apple Computer, Inc}
rawtitle: [{Bell and Howell} floating point {Basic} programming reference manual]
remark:
Cover title. ``Reprinted with permission of Apple Computer, Inc.'' Companion volume: Floating point Basic tutorial manual. Quick reference guide on folded, inserted leaf.

entry:
@Manual{BellHowellCo:1978:BHF,
  author =       "{Bell and Howell Co} and {Apple Computer, Inc}",
  title =        "[{Bell and Howell} floating point {Basic} programming
                 reference manual]",
  organization = "Bell and Howell, Audio-Visual Products Division",
  address =      "Chicago, IL, USA",
  pages =        "xiii + 168",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming.; BASIC (Computer
                 program language)",
  remark =       "Cover title. ``Reprinted with permission of Apple
                 Computer, Inc.'' Companion volume: Floating point Basic
                 tutorial manual. Quick reference guide on folded,
                 inserted leaf.",
}


bibtype: article
filename: fparith.bib
label: Blue:1978:PFP
author: James L. Blue
title: A Portable Fortran Program to Find the Euclidean Norm of a Vector
journal: j-TOMS
volume: 4
number: 1
pages: 15--23
month: mar
monthnumber: 3
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355769.355771
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 68A10
MRnumber: 57 \#18205
bibdate: Sat Aug 27 23:14:36 1994
bibtimestamp: 1994.08.27 23:14:36 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
reviewer: A. D. Booth
rawauthor: James L. Blue
rawtitle: A Portable {Fortran} Program to Find the {Euclidean} Norm of a Vector
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib

keywords:
BLAS; floating-point arithmetic; floating-point overflow; floating-point underflow; nla; norm; software

entry:
@Article{Blue:1978:PFP,
  author =       "James L. Blue",
  title =        "A Portable {Fortran} Program to Find the {Euclidean}
                 Norm of a Vector",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "15--23",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355771",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10",
  MRnumber =     "57 \#18205",
  bibdate =      "Sat Aug 27 23:14:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; floating-point arithmetic; floating-point
                 overflow; floating-point underflow; nla; norm;
                 software",
  reviewer =     "A. D. Booth",
}


bibtype: techreport
filename: fparith.bib
label: Boehmer:1978:TAF
author: K. Boehmer and J. M. Yohe
title: Triplex Arithmetic for Fortran
type: MRC Technical Summary
number: 1901
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 38
month: dec
monthnumber: 12
year: 1978
bibdate: Fri Jan 12 11:37:56 1996
bibtimestamp: 1996.01.12 11:37:56 ???
keywords: Approximation theory.; Equations, Abelian.; Spline theory.
acknowledgement: ack-jr
rawauthor: K. Boehmer and J. M. Yohe
rawtitle: {Triplex} Arithmetic for {Fortran}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/intarith.bib

abstract:
Triplex arithmetic is a variant of interval arithmetic in which a 'main' value is computed in addition to the endpoints of the containing interval. The 'main' value is, in general, the value that would have been computed had properly-rounded real arithmetic been used to compute the results of the calculation; it may in some sense, be regarded as the 'most probable' value of the result of the calculation. The endpoints of the interval define the worst-case range of the possible values of the computation. This report describes a FORTRAN implementation of triplex arithmetic in both single and multiple precision. The package described in this report is designed to be used with the AUGMENT precompiler: this makes triplex arithmetic particularly easy to use.

rawabstract:
Triplex arithmetic is a variant of interval arithmetic in which a 'main' value is computed in addition to the endpoints of the containing interval. The 'main' value is, in general, the value that would have been computed had properly-rounded real arithmetic been used to compute the results of the calculation; it may in some sense, be regarded as the 'most probable' value of the result of the calculation. The endpoints of the interval define the worst-case range of the possible values of the computation. This report describes a FORTRAN implementation of triplex arithmetic in both single and multiple precision. The package described in this report is designed to be used with the AUGMENT precompiler: this makes triplex arithmetic particularly easy to use.

entry:
@TechReport{Boehmer:1978:TAF,
  author =       "K. Boehmer and J. M. Yohe",
  title =        "{Triplex} Arithmetic for {Fortran}",
  type =         "MRC Technical Summary",
  number =       "1901",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "38",
  month =        dec,
  year =         "1978",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intarith.bib",
  abstract =     "Triplex arithmetic is a variant of interval arithmetic
                 in which a 'main' value is computed in addition to the
                 endpoints of the containing interval. The 'main' value
                 is, in general, the value that would have been computed
                 had properly-rounded real arithmetic been used to
                 compute the results of the calculation; it may in some
                 sense, be regarded as the 'most probable' value of the
                 result of the calculation. The endpoints of the
                 interval define the worst-case range of the possible
                 values of the computation. This report describes a
                 FORTRAN implementation of triplex arithmetic in both
                 single and multiple precision. The package described in
                 this report is designed to be used with the AUGMENT
                 precompiler: this makes triplex arithmetic particularly
                 easy to use.",
  acknowledgement = ack-jr,
  keywords =     "Approximation theory.; Equations, Abelian.; Spline
                 theory.",
}


bibtype: phdthesis
filename: fparith.bib
label: Bohlender:1978:GBM
author: G. Bohlender
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1978
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 ???
keywords: accurate floating-point summation
acknowledgement: ack-nj
rawauthor: G. Bohlender
title:
Genaue Berechnung mehrfacher Summen, Produkte und Wurzeln von Gleitkommazahlen und allgemeine Arithmetik in hoheren Programmiersprachen toenglish Accurate Computation of Multiple Sums, Products and Roots of Floating-Point Numbers and General Arithmetic in High-Level Programming Languages endtoenglish 

rawtitle:
{Genaue Berechnung mehrfacher Summen, Produkte und Wurzeln von Gleitkommazahlen und allgemeine Arithmetik in h{\"o}heren Programmiersprachen} \toenglish {Accurate Computation of Multiple Sums, Products and Roots of Floating-Point Numbers and General Arithmetic in High-Level Programming Languages} \endtoenglish

entry:
@PhdThesis{Bohlender:1978:GBM,
  author =       "G. Bohlender",
  title =        "{Genaue Berechnung mehrfacher Summen, Produkte und
                 Wurzeln von Gleitkommazahlen und allgemeine Arithmetik
                 in h{\"o}heren Programmiersprachen} \toenglish
                 {Accurate Computation of Multiple Sums, Products and
                 Roots of Floating-Point Numbers and General Arithmetic
                 in High-Level Programming Languages} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1978",
  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,
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Boney:1978:MRW
author: J. Boney
title: Math in the Real World
journal: j-BYTE
volume: 3
number: 9
pages: 114--119
month: sep
monthnumber: 9
year: 1978
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
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: BYTE Magazine
acknowledgement: ack-nj
rawauthor: J. Boney
rawtitle: Math in the Real World
entry:
@Article{Boney:1978:MRW,
  author =       "J. Boney",
  title =        "Math in the Real World",
  journal =      j-BYTE,
  volume =       "3",
  number =       "9",
  pages =        "114--119",
  month =        sep,
  year =         "1978",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  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 =     "BYTE Magazine",
}


bibtype: article
filename: fparith.bib
label: Brady:1978:MBL
author: W. G. Brady
title: More on Benford's Law
journal: j-FIB-QUART
volume: 16
number: 1
pages: 51--52
month: feb
monthnumber: 2
year: 1978
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:59:24 MDT 2011
bibtimestamp: 2011.10.20 17:59:24 MDT
URL: http://www.fq.math.ca/Scanned/16-1/brady.pdf
fjournal: The Fibonacci Quarterly
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: W. G. Brady
rawtitle: More on {Benford}'s Law
bibsource:
http://www.fq.math.ca/16-1.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Brady:1978:MBL,
  author =       "W. G. Brady",
  title =        "More on {Benford}'s Law",
  journal =      j-FIB-QUART,
  volume =       "16",
  number =       "1",
  pages =        "51--52",
  month =        feb,
  year =         "1978",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:24 MDT 2011",
  bibsource =    "http://www.fq.math.ca/16-1.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/16-1/brady.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: techreport
filename: fparith.bib
label: Brent:1978:AIB
author: R. P. Brent and J. A. Hooper and J. M. Yohe
title: An Augment Interface for Brent's Multiple Precision Arithmetic Package
type: MRC Technical Summary
number: 1868
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 51--52
year: 1978
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 ???
note: Published In: ACM Trans. Math. Software 6, 146--149, 1980
acknowledgement: ack-jr
rawauthor: R. P. Brent and J. A. Hooper and J. M. Yohe
rawnote: Published In: ACM Trans. Math. Software 6, 146--149, 1980
rawtitle: An {Augment} Interface for {Brent}'s {Multiple Precision Arithmetic Package}
entry:
@TechReport{Brent:1978:AIB,
  author =       "R. P. Brent and J. A. Hooper and J. M. Yohe",
  title =        "An {Augment} Interface for {Brent}'s {Multiple
                 Precision Arithmetic Package}",
  type =         "MRC Technical Summary",
  number =       "1868",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  year =         "1978",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published In: ACM Trans. Math. Software 6, 146--149,
                 1980",
  acknowledgement = ack-jr,
}


bibtype: article
filename: fparith.bib
label: Brent:1978:AMF
author: Richard P. Brent
title: Algorithm 524: MP, A Fortran Multiple-Precision Arithmetic Package [A1]
journal: j-TOMS
volume: 4
number: 1
pages: 71--81
month: mar
monthnumber: 3
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355769.355776
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Sep 05 22:49:15 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.05 22:49:15 ???
note: See also cite Brent:1979:RMF,Brent:1980:AIB.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Richard P. Brent
rawnote: See also \cite{Brent:1979:RMF,Brent:1980:AIB}.
rawtitle: Algorithm 524: {MP}, {A Fortran} Multiple-Precision Arithmetic Package [{A1}]
entry:
@Article{Brent:1978:AMF,
  author =       "Richard P. Brent",
  title =        "Algorithm 524: {MP}, {A Fortran} Multiple-Precision
                 Arithmetic Package [{A1}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "71--81",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355776",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 22:49:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Brent:1979:RMF,Brent:1980:AIB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Brent:1978:FMP
author: Richard P. Brent
title: A Fortran Multiple-Precision Arithmetic Package
journal: j-TOMS
volume: 4
number: 1
pages: 57--70
month: mar
monthnumber: 3
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355769.355775
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 23:13:25 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.27 23:13:25 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Richard P. Brent
rawtitle: {A Fortran} Multiple-Precision Arithmetic Package
entry:
@Article{Brent:1978:FMP,
  author =       "Richard P. Brent",
  title =        "{A Fortran} Multiple-Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "57--70",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355775",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Case:1978:AIS
author: Richard P. Case and Andris Padegs
title: Architecture of the IBM System / 370
journal: j-CACM
volume: 21
number: 1
pages: 73--96
month: jan
monthnumber: 1
year: 1978
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Jan 29 18:00:28 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.01.29 18:00:28 ???
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Richard P. Case and Andris Padegs
rawtitle: Architecture of the {IBM System}\slash 370
entry:
@Article{Case:1978:AIS,
  author =       "Richard P. Case and Andris Padegs",
  title =        "Architecture of the {IBM System}\slash 370",
  journal =      j-CACM,
  volume =       "21",
  number =       "1",
  pages =        "73--96",
  month =        jan,
  year =         "1978",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Jan 29 18:00:28 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: techreport
filename: fparith.bib
label: Cherry:1978:BAP
author: Lorinda L. Cherry and Robert Morris
title: BC --- An Arbitrary Precision Desk Calculator Language
type: Technical Memorandum
number: 1053
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: 2 + 14
day: 12
month: nov
monthnumber: 11
year: 1978
bibdate: Tue Jun 06 08:07:45 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib
bibtimestamp: 2023.06.06 08:07:45 ???
remark: Available in PDF file of cite [pp. 383--398]Dolotta:1977:DPU.
acknowledgement: ack-nhfb
authordates: Lorinda L. Cherry (18 November 1944--February 2022); Robert Morris (25 July 1932--26 June 2011)
rawauthor: Lorinda L. Cherry and Robert Morris
rawtitle: {BC} --- An Arbitrary Precision Desk Calculator Language
abstract:
BC is a language and a compiler for doing arbitrary precision arithmetic on the PDP-11 under the UNIX time-sharing system. The output of the compiler is interpreted and executed by a collection of routines which can input, output. and do arithmetic on indefinitely large integers and on scaled fixed-point numbers.par These routines are themselves based on a dynamic storage allocator. Overflow does not occur until all available core storage is exhausted.par The language has a complete control structure as well as immediate-mode operation. Functions can be defined and saved for later execution.par Two five hundred-digit numbers can be multiplied to give a thousand digit result in about ten seconds.par A small collection of library functions is also available, including sin. cos, arctan, log, exponential, and Bessel functions of integer order.par Some of the uses of this compiler arepar * to do computation with large integers.par * to do computation accurate to many decimal places,par * conversion of numbers from one base to another base.

rawabstract:
BC is a language and a compiler for doing arbitrary precision arithmetic on the PDP-11 under the UNIX time-sharing system. The output of the compiler is interpreted and executed by a collection of routines which can input, output. and do arithmetic on indefinitely large integers and on scaled fixed-point numbers.\par These routines are themselves based on a dynamic storage allocator. Overflow does not occur until all available core storage is exhausted.\par The language has a complete control structure as well as immediate-mode operation. Functions can be defined and saved for later execution.\par Two five hundred-digit numbers can be multiplied to give a thousand digit result in about ten seconds.\par A small collection of library functions is also available, including sin. cos, arctan, log, exponential, and Bessel functions of integer order.\par Some of the uses of this compiler are\par * to do computation with large integers.\par * to do computation accurate to many decimal places,\par * conversion of numbers from one base to another base.

entry:
@TechReport{Cherry:1978:BAP,
  author =       "Lorinda L. Cherry and Robert Morris",
  title =        "{BC} --- An Arbitrary Precision Desk Calculator
                 Language",
  type =         "Technical Memorandum",
  number =       "1053",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "2 + 14",
  day =          "12",
  month =        nov,
  year =         "1978",
  bibdate =      "Tue Jun 06 08:07:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "BC is a language and a compiler for doing arbitrary
                 precision arithmetic on the PDP-11 under the UNIX
                 time-sharing system. The output of the compiler is
                 interpreted and executed by a collection of routines
                 which can input, output. and do arithmetic on
                 indefinitely large integers and on scaled fixed-point
                 numbers.\par

                 These routines are themselves based on a dynamic
                 storage allocator. Overflow does not occur until all
                 available core storage is exhausted.\par

                 The language has a complete control structure as well
                 as immediate-mode operation. Functions can be defined
                 and saved for later execution.\par

                 Two five hundred-digit numbers can be multiplied to
                 give a thousand digit result in about ten
                 seconds.\par

                 A small collection of library functions is also
                 available, including sin. cos, arctan, log,
                 exponential, and Bessel functions of integer
                 order.\par

                 Some of the uses of this compiler are\par

                 * to do computation with large integers.\par

                 * to do computation accurate to many decimal
                 places,\par

                 * conversion of numbers from one base to another
                 base.",
  abstract-2 =   "BC is a language and a compiler for doing arbitrary
                 precision arithmetic on the PDP-11 und UNIX
                 Time-Sharing System.",
  acknowledgement = ack-nhfb,
  author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
                 Robert Morris (25 July 1932--26 June 2011)",
  remark =       "Available in PDF file of \cite[pp.
                 383--398]{Dolotta:1977:DPU}.",
}


bibtype: inproceedings
filename: fparith.bib
label: Chow:1978:LDR
author: Catherine Y. Chow and James E. Robertson
title: Logical Design of a Redundant Binary Adder
crossref: IEEE:1978:PSC
pages: 109--115
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Chow.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Catherine Y. Chow and James E. Robertson
rawtitle: Logical Design of a Redundant Binary Adder
abstract:
This paper investigates the logical design of a redundant binary adder with two input digits and one output digit, all in the digit set $ bar 1, 0, 1 $. Redundant binary arithmetic structures in which all digit sets are $ bar 1, 0, 1 $ were first discussed by Avizienis in 1961. Borovec studied the logical design of a class of such binary adders and subtracters in 1968. At that time, a variation of the adder / subtracter was overlooked. This paper studies the logical design of this variation. The sum digit is still a function only of the digits in three adjacent digital positions of the operands. ``Coupled don't cares'' are encountered, but have not introduced too much difficulty. The nine distinct formats (under permutation and negation) of representing three values with two bits given by Robertson are used. The simplest adder / subtracter designs from this variation are less complex than the simplest designs previously known.

rawabstract:
This paper investigates the logical design of a redundant binary adder with two input digits and one output digit, all in the digit set $ \{ \bar {1}, 0, 1 \} $. Redundant binary arithmetic structures in which all digit sets are $ \{ \bar {1}, 0, 1 \} $ were first discussed by Avizienis in 1961. Borovec studied the logical design of a class of such binary adders and subtracters in 1968. At that time, a variation of the adder\slash subtracter was overlooked. This paper studies the logical design of this variation. The sum digit is still a function only of the digits in three adjacent digital positions of the operands. ``Coupled don't cares'' are encountered, but have not introduced too much difficulty. The nine distinct formats (under permutation and negation) of representing three values with two bits given by Robertson are used. The simplest adder\slash subtracter designs from this variation are less complex than the simplest designs previously known.

entry:
@InProceedings{Chow:1978:LDR,
  author =       "Catherine Y. Chow and James E. Robertson",
  title =        "Logical Design of a Redundant Binary Adder",
  crossref =     "IEEE:1978:PSC",
  pages =        "109--115",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Chow.pdf",
  abstract =     "This paper investigates the logical design of a
                 redundant binary adder with two input digits and one
                 output digit, all in the digit set $ \{ \bar {1}, 0, 1
                 \} $. Redundant binary arithmetic structures in which
                 all digit sets are $ \{ \bar {1}, 0, 1 \} $ were first
                 discussed by Avizienis in 1961. Borovec studied the
                 logical design of a class of such binary adders and
                 subtracters in 1968. At that time, a variation of the
                 adder\slash subtracter was overlooked. This paper
                 studies the logical design of this variation. The sum
                 digit is still a function only of the digits in three
                 adjacent digital positions of the operands. ``Coupled
                 don't cares'' are encountered, but have not introduced
                 too much difficulty. The nine distinct formats (under
                 permutation and negation) of representing three values
                 with two bits given by Robertson are used. The simplest
                 adder\slash subtracter designs from this variation are
                 less complex than the simplest designs previously
                 known.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Cohen:1978:MAI
author: Danny Cohen
title: Mathematical Approach to Iterative Computation Networks
crossref: IEEE:1978:PSC
pages: 226--237
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Cohen.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Danny Cohen
rawtitle: Mathematical Approach to Iterative Computation Networks
abstract:
This paper deals with design principles for iterative computation networks. Such computation networks are used for performing repetitive computations which typically are not data dependent. Most of the signal processing algorithms. like FFT and filtering, belong to this class.par The main idea in this paper is the development of mathematical notation for expressing such designs. This notation captures the important features and properties of these computation networks, and can be used both for analyzing and for designing computational networks.

rawabstract:
This paper deals with design principles for iterative computation networks. Such computation networks are used for performing repetitive computations which typically are not data dependent. Most of the signal processing algorithms. like FFT and filtering, belong to this class.\par The main idea in this paper is the development of mathematical notation for expressing such designs. This notation captures the important features and properties of these computation networks, and can be used both for analyzing and for designing computational networks.

entry:
@InProceedings{Cohen:1978:MAI,
  author =       "Danny Cohen",
  title =        "Mathematical Approach to Iterative Computation
                 Networks",
  crossref =     "IEEE:1978:PSC",
  pages =        "226--237",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Cohen.pdf",
  abstract =     "This paper deals with design principles for iterative
                 computation networks. Such computation networks are
                 used for performing repetitive computations which
                 typically are not data dependent. Most of the signal
                 processing algorithms. like FFT and filtering, belong
                 to this class.\par

                 The main idea in this paper is the development of
                 mathematical notation for expressing such designs. This
                 notation captures the important features and properties
                 of these computation networks, and can be used both for
                 analyzing and for designing computational networks.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: techreport
filename: fparith.bib
label: Coonen:1978:SPS
author: Jerome T. Coonen
title: Specification for a proposed standard for floating point arithmetic
type: Memorandum
number: ERL M78/72
institution: University of California, Berkeley
address: Berkeley, CA, USA
pages: 226--237
year: 1978
bibdate: Wed Nov 24 09:10:35 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 09:10:35 ???
acknowledgement: ack-nhfb
rawauthor: Jerome T. Coonen
rawtitle: Specification for a proposed standard for floating point arithmetic
entry:
@TechReport{Coonen:1978:SPS,
  author =       "Jerome T. Coonen",
  title =        "Specification for a proposed standard for floating
                 point arithmetic",
  type =         "Memorandum",
  number =       "ERL M78/72",
  institution =  "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  year =         "1978",
  bibdate =      "Wed Nov 24 09:10:35 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Corsini:1978:USM
author: P. Corsini and G. Frosini
title: Uniform Shift Multiplication Algorithms Without Overflow
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 3
pages: 256--258
month: mar
monthnumber: 3
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675081
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:27 MDT 2011
bibtimestamp: 2011.07.11 08:13:27 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675081
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Corsini and G. Frosini
rawtitle: Uniform Shift Multiplication Algorithms Without Overflow
entry:
@Article{Corsini:1978:USM,
  author =       "P. Corsini and G. Frosini",
  title =        "Uniform Shift Multiplication Algorithms Without
                 Overflow",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "3",
  pages =        "256--258",
  month =        mar,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675081",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:27 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=1675081",
  acknowledgement = 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: Crary:1978:APT
author: F. D. Crary and J. M. Yohe
title: The Augment Precompiler as a Tool for the Development of Special Purpose Arithmetic Packages
type: MRC Technical Summary
number: 1892
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 256--258
year: 1978
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 ???
acknowledgement: ack-jr
rawauthor: F. D. Crary and J. M. Yohe
rawtitle: The {Augment} Precompiler as a Tool for the Development of Special Purpose Arithmetic Packages
entry:
@TechReport{Crary:1978:APT,
  author =       "F. D. Crary and J. M. Yohe",
  title =        "The {Augment} Precompiler as a Tool for the
                 Development of Special Purpose Arithmetic Packages",
  type =         "MRC Technical Summary",
  number =       "1892",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  year =         "1978",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-jr,
}


bibtype: inproceedings
filename: fparith.bib
label: Dadda:1978:MAB
author: Luigi Dadda
title: Multiple Addition of Binary Serial Numbers
crossref: IEEE:1978:PSC
pages: 140--148
year: 1978
bibdate: Wed Nov 14 17:48:30 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:48:30 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Dadda.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
authordates: 29 April 1923--26 October 2012
rawauthor: Luigi Dadda
rawtitle: Multiple Addition of Binary Serial Numbers
abstract:
It is shown how circuits for the addition of several serial binary numbers can be obtained as a combination of parallel counters and memory cells.par The various schemes belong to one of three different classes, characterized by the way in which carries, produced by parallel counters, are treated.par A comparison is made between the various schemes, in terms of speed and complexity.

rawabstract:
It is shown how circuits for the addition of several serial binary numbers can be obtained as a combination of parallel counters and memory cells.\par The various schemes belong to one of three different classes, characterized by the way in which carries, produced by parallel counters, are treated.\par A comparison is made between the various schemes, in terms of speed and complexity.

entry:
@InProceedings{Dadda:1978:MAB,
  author =       "Luigi Dadda",
  title =        "Multiple Addition of Binary Serial Numbers",
  crossref =     "IEEE:1978:PSC",
  pages =        "140--148",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:48:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Dadda.pdf",
  abstract =     "It is shown how circuits for the addition of several
                 serial binary numbers can be obtained as a combination
                 of parallel counters and memory cells.\par

                 The various schemes belong to one of three different
                 classes, characterized by the way in which carries,
                 produced by parallel counters, are treated.\par

                 A comparison is made between the various schemes, in
                 terms of speed and complexity.",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-4",
}


bibtype: article
filename: fparith.bib
label: Debnath:1978:EMO
author: R. C. Debnath and D. A. Pucknell
title: Erratum: On multiplicative overflow detection in residue number system
journal: j-ELECT-LETTERS
volume: 14
number: 12
pages: 385
day: 8
month: jun
monthnumber: 6
year: 1978
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19780260
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
note: See cite Debnath:1978:MOD
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4241130
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: R. C. Debnath and D. A. Pucknell
rawnote: See \cite{Debnath:1978:MOD}
rawtitle: Erratum: On multiplicative overflow detection in residue number system
entry:
@Article{Debnath:1978:EMO,
  author =       "R. C. Debnath and D. A. Pucknell",
  title =        "Erratum: On multiplicative overflow detection in
                 residue number system",
  journal =      j-ELECT-LETTERS,
  volume =       "14",
  number =       "12",
  pages =        "385",
  day =          "8",
  month =        jun,
  year =         "1978",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19780260",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Debnath:1978:MOD}",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4241130",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
}


bibtype: article
filename: fparith.bib
label: Debnath:1978:MOD
author: R. C. Debnath and D. A. Pucknell
title: On multiplicative overflow detection in residue number system
journal: j-ELECT-LETTERS
volume: 14
number: 5
pages: 129--130
year: 1978
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19780088
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:57 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:57 MST
note: See erratum cite Debnath:1978:EMO.
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4240881
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: R. C. Debnath and D. A. Pucknell
rawnote: See erratum \cite{Debnath:1978:EMO}.
rawtitle: On multiplicative overflow detection in residue number system
entry:
@Article{Debnath:1978:MOD,
  author =       "R. C. Debnath and D. A. Pucknell",
  title =        "On multiplicative overflow detection in residue number
                 system",
  journal =      j-ELECT-LETTERS,
  volume =       "14",
  number =       "5",
  pages =        "129--130",
  month =        "????",
  year =         "1978",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19780088",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See erratum \cite{Debnath:1978:EMO}.",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4240881",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A general method for the detection of multiplicative
                 overflow has been developed. The method has been found
                 suitable in 16--15-mod residue system from the
                 consideration of cost and speed. A circuit for
                 16--15-mod-multiplicative overflow detection \ldots{}",
}


bibtype: misc
filename: fparith.bib
label: DEC-ES:1978:VIS
author: Digital Equipment Corporation.Educational Services
title: VAX-11 instruction set
publisher: Digital Equipment Corporation
address: Maynard, MA, USA
pages: 129--130
year: 1978
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
note: 13 videocassettes (ca. 585 min.)
keywords: decimal floating-point arithmetic; VAX-11 (Computer) --- Programming.
acknowledgement: ack-nhfb
rawauthor: {Digital Equipment Corporation.Educational Services}
rawnote: 13 videocassettes (ca. 585 min.)
rawtitle: {VAX-11} instruction set
remark:
Accompanied by 11 volumes of print materials, 1981. [1] Instruction formats and addressing modes, lesson 1 --- [2] Instruction formats and addressing modes, lessons 2 and 3 --- [3] Integer, logical, and branch instructions, lessons 1 and 2 --- [4] Integer, logical, and branch instructions, lessons 3 and 4 --- [5] Character string instructions, lessons 1 and 2 --- [6] Character string instructions, lessons 3 and 4 --- [7] Decimal string instructions, lessons 1 and 2 --- [8] Decimal string instructions, lessons 3, 4, and 5 --- [9] Special instructions --- [10] Procedures and subroutine instructions --- [11] Stack and address instructions --- [12] Variable bit field instructions --- [13] Floating point instructions. Provides an introduction to the VAX-11 computer system.

entry:
@Misc{DEC-ES:1978:VIS,
  author =       "{Digital Equipment Corporation.Educational Services}",
  title =        "{VAX-11} instruction set",
  publisher =    "Digital Equipment Corporation",
  address =      "Maynard, MA, USA",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "13 videocassettes (ca. 585 min.)",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; VAX-11 (Computer)
                 --- Programming.",
  remark =       "Accompanied by 11 volumes of print materials, 1981.
                 [1] Instruction formats and addressing modes, lesson 1
                 --- [2] Instruction formats and addressing modes,
                 lessons 2 and 3 --- [3] Integer, logical, and branch
                 instructions, lessons 1 and 2 --- [4] Integer, logical,
                 and branch instructions, lessons 3 and 4 --- [5]
                 Character string instructions, lessons 1 and 2 --- [6]
                 Character string instructions, lessons 3 and 4 --- [7]
                 Decimal string instructions, lessons 1 and 2 --- [8]
                 Decimal string instructions, lessons 3, 4, and 5 ---
                 [9] Special instructions --- [10] Procedures and
                 subroutine instructions --- [11] Stack and address
                 instructions --- [12] Variable bit field instructions
                 --- [13] Floating point instructions. Provides an
                 introduction to the VAX-11 computer system.",
}


bibtype: article
filename: fparith.bib
label: Diamond:1978:SRI
author: Harold G. Diamond
title: Stability of Rounded Off Inverses Under Iteration
journal: j-MATH-COMPUT
volume: 32
number: 141
pages: 227--232
month: jan
monthnumber: 1
year: 1978
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
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: function approximation; iterative methods; positive integer; rounded off inverse stability
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4130 (Interpolation and function approximation)
corpsource: Department of Math., University of Illinois, Urbana, IL, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Harold G. Diamond
rawtitle: Stability of Rounded Off Inverses Under Iteration
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database; Parallel/par.lin.alg.bib

entry:
@Article{Diamond:1978:SRI,
  author =       "Harold G. Diamond",
  title =        "Stability of Rounded Off Inverses Under Iteration",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "227--232",
  month =        jan,
  year =         "1978",
  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;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database; Parallel/par.lin.alg.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Department of Math., University of Illinois, Urbana,
                 IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function approximation; iterative methods; positive
                 integer; rounded off inverse stability",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Egbert:1978:PCA
author: W. E. Egbert
title: Personal Calculator Algorithms IV: Logarithmic Functions
journal: j-HEWLETT-PACKARD-J
volume: 29
number: 8
pages: 29--32
month: apr
monthnumber: 4
year: 1978
CODEN: HPJOAX
ISSN: 0018-1153 OR 00181153
bibdate: Thu Sep 1 10:16:09 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 10:16:09 ???
fjournal: Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company
acknowledgement: ack-nj
rawauthor: W. E. Egbert
rawtitle: Personal Calculator Algorithms {IV}: Logarithmic Functions
entry:
@Article{Egbert:1978:PCA,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {IV}: Logarithmic
                 Functions",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "29",
  number =       "8",
  pages =        "29--32",
  month =        apr,
  year =         "1978",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:16:09 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 =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1978:AME
author: M. D. Ercegovac and M. M. Takata
title: An Arithmetic Module for Efficient Evaluation of Functions
crossref: IEEE:1978:PSC
pages: 190--199
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac_Takata.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: M. D. Ercegovac and M. M. Takata
rawtitle: An Arithmetic Module for Efficient Evaluation of Functions
abstract:
The organization and design of an arithmetic module (Basic Byte-Slice Module --- BBM) is presented. A network of BBWs implements an efficient digit-by-digit method for fast evaluation of polynomial and rational functions. Verification of the BBW design, its feasibility in present LSI technologies and its performance are discussed. The proposed BBW is characterized by a small number of input / output terminals, a uniform internal structure, and simple control and inter-module communication requirements.

rawabstract:
The organization and design of an arithmetic module (Basic Byte-Slice Module --- BBM) is presented. A network of BBWs implements an efficient digit-by-digit method for fast evaluation of polynomial and rational functions. Verification of the BBW design, its feasibility in present LSI technologies and its performance are discussed. The proposed BBW is characterized by a small number of input\slash output terminals, a uniform internal structure, and simple control and inter-module communication requirements.

entry:
@InProceedings{Ercegovac:1978:AME,
  author =       "M. D. Ercegovac and M. M. Takata",
  title =        "An Arithmetic Module for Efficient Evaluation of
                 Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "190--199",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac_Takata.pdf",
  abstract =     "The organization and design of an arithmetic module
                 (Basic Byte-Slice Module --- BBM) is presented. A
                 network of BBWs implements an efficient digit-by-digit
                 method for fast evaluation of polynomial and rational
                 functions. Verification of the BBW design, its
                 feasibility in present LSI technologies and its
                 performance are discussed. The proposed BBW is
                 characterized by a small number of input\slash output
                 terminals, a uniform internal structure, and simple
                 control and inter-module communication requirements.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1978:FIS
author: Milos D. Ercegovac and Algirdas Avizienis
title: The Fourth IEEE Symposium on Computer Arithmetic: Foreword
crossref: IEEE:1978:PSC
pages: v--v
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac and Algirdas Avizienis
rawtitle: The {Fourth IEEE Symposium on Computer Arithmetic}: Foreword
URL:
http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_contents.pdf; http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_foreword.pdf; http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_preface.pdf

entry:
@InProceedings{Ercegovac:1978:FIS,
  author =       "Milo{\v{s}} D. Ercegovac and Algirdas Avizienis",
  title =        "The {Fourth IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "IEEE:1978:PSC",
  pages =        "v--v",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1978:LSR
author: Milos D. Ercegovac
title: An On-Line Square Rooting Algorithm
crossref: IEEE:1978:PSC
pages: 183--189
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac
rawtitle: An On-Line Square Rooting Algorithm
abstract:
An on-line algorithm for computing square roots in a radix 2, normalized floating-point number system with the redundant digit set $ - 1, 0, 1 $ is described. The algorithm has on-line delay of one and it is amenable for modular implementation. A systematic approach, used in deriving this algorithm, is presented in detail.

rawabstract:
An on-line algorithm for computing square roots in a radix 2, normalized floating-point number system with the redundant digit set $ \{ - 1, 0, 1 \} $ is described. The algorithm has on-line delay of one and it is amenable for modular implementation. A systematic approach, used in deriving this algorithm, is presented in detail.

entry:
@InProceedings{Ercegovac:1978:LSR,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "An On-Line Square Rooting Algorithm",
  crossref =     "IEEE:1978:PSC",
  pages =        "183--189",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
  abstract =     "An on-line algorithm for computing square roots in a
                 radix 2, normalized floating-point number system with
                 the redundant digit set $ \{ - 1, 0, 1 \} $ is
                 described. The algorithm has on-line delay of one and
                 it is amenable for modular implementation. A systematic
                 approach, used in deriving this algorithm, is presented
                 in detail.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: techreport
filename: fparith.bib
label: Espelid:1978:FPS
author: Terje O. Espelid
title: On floating-point summation
type: Report
number: 67
institution: Department of Applied Mathematics, University of Bergen
address: Bergen, Norway
pages: 24
year: 1978
bibdate: Thu May 09 08:03:27 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:03:27 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: Terje O. Espelid
rawtitle: On floating-point summation
entry:
@TechReport{Espelid:1978:FPS,
  author =       "Terje O. Espelid",
  title =        "On floating-point summation",
  type =         "Report",
  number =       "67",
  institution =  "Department of Applied Mathematics, University of
                 Bergen",
  address =      "Bergen, Norway",
  pages =        "24",
  year =         "1978",
  bibdate =      "Thu May 09 08:03:27 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: periodical
filename: fparith.bib
label: FloatingPointSystems:1978:P
author: Floating Point Systems, Inc
title: To the point
publisher: Floating Point Systems
address: Portland, OR, USA
pages: 24
year: 1978
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: Floating Point Systems, Inc. --- Periodicals.
remark: ``Employee newsletter.'' Title from caption.
acknowledgement: ack-nhfb
rawauthor: {Floating Point Systems, Inc}
rawtitle: To the point
entry:
@Periodical{FloatingPointSystems:1978:P,
  author =       "{Floating Point Systems, Inc}",
  title =        "To the point",
  publisher =    "Floating Point Systems",
  address =      "Portland, OR, USA",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  alttitle =     "To the point (Portland, Or.)",
  keywords =     "Floating Point Systems, Inc. --- Periodicals.",
  remark =       "``Employee newsletter.'' Title from caption.",
}


bibtype: article
filename: fparith.bib
label: Fox:1978:AFP
author: P. A. Fox and A. D. Hall and N. L. Schryer
title: Algorithm 528: Framework for a Portable Library [Z]
journal: j-TOMS
volume: 4
number: 2
pages: 177--188
month: jun
monthnumber: 6
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355780.355789
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 23:30:46 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.27 23:30:46 ???
note: See remarks cite Fox:1979:RFP,Gay:1999:SAF.
fjournal: ACM Transactions on Mathematical Software (TOMS)
language: English
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: P. A. Fox and A. D. Hall and N. L. Schryer
rawnote: See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.
rawtitle: {Algorithm 528}: Framework for a Portable Library [{Z}]
annote:
The three program packages presented here provide a framework for a portable FORTRAN subroutine library. They were developed for the BELL Laboratories library PORT(1). The packages are: machine-dependent constants, automatic error handling, and dynamic storage allocation using a stack.

entry:
@Article{Fox:1978:AFP,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "{Algorithm 528}: Framework for a Portable Library
                 [{Z}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "177--188",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355789",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:30:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.",
  acknowledgement = ack-nhfb,
  annote =       "The three program packages presented here provide a
                 framework for a portable FORTRAN subroutine library.
                 They were developed for the BELL Laboratories library
                 PORT(1). The packages are: machine-dependent constants,
                 automatic error handling, and dynamic storage
                 allocation using a stack.",
  country =      "USA",
  date =         "19/03/80",
  descriptors =  "Reliability; program construction; mathematical
                 method; FORTRAN; portability; error handling; memory
                 management; library",
  enum =         "988",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  language =     "English",
  location =     "RWTH-AC-DFV: TELL",
  references =   "1",
  revision =     "20/03/92",
}


bibtype: article
filename: fparith.bib
label: Fox:1978:PMS
author: P. A. Fox and A. D. Hall and N. L. Schryer
title: The PORT Mathematical Subroutine Library
journal: j-TOMS
volume: 4
number: 2
pages: 104--126
month: jun
monthnumber: 6
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355780.355783
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 23:13:25 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.27 23:13:25 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: dynamic storage allocation; error handling; libraries; numerical analysis; portability
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: P. A. Fox and A. D. Hall and N. L. Schryer
rawtitle: The {PORT} Mathematical Subroutine Library
abstract:
The development at Bell Laboratories of PORT, a library of portable Fortran programs for numerical computation, is discussed. Portability is achieved by careful language specification, together with the key technique of specifying computer classes by means of predefined machine constants. The library is built around an automatic error-handling facility and a dynamic storage allocation scheme, both of which are implemented portably. These, together with the modular structure of the library, lead to simplified calling sequences and ease of use.

rawabstract:
The development at Bell Laboratories of PORT, a library of portable Fortran programs for numerical computation, is discussed. Portability is achieved by careful language specification, together with the key technique of specifying computer classes by means of predefined machine constants. The library is built around an automatic error-handling facility and a dynamic storage allocation scheme, both of which are implemented portably. These, together with the modular structure of the library, lead to simplified calling sequences and ease of use.

entry:
@Article{Fox:1978:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "104--126",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The development at Bell Laboratories of PORT, a
                 library of portable Fortran programs for numerical
                 computation, is discussed. Portability is achieved by
                 careful language specification, together with the key
                 technique of specifying computer classes by means of
                 predefined machine constants. The library is built
                 around an automatic error-handling facility and a
                 dynamic storage allocation scheme, both of which are
                 implemented portably. These, together with the modular
                 structure of the library, lead to simplified calling
                 sequences and ease of use.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "dynamic storage allocation; error handling; libraries;
                 numerical analysis; portability",
}


bibtype: manual
filename: fparith.bib
label: FPS:1978:AAP
title: AP-120B Array Processor handbook
organization: Floating Point Systems, Inc.
address: Portland, OR, USA
year: 1978
bibdate: Fri Nov 09 10:52:30 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:52:30 ???
acknowledgement: ack-nhfb
key: FPS
rawtitle: {AP-120B} Array Processor handbook
entry:
@Manual{FPS:1978:AAP,
  key =          "FPS",
  title =        "{AP-120B} Array Processor handbook",
  organization = "Floating Point Systems, Inc.",
  address =      "Portland, OR, USA",
  pages =        "????",
  year =         "1978",
  bibdate =      "Fri Nov 09 10:52:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Fraley:1978:ZIR
author: B. Fraley
title: Zeros and Infinities Revisited and Gradual Underflow
type: Technical report
institution: HP Laboratories
address: 3500 Deer Creek Road, Palo Alto, CA 94304, USA
day: 28
month: dec
monthnumber: 12
year: 1978
bibdate: Fri Nov 09 10:53:38 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:53:38 ???
acknowledgement: ack-nhfb
rawauthor: B. Fraley
rawtitle: Zeros and Infinities Revisited and Gradual Underflow
entry:
@TechReport{Fraley:1978:ZIR,
  author =       "B. Fraley",
  title =        "Zeros and Infinities Revisited and Gradual Underflow",
  type =         "Technical report",
  institution =  "HP Laboratories",
  address =      "3500 Deer Creek Road, Palo Alto, CA 94304, USA",
  pages =        "????",
  day =          "28",
  month =        dec,
  year =         "1978",
  bibdate =      "Fri Nov 09 10:53:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Frankowski:1978:RME
author: Krzysztof S. Frankowski
title: A Realistic Model for Error Estimates in the Evaluation of Elementary Functions
crossref: IEEE:1978:PSC
pages: 70--74
year: 1978
bibdate: Thu Sep 01 11:22:03 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 11:22:03 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Frankowski.pdf
keywords: ARITH-4
acknowledgement: ack-nj
rawauthor: Krzysztof S. Frankowski
rawtitle: A Realistic Model for Error Estimates in the Evaluation of Elementary Functions
abstract:
Floating point error analysis, as described by J. H. Wilkinson (1963) has two known drawbacks: it is too pessimistic and too cumbersome for everyday use. This paper describes a realistic model for error analysis, gives examples of simple formulae frequently used in the calculation of elementary functions, and analyses the error generated in single precision computations with these formulae, using the proposed model for error analysis. The paper also presents error bounds for various polynomial evaluations, as predicted by the model. Model verification is done using double precision arithmetic.

rawabstract:
Floating point error analysis, as described by J. H. Wilkinson (1963) has two known drawbacks: it is too pessimistic and too cumbersome for everyday use. This paper describes a realistic model for error analysis, gives examples of simple formulae frequently used in the calculation of elementary functions, and analyses the error generated in single precision computations with these formulae, using the proposed model for error analysis. The paper also presents error bounds for various polynomial evaluations, as predicted by the model. Model verification is done using double precision arithmetic.

entry:
@InProceedings{Frankowski:1978:RME,
  author =       "Krzysztof S. Frankowski",
  title =        "A Realistic Model for Error Estimates in the
                 Evaluation of Elementary Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "70--74",
  year =         "1978",
  bibdate =      "Thu Sep 01 11:22:03 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/arith4/papers/ARITH4_Frankowski.pdf",
  abstract =     "Floating point error analysis, as described by J. H.
                 Wilkinson (1963) has two known drawbacks: it is too
                 pessimistic and too cumbersome for everyday use. This
                 paper describes a realistic model for error analysis,
                 gives examples of simple formulae frequently used in
                 the calculation of elementary functions, and analyses
                 the error generated in single precision computations
                 with these formulae, using the proposed model for error
                 analysis. The paper also presents error bounds for
                 various polynomial evaluations, as predicted by the
                 model. Model verification is done using double
                 precision arithmetic.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Gajski:1978:DAE
author: Daniel D. Gajski and L. P. Rubinfield
title: Design of Arithmetic Elements for Burroughs Scientific Processor
crossref: IEEE:1978:PSC
pages: 245--256
year: 1978
bibdate: Fri Nov 09 10:54:59 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:54:59 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Gajski.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Daniel D. Gajski and L. P. Rubinfield
rawtitle: Design of Arithmetic Elements for {Burroughs Scientific Processor}
abstract:
The design criteria and implementation of the Arithmetic Element (AE) of the Burroughs Scientific Processor, a vector machine intended for scientific computation requiring speed of up to 50 million floating-point operations per second, is discussed. An array of 16 AEs operate in lockstep mode, executing the same instruction on 16 sets of data. The 16 AEs are one stage in a pipeline which consists of 17 memory modules, an input alignment network, and an output alignment net-work. The AE itself is not pipelined. It can perform over one hundred different operations including a floating-point addition / subtraction and multiplication, division, square root, among the others. Eight registers are provided for the storage of intermediate values and results. Modulo 3 residue arithmetic is used for checking hardware failures.

rawabstract:
The design criteria and implementation of the Arithmetic Element (AE) of the Burroughs Scientific Processor, a vector machine intended for scientific computation requiring speed of up to 50 million floating-point operations per second, is discussed. An array of 16 AEs operate in lockstep mode, executing the same instruction on 16 sets of data. The 16 AEs are one stage in a pipeline which consists of 17 memory modules, an input alignment network, and an output alignment net-work. The AE itself is not pipelined. It can perform over one hundred different operations including a floating-point addition\slash subtraction and multiplication, division, square root, among the others. Eight registers are provided for the storage of intermediate values and results. Modulo 3 residue arithmetic is used for checking hardware failures.

entry:
@InProceedings{Gajski:1978:DAE,
  author =       "Daniel D. Gajski and L. P. Rubinfield",
  title =        "Design of Arithmetic Elements for {Burroughs
                 Scientific Processor}",
  crossref =     "IEEE:1978:PSC",
  pages =        "245--256",
  year =         "1978",
  bibdate =      "Fri Nov 09 10:54:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Gajski.pdf",
  abstract =     "The design criteria and implementation of the
                 Arithmetic Element (AE) of the Burroughs Scientific
                 Processor, a vector machine intended for scientific
                 computation requiring speed of up to 50 million
                 floating-point operations per second, is discussed. An
                 array of 16 AEs operate in lockstep mode, executing the
                 same instruction on 16 sets of data. The 16 AEs are one
                 stage in a pipeline which consists of 17 memory
                 modules, an input alignment network, and an output
                 alignment net-work. The AE itself is not pipelined. It
                 can perform over one hundred different operations
                 including a floating-point addition\slash subtraction
                 and multiplication, division, square root, among the
                 others. Eight registers are provided for the storage of
                 intermediate values and results. Modulo 3 residue
                 arithmetic is used for checking hardware failures.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Garcia:1978:AES
author: Oscar N. Garcia and Harvey Glass and Stanley C. Haines
crossref: IEEE:1978:PSC
pages: 97--103
year: 1978
bibdate: Wed Nov 14 17:49:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:49:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Garcia.pdf
keywords: ARITH-4; average worst case carry chain; binary addition; carry propagation
acknowledgement: ack-nhfb
rawauthor: Oscar N. Garcia and Harvey Glass and Stanley C. Haines
title:
An Approximate and Empirical Study of the Distribution of Adder Inputs and Maximum Carry Length Propagation

abstract:
This paper investigates, using sampled data, the commonly used hypothesis that integer operands reaching the adder of a computer are uniformly distributed. Questions raised on the validity of that hypothesis are reinforced and their impact on the calculation of the average of the worst case length of carry propagation is considered. An approximate formula is developed for the worst case carry chain length when the arithmetic operands are restricted in magnitude.

rawabstract:
This paper investigates, using sampled data, the commonly used hypothesis that integer operands reaching the adder of a computer are uniformly distributed. Questions raised on the validity of that hypothesis are reinforced and their impact on the calculation of the average of the worst case length of carry propagation is considered. An approximate formula is developed for the worst case carry chain length when the arithmetic operands are restricted in magnitude.

rawtitle:
An Approximate and Empirical Study of the Distribution of Adder Inputs and Maximum Carry Length Propagation

entry:
@InProceedings{Garcia:1978:AES,
  author =       "Oscar N. Garcia and Harvey Glass and Stanley C.
                 Haines",
  title =        "An Approximate and Empirical Study of the Distribution
                 of Adder Inputs and Maximum Carry Length Propagation",
  crossref =     "IEEE:1978:PSC",
  pages =        "97--103",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:49:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Garcia.pdf",
  abstract =     "This paper investigates, using sampled data, the
                 commonly used hypothesis that integer operands reaching
                 the adder of a computer are uniformly distributed.
                 Questions raised on the validity of that hypothesis are
                 reinforced and their impact on the calculation of the
                 average of the worst case length of carry propagation
                 is considered. An approximate formula is developed for
                 the worst case carry chain length when the arithmetic
                 operands are restricted in magnitude.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; average worst case carry chain; binary
                 addition; carry propagation",
}


bibtype: article
filename: fparith.bib
label: Garner:1978:TCA
author: H. L. Garner
title: Theory of Computer Addition and Overflows
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 4
pages: 297--301
month: apr
monthnumber: 4
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675101
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:28 MDT 2011
bibtimestamp: 2011.07.11 08:13:28 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675101
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. L. Garner
rawtitle: Theory of Computer Addition and Overflows
abstract:
Computer addition is a groupoid. If an additive identity exists it is unique. If(and only if) addition is defined with the compute through the overflow (CTO) property, then a finite ring of integers is the homomorphic image of the computer number system and addition. Stated another way, the necessary and sufficient condition for CTO is a congruence relation on the integers. Also, if the number system has CTO capabilities for addition, it also has extended CTO properties for addition. A technique is presented for determining the correct sum in the extended compute through overflow (ECTO) mode of computation.

keywords:
additive identity; compute through overflow (CTO); computer arithmetic; models of computer arithmetic; number systems; overflow behavior

rawabstract:
Computer addition is a groupoid. If an additive identity exists it is unique. If(and only if) addition is defined with the compute through the overflow (CTO) property, then a finite ring of integers is the homomorphic image of the computer number system and addition. Stated another way, the necessary and sufficient condition for CTO is a congruence relation on the integers. Also, if the number system has CTO capabilities for addition, it also has extended CTO properties for addition. A technique is presented for determining the correct sum in the extended compute through overflow (ECTO) mode of computation.

entry:
@Article{Garner:1978:TCA,
  author =       "H. L. Garner",
  title =        "Theory of Computer Addition and Overflows",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "4",
  pages =        "297--301",
  month =        apr,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675101",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:28 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=1675101",
  abstract =     "Computer addition is a groupoid. If an additive
                 identity exists it is unique. If(and only if) addition
                 is defined with the compute through the overflow (CTO)
                 property, then a finite ring of integers is the
                 homomorphic image of the computer number system and
                 addition. Stated another way, the necessary and
                 sufficient condition for CTO is a congruence relation
                 on the integers. Also, if the number system has CTO
                 capabilities for addition, it also has extended CTO
                 properties for addition. A technique is presented for
                 determining the correct sum in the extended compute
                 through overflow (ECTO) mode of computation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "additive identity; compute through overflow (CTO);
                 computer arithmetic; models of computer arithmetic;
                 number systems; overflow behavior",
}


bibtype: incollection
filename: fparith.bib
label: Gautschi:1978:QNC
author: Walter Gautschi
title: Questions of numerical conditions related to polynomials
volume: 41
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: 45--72
year: 1978
MRclass: 65D99
MRnumber: 519056
MRreviewer: Gerhard Merz
bibdate: Fri Feb 9 15:26:45 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.02.09 15:26:45 ???
series: Publ. Math. Res. Center University of Wisconsin
acknowledgement: ack-nhfb
rawauthor: Walter Gautschi
rawtitle: Questions of numerical conditions related to polynomials
booktitle:
Recent advances in numerical analysis (Proc. Sympos., Math. Res. Center, University of Wisconsin, Madison, Wis., 1978)

rawbooktitle:
Recent advances in numerical analysis ({Proc. Sympos., Math. Res. Center, University of Wisconsin, Madison, Wis., 1978})

entry:
@InCollection{Gautschi:1978:QNC,
  author =       "Walter Gautschi",
  booktitle =    "Recent advances in numerical analysis ({Proc. Sympos.,
                 Math. Res. Center, University of Wisconsin, Madison,
                 Wis., 1978})",
  title =        "Questions of numerical conditions related to
                 polynomials",
  volume =       "41",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "45--72",
  year =         "1978",
  MRclass =      "65D99",
  MRnumber =     "519056",
  MRreviewer =   "Gerhard Merz",
  bibdate =      "Fri Feb 9 15:26:45 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Publ. Math. Res. Center University of Wisconsin",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Good:1978:CMA
author: I. J. Good
title: C 24. A method for avoiding overflows and underflows
journal: j-J-STAT-COMPUT-SIMUL
volume: 8
number: 2
pages: 162--163
year: 1978
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949657808810261
ISSNL: 0094-9655 OR 00949655
bibdate: Tue Apr 22 09:10:43 MDT 2014
bibtimestamp: 2014.04.22 09:10:43 MDT
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
rawauthor: I. J. Good
rawtitle: {C 24}. {A} method for avoiding overflows and underflows
ISSN:
0094-9655 (print), 1026-7778 (electronic), 1563-5163 OR 00949655 (print), 10267778 (electronic), 15635163

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

entry:
@Article{Good:1978:CMA,
  author =       "I. J. Good",
  title =        "{C 24}. {A} method for avoiding overflows and
                 underflows",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "8",
  number =       "2",
  pages =        "162--163",
  year =         "1978",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657808810261",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:43 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}


bibtype: article
filename: fparith.bib
label: Goodman:1978:ITD
author: R. Goodman and J. Bustoz and A. Feldstein
title: Improved Trailing Digits Estimates Applied to Optimal Computer Arithmetic
journal: j-SIAM-REVIEW
volume: 20
number: 3
pages: 625--625
year: 1978
CODEN: SIREAD
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: R. Goodman and J. Bustoz and A. Feldstein
rawtitle: Improved Trailing Digits Estimates Applied to Optimal Computer Arithmetic
entry:
@Article{Goodman:1978:ITD,
  author =       "R. Goodman and J. Bustoz and A. Feldstein",
  title =        "Improved Trailing Digits Estimates Applied to Optimal
                 Computer Arithmetic",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "3",
  pages =        "625--625",
  month =        "????",
  year =         "1978",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "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",
}


bibtype: book
filename: fparith.bib
label: Hamacher:1978:CO
author: V. Carl Hamacher and Zvonko G. Vranesic and Safwat G. Zaky
title: Computer organization
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xiv + 465
year: 1978
ISBN: 0-07-025681-0 OR 0070256810
ISBN13: 978-0-07-025681-1 OR 9780070256811
LCCN: QA76.9.A73 H35
bibdate: Sat May 18 14:24:11 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:24:11 ???
series: McGraw-Hill series in computer organization and architecture
acknowledgement: ack-nhfb
rawauthor: V. Carl Hamacher and Zvonko G. Vranesic and Safwat G. Zaky
rawtitle: Computer organization
entry:
@Book{Hamacher:1978:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xiv + 465",
  year =         "1978",
  ISBN =         "0-07-025681-0",
  ISBN-13 =      "978-0-07-025681-1",
  LCCN =         "QA76.9.A73 H35",
  bibdate =      "Sat May 18 14:24:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Horspool:1978:EAU
author: R. Nigel Horspool and Eric C. R. Hehner
title: Exact Arithmetic Using a Variable-Length $p$-adic Representation
crossref: IEEE:1978:PSC
pages: 10--14
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Horspool.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: R. Nigel Horspool and Eric C. R. Hehner
rawtitle: Exact Arithmetic Using a Variable-Length $p$-adic Representation
abstract:
The $p$-adic number system is introduced and developed into a form suitable for performing exact arithmetic in computers. The proposed representation has several desirable attributes: the four standard arithmetic operations have a simple consistent form, the programmer has the ability to choose the precise degree of accuracy in his calculations and the variable-length nature of the representation achieves compact encodings

rawabstract:
The $p$-adic number system is introduced and developed into a form suitable for performing exact arithmetic in computers. The proposed representation has several desirable attributes: the four standard arithmetic operations have a simple consistent form, the programmer has the ability to choose the precise degree of accuracy in his calculations and the variable-length nature of the representation achieves compact encodings

entry:
@InProceedings{Horspool:1978:EAU,
  author =       "R. Nigel Horspool and Eric C. R. Hehner",
  title =        "Exact Arithmetic Using a Variable-Length $p$-adic
                 Representation",
  crossref =     "IEEE:1978:PSC",
  pages =        "10--14",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Horspool.pdf",
  abstract =     "The $p$-adic number system is introduced and developed
                 into a form suitable for performing exact arithmetic in
                 computers. The proposed representation has several
                 desirable attributes: the four standard arithmetic
                 operations have a simple consistent form, the
                 programmer has the ability to choose the precise degree
                 of accuracy in his calculations and the variable-length
                 nature of the representation achieves compact
                 encodings",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Hull:1978:DFP
author: T. E. Hull
title: Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation
crossref: IEEE:1978:PSC
pages: 63--69
year: 1978
DOI: https://doi.org/10.1109/arith.1978.6155780
bibdate: Thu Sep 01 12:14:34 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 12:14:34 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hull.pdf
keywords: ARITH-4; decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: T. E. Hull
rawtitle: Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation
abstract:
The purpose of this paper is to summarize proposed specifications for floating-point arithmetic and elementary functions. The topics considered are: the base of the number system, precision control, number representation, arithmetic operations, other basic operations, elementary functions, and exception handling. The possibility of doing without fixed-point arithmetic is also discussed.par The specifications are intended to be entirely at the level of a programming language such as Fortran. The emphasis is on convenience and simplicity from the user's point of view. The specifications are not complete in every detail, but it is intended that they be complete ``in spirit'' --- some further details, especially syntactic details, would have to be provided, but the proposals are otherwise relatively complete.

remark:
Refined and implemented later by cite Cohen:1983:CCP. The paper begins with the quote ``ldots the expression $ 25 + 1 / 3 $ yields the value $ 5.333333 $ in PL/I, and $ .333334 $ in PL/C ldots '', Conway and Gries, An Introduction to Programming, 1975, p. 24.

rawabstract:
The purpose of this paper is to summarize proposed specifications for floating-point arithmetic and elementary functions. The topics considered are: the base of the number system, precision control, number representation, arithmetic operations, other basic operations, elementary functions, and exception handling. The possibility of doing without fixed-point arithmetic is also discussed.\par The specifications are intended to be entirely at the level of a programming language such as Fortran. The emphasis is on convenience and simplicity from the user's point of view. The specifications are not complete in every detail, but it is intended that they be complete ``in spirit'' --- some further details, especially syntactic details, would have to be provided, but the proposals are otherwise relatively complete.

entry:
@InProceedings{Hull:1978:DFP,
  author =       "T. E. Hull",
  title =        "Desirable Floating-Point Arithmetic and Elementary
                 Functions for Numerical Computation",
  crossref =     "IEEE:1978:PSC",
  pages =        "63--69",
  year =         "1978",
  DOI =          "https://doi.org/10.1109/arith.1978.6155780",
  bibdate =      "Thu Sep 01 12:14:34 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/arith4/papers/ARITH4_Hull.pdf",
  abstract =     "The purpose of this paper is to summarize proposed
                 specifications for floating-point arithmetic and
                 elementary functions. The topics considered are: the
                 base of the number system, precision control, number
                 representation, arithmetic operations, other basic
                 operations, elementary functions, and exception
                 handling. The possibility of doing without fixed-point
                 arithmetic is also discussed.\par

                 The specifications are intended to be entirely at the
                 level of a programming language such as Fortran. The
                 emphasis is on convenience and simplicity from the
                 user's point of view. The specifications are not
                 complete in every detail, but it is intended that they
                 be complete ``in spirit'' --- some further details,
                 especially syntactic details, would have to be
                 provided, but the proposals are otherwise relatively
                 complete.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4; decimal floating-point arithmetic",
  remark =       "Refined and implemented later by
                 \cite{Cohen:1983:CCP}. The paper begins with the
                 quote

                 ``\ldots{} the expression $ 25 + 1 / 3 $ yields the
                 value $ 5.333333 $ in PL/I, and $ .333334 $ in PL/C
                 \ldots{}'', Conway and Gries, An Introduction to
                 Programming, 1975, p. 24.",
}


bibtype: inproceedings
filename: fparith.bib
label: Hwang:1978:IRR
author: Kai Hwang and T. P. Chang
title: An Interleaved Rational / Radix Arithmetic System for High-Precision Computations
crossref: IEEE:1978:PSC
pages: 15--24
year: 1978
bibdate: Wed Nov 14 17:49:59 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:49:59 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hwang.pdf
keywords: ARITH-4; Farey rational numbers
acknowledgement: ack-nhfb
rawauthor: Kai Hwang and T. P. Chang
rawtitle: An Interleaved Rational\slash Radix Arithmetic System for High-Precision Computations
abstract:
A new interleaved rational / radix number system is proposed for upgrading the precision of normalized Floating-Point (FLP) arithmetic operations without increasing the basic word length. A complete set of rational rounding and arithmetic algorithms are developed. The Average Relative Representation Error (ARRE) of the proposed flexible FLP system is computed through a series of simulation studies on CDC 6500. Our results show a 10% improvement of representation accuracy when compared with the ARRE of conventional FLP system. The architecture of a rational FLP arithmetic processor is also presented. Tradeoffs between operating speed and computing accuracy are discussed.

rawabstract:
A new interleaved rational\slash radix number system is proposed for upgrading the precision of normalized Floating-Point (FLP) arithmetic operations without increasing the basic word length. A complete set of rational rounding and arithmetic algorithms are developed. The Average Relative Representation Error (ARRE) of the proposed flexible FLP system is computed through a series of simulation studies on CDC 6500. Our results show a 10\% improvement of representation accuracy when compared with the ARRE of conventional FLP system. The architecture of a rational FLP arithmetic processor is also presented. Tradeoffs between operating speed and computing accuracy are discussed.

entry:
@InProceedings{Hwang:1978:IRR,
  author =       "Kai Hwang and T. P. Chang",
  title =        "An Interleaved Rational\slash Radix Arithmetic System
                 for High-Precision Computations",
  crossref =     "IEEE:1978:PSC",
  pages =        "15--24",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:49:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hwang.pdf",
  abstract =     "A new interleaved rational\slash radix number system
                 is proposed for upgrading the precision of normalized
                 Floating-Point (FLP) arithmetic operations without
                 increasing the basic word length. A complete set of
                 rational rounding and arithmetic algorithms are
                 developed. The Average Relative Representation Error
                 (ARRE) of the proposed flexible FLP system is computed
                 through a series of simulation studies on CDC 6500. Our
                 results show a 10\% improvement of representation
                 accuracy when compared with the ARRE of conventional
                 FLP system. The architecture of a rational FLP
                 arithmetic processor is also presented. Tradeoffs
                 between operating speed and computing accuracy are
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; Farey rational numbers",
}


bibtype: manual
filename: fparith.bib
label: Intel:1978:FAL
author: Intel Corporation
title: 8080 / 8085 floating-point arithmetic library: user's manual
organization: Intel Corporation
address: Santa Clara, CA, USA
pages: various
year: 1978
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: Intel 8080 (Microprocessor) --- Programming.; Intel 8085 (Microprocessor) --- Programming.
remark: ``Manual order number: 9800452B.''
acknowledgement: ack-nhfb
rawauthor: {Intel Corporation}
rawtitle: 8080\slash 8085 floating-point arithmetic library: user's manual
entry:
@Manual{Intel:1978:FAL,
  author =       "{Intel Corporation}",
  title =        "8080\slash 8085 floating-point arithmetic library:
                 user's manual",
  organization = "Intel Corporation",
  address =      "Santa Clara, CA, USA",
  pages =        "various",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Intel 8080 (Microprocessor) --- Programming.; Intel
                 8085 (Microprocessor) --- Programming.",
  remark =       "``Manual order number: 9800452B.''",
}


bibtype: inproceedings
filename: fparith.bib
label: Jullien:1978:ARN
author: G. A. Jullien and W. C. Miller
title: Application of the Residue Number System to Computer Processing of Digital Signals
crossref: IEEE:1978:PSC
pages: 220--225
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Jullien.pdf
keywords: ARITH-4; residue number system
acknowledgement: ack-nhfb
rawauthor: G. A. Jullien and W. C. Miller
rawtitle: Application of the Residue Number System to Computer Processing of Digital Signals
abstract:
The residue number system offers parallel processing, digital hardware implementations for the binary operations of addition, subtraction and multiplication. This paper discusses the use of the residue number system in implementing digital signal processing functions, in which these binary operations abound. The paper covers implementations using arrays of read only memories, and briefly discusses the use of parallel microprocessor structures. ROM array implementations of scaling operations are also presented.

rawabstract:
The residue number system offers parallel processing, digital hardware implementations for the binary operations of addition, subtraction and multiplication. This paper discusses the use of the residue number system in implementing digital signal processing functions, in which these binary operations abound. The paper covers implementations using arrays of read only memories, and briefly discusses the use of parallel microprocessor structures. ROM array implementations of scaling operations are also presented.

entry:
@InProceedings{Jullien:1978:ARN,
  author =       "G. A. Jullien and W. C. Miller",
  title =        "Application of the Residue Number System to Computer
                 Processing of Digital Signals",
  crossref =     "IEEE:1978:PSC",
  pages =        "220--225",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Jullien.pdf",
  abstract =     "The residue number system offers parallel processing,
                 digital hardware implementations for the binary
                 operations of addition, subtraction and multiplication.
                 This paper discusses the use of the residue number
                 system in implementing digital signal processing
                 functions, in which these binary operations abound. The
                 paper covers implementations using arrays of read only
                 memories, and briefly discusses the use of parallel
                 microprocessor structures. ROM array implementations of
                 scaling operations are also presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; residue number system",
}


bibtype: article
filename: fparith.bib
label: Jullien:1978:RNS
author: G. A. Jullien
title: Residue Number Scaling and Other Operations Using ROM Arrays
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 4
pages: 325--336
month: apr
monthnumber: 4
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675105
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:28 MDT 2011
bibtimestamp: 2011.07.11 08:13:28 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: G. A. Jullien
rawtitle: Residue Number Scaling and Other Operations Using {ROM} Arrays
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675105; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35168

entry:
@Article{Jullien:1978:RNS,
  author =       "G. A. Jullien",
  title =        "Residue Number Scaling and Other Operations Using
                 {ROM} Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "4",
  pages =        "325--336",
  month =        apr,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675105",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:28 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=1675105;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35168",
  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 =      "Over the last two decades there has been considerable
                 interest in the implementation of digital computer
                 elements using hardware based on the residue number
                 system. This paper considers implementing such systems
                 with arrays of look-up tables placed \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Kahan:1978:KSI
author: W. Kahan and B. N. Parlett
title: Konnen Sie sich auf Ihren Rechner verlassen? (German) [Can you count on your calculator?]
journal: Jahrbuch Uberblicke Mathematik
pages: 199--216
year: 1978
bibdate: Fri Nov 11 06:36:51 MST 2005
bibtimestamp: 2005.11.11 06:36:51 MST
keywords: Automated Algorithms; Error of Computation; Pocket Calculator
language: German
ZMnumber: 0397.65081
acknowledgement: ack-nhfb
rawauthor: W. Kahan and B. N. Parlett
rawtitle: {K{\"o}nnen Sie sich auf Ihren Rechner verlassen?} ({German}) [Can you count on your calculator?]
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Kahan:1978:KSI,
  author =       "W. Kahan and B. N. Parlett",
  title =        "{K{\"o}nnen Sie sich auf Ihren Rechner verlassen?}
                 ({German}) [Can you count on your calculator?]",
  journal =      "{Jahrbuch {\"U}berblicke Mathematik}",
  volume =       "??",
  pages =        "199--216",
  year =         "1978",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0397.65081",
  acknowledgement = ack-nhfb,
  classmath =    "*65Y99 Computer aspects of numerical algorithms 65D20
                 Computation of special functions 00A99 Miscellaneous
                 topics in general mathematics",
  keywords =     "Automated Algorithms; Error of Computation; Pocket
                 Calculator",
  language =     "German",
}


bibtype: inproceedings
filename: fparith.bib
label: Koren:1978:UAC
author: Israel Koren and Yoram Maliniak
title: A Unified Approach to a Class of Number Systems
crossref: IEEE:1978:PSC
pages: 25--28
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Koren.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Israel Koren and Yoram Maliniak
rawtitle: A Unified Approach to a Class of Number Systems
abstract:
A unified approach to a broad class of number systems is proposed in this paper. This class contains all positive and negative radix systems and other well-known number systems. The proposed approach enables us to develop a single set of algorithms for arithmetic operations and conversion methods between number systems.

rawabstract:
A unified approach to a broad class of number systems is proposed in this paper. This class contains all positive and negative radix systems and other well-known number systems. The proposed approach enables us to develop a single set of algorithms for arithmetic operations and conversion methods between number systems.

entry:
@InProceedings{Koren:1978:UAC,
  author =       "Israel Koren and Yoram Maliniak",
  title =        "A Unified Approach to a Class of Number Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "25--28",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Koren.pdf",
  abstract =     "A unified approach to a broad class of number systems
                 is proposed in this paper. This class contains all
                 positive and negative radix systems and other
                 well-known number systems. The proposed approach
                 enables us to develop a single set of algorithms for
                 arithmetic operations and conversion methods between
                 number systems.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Kornerup:1978:FAF
author: Peter Kornerup and David W. Matula
title: A Feasibility Analysis of Fixed-Slash and Floating-Slash Arithmetic
crossref: IEEE:1978:PSC
pages: {39--47}
year: 1978
bibdate: Wed Nov 14 17:50:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:50:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Kornerup.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Peter Kornerup and David W. Matula
rawtitle: A Feasibility Analysis of Fixed-Slash and Floating-Slash Arithmetic
abstract:
An investigation of the feasibility of a finite precision approximate rational arithmetic based on fixed-slash representation of rational numbers is presented. Worst-case and average-case complexity analyses of the involved rounding algorithm (an extended shift-subtract gcd algorithm) are presented. The results are applied to a proposed hardware realization of a fixed-slash arithmetic unit.

rawabstract:
An investigation of the feasibility of a finite precision approximate rational arithmetic based on fixed-slash representation of rational numbers is presented. Worst-case and average-case complexity analyses of the involved rounding algorithm (an extended shift-subtract gcd algorithm) are presented. The results are applied to a proposed hardware realization of a fixed-slash arithmetic unit.

entry:
@InProceedings{Kornerup:1978:FAF,
  author =       "Peter Kornerup and David W. Matula",
  title =        "A Feasibility Analysis of Fixed-Slash and
                 Floating-Slash Arithmetic",
  crossref =     "IEEE:1978:PSC",
  pages =        "{39--47}",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:50:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Kornerup.pdf",
  abstract =     "An investigation of the feasibility of a finite
                 precision approximate rational arithmetic based on
                 fixed-slash representation of rational numbers is
                 presented. Worst-case and average-case complexity
                 analyses of the involved rounding algorithm (an
                 extended shift-subtract gcd algorithm) are presented.
                 The results are applied to a proposed hardware
                 realization of a fixed-slash arithmetic unit.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Krishnamurthy:1978:MPP
author: E. V. Krishnamurthy and H. Venkateswaran
title: Multivariable Polynomial Processing --- Applications to Interpolation
crossref: IEEE:1978:PSC
pages: 81--87
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Krishnamurthy.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: E. V. Krishnamurthy and H. Venkateswaran
rawtitle: Multivariable Polynomial Processing --- Applications to Interpolation
abstract:
A data-structure suitable for multivariable polynomial processing in introduced. Using this data structure, arithmetic algorithms are described for addition, subtraction and multiplication of multivariable polynomials; also algorithms are described for forming the inner product and tensor product of vectors, Those components are multivariable polynomials. Application of these algorithms for multivariable cardinal spline approximation is described in detail.

rawabstract:
A data-structure suitable for multivariable polynomial processing in introduced. Using this data structure, arithmetic algorithms are described for addition, subtraction and multiplication of multivariable polynomials; also algorithms are described for forming the inner product and tensor product of vectors, Those components are multivariable polynomials. Application of these algorithms for multivariable cardinal spline approximation is described in detail.

entry:
@InProceedings{Krishnamurthy:1978:MPP,
  author =       "E. V. Krishnamurthy and H. Venkateswaran",
  title =        "Multivariable Polynomial Processing --- Applications
                 to Interpolation",
  crossref =     "IEEE:1978:PSC",
  pages =        "81--87",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Krishnamurthy.pdf",
  abstract =     "A data-structure suitable for multivariable polynomial
                 processing in introduced. Using this data structure,
                 arithmetic algorithms are described for addition,
                 subtraction and multiplication of multivariable
                 polynomials; also algorithms are described for forming
                 the inner product and tensor product of vectors, Those
                 components are multivariable polynomials. Application
                 of these algorithms for multivariable cardinal spline
                 approximation is described in detail.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: book
filename: fparith.bib
label: Kuck:1978:SCC
author: David J. Kuck
title: The structure of computers and computations
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xxii + 611
year: 1978
ISBN: 0-471-02716-2 (vol. 1), 0-471-08138-8 OR 0471027162 (vol. 1), 0471081388
ISBN13: 978-0-471-02716-4 (vol. 1), 978-0-471-08138-8 OR 9780471027164 (vol. 1), 9780471081388
LCCN: QA76.9.A73 K83
bibdate: Mon May 20 05:05:46 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.20 05:05:46 ???
note: See Chapter 3 for floating-point arithmetic discussion.
acknowledgement: ack-nhfb
rawauthor: David J. Kuck
rawnote: See Chapter 3 for floating-point arithmetic discussion.
rawtitle: The structure of computers and computations
entry:
@Book{Kuck:1978:SCC,
  author =       "David J. Kuck",
  title =        "The structure of computers and computations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xxii + 611",
  year =         "1978",
  ISBN =         "0-471-02716-2 (vol. 1), 0-471-08138-8",
  ISBN-13 =      "978-0-471-02716-4 (vol. 1), 978-0-471-08138-8",
  LCCN =         "QA76.9.A73 K83",
  bibdate =      "Mon May 20 05:05:46 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See Chapter 3 for floating-point arithmetic
                 discussion.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Liddiard:1978:RSF
author: L. A. Liddiard
title: Required Scientific Floating Point Arithmetic
crossref: IEEE:1978:PSC
pages: 56--62
year: 1978
bibdate: Thu Sep 01 11:06:57 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 11:06:57 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Liddiard.pdf
acknowledgement: ack-nj
rawauthor: L. A. Liddiard
rawtitle: Required Scientific Floating Point Arithmetic
abstract:
Previous papers in computer arithmetic have shown that correct rounded floating point with good arithmetic properties can be attained using guard digits and careful algorithms on the floating point fractions. This paper combines that body of knowledge with proposed exponent forms that are closed with respect to inversion and detection and recovery of exponent under- and overflow. In addition radix 2 is shown to be the only base radix meeting minimal variation of precision, a condition necessary for the safe use of floating point. An effort is made to establish objective criteria in answer to the question ``What is the best division of the computer word into exponent and fraction parts?''. Combining the previous results allows a required scientific floating point arithmetic to be portrayed and compared with available arithmetic on current computers.

keywords:
ARITH-4; arithmetic properties; correct rounding; exponent over; Floating point exponents; floating-point arithmetic; optimal base radix

rawabstract:
Previous papers in computer arithmetic have shown that correct rounded floating point with good arithmetic properties can be attained using guard digits and careful algorithms on the floating point fractions. This paper combines that body of knowledge with proposed exponent forms that are closed with respect to inversion and detection and recovery of exponent under- and overflow. In addition radix 2 is shown to be the only base radix meeting minimal variation of precision, a condition necessary for the safe use of floating point. An effort is made to establish objective criteria in answer to the question ``What is the best division of the computer word into exponent and fraction parts?''. Combining the previous results allows a required scientific floating point arithmetic to be portrayed and compared with available arithmetic on current computers.

entry:
@InProceedings{Liddiard:1978:RSF,
  author =       "L. A. Liddiard",
  title =        "Required Scientific Floating Point Arithmetic",
  crossref =     "IEEE:1978:PSC",
  pages =        "56--62",
  year =         "1978",
  bibdate =      "Thu Sep 01 11:06:57 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/arith4/papers/ARITH4_Liddiard.pdf",
  abstract =     "Previous papers in computer arithmetic have shown that
                 correct rounded floating point with good arithmetic
                 properties can be attained using guard digits and
                 careful algorithms on the floating point fractions.
                 This paper combines that body of knowledge with
                 proposed exponent forms that are closed with respect to
                 inversion and detection and recovery of exponent under-
                 and overflow. In addition radix 2 is shown to be the
                 only base radix meeting minimal variation of precision,
                 a condition necessary for the safe use of floating
                 point. An effort is made to establish objective
                 criteria in answer to the question ``What is the best
                 division of the computer word into exponent and
                 fraction parts?''. Combining the previous results
                 allows a required scientific floating point arithmetic
                 to be portrayed and compared with available arithmetic
                 on current computers.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4; arithmetic properties; correct rounding;
                 exponent over; Floating point exponents; floating-point
                 arithmetic; optimal base radix",
}


bibtype: inproceedings
filename: fparith.bib
label: Lillevik:1978:CDA
author: Sigurd L. Lillevik and P. David Fisher
title: Computational Design Alternatives with Microprocessor-Based Systems
crossref: IEEE:1978:PSC
pages: 267--272
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lillevik.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Sigurd L. Lillevik and P. David Fisher
rawtitle: Computational Design Alternatives with Microprocessor-Based Systems
abstract:
This paper examines and characterizes four elemental hardware computational design alternatives (CDA's) and presents a structured approach to computational section design which incorporates a rigorous, theoretic foundation. The DIRECT CDA incorporates a single microprocessor ($ mu $P) and memory. The AU CDA contains a $ mu $P, memory, and arithmetic unit. $ mu $P, memory, and calculator chip comprise the CALC CDA. Finally, several $ mu $P's and memories in a Master / Slave arrangement implement the multiple-$ mu $P m$ mu $P CDA. A common set of attributes --- precision, speed and cost --- facilitates comparison. Using these attributes, Multiattribute Utility Theory assesses a numeric quantity, the utility, to represent each CDA's relative usefulness. Thus, design involves selecting the CDA with the greatest utility.

rawabstract:
This paper examines and characterizes four elemental hardware computational design alternatives (CDA's) and presents a structured approach to computational section design which incorporates a rigorous, theoretic foundation. The DIRECT CDA incorporates a single microprocessor ($ \mu $P) and memory. The AU CDA contains a $ \mu $P, memory, and arithmetic unit. $ \mu $P, memory, and calculator chip comprise the CALC CDA. Finally, several $ \mu $P's and memories in a Master\slash Slave arrangement implement the multiple-$ \mu $P m$ \mu $P CDA. A common set of attributes --- precision, speed and cost --- facilitates comparison. Using these attributes, Multiattribute Utility Theory assesses a numeric quantity, the utility, to represent each CDA's relative usefulness. Thus, design involves selecting the CDA with the greatest utility.

entry:
@InProceedings{Lillevik:1978:CDA,
  author =       "Sigurd L. Lillevik and P. David Fisher",
  title =        "Computational Design Alternatives with
                 Microprocessor-Based Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "267--272",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lillevik.pdf",
  abstract =     "This paper examines and characterizes four elemental
                 hardware computational design alternatives (CDA's) and
                 presents a structured approach to computational section
                 design which incorporates a rigorous, theoretic
                 foundation. The DIRECT CDA incorporates a single
                 microprocessor ($ \mu $P) and memory. The AU CDA
                 contains a $ \mu $P, memory, and arithmetic unit. $ \mu
                 $P, memory, and calculator chip comprise the CALC CDA.
                 Finally, several $ \mu $P's and memories in a
                 Master\slash Slave arrangement implement the multiple-$
                 \mu $P m$ \mu $P CDA. A common set of attributes ---
                 precision, speed and cost --- facilitates comparison.
                 Using these attributes, Multiattribute Utility Theory
                 assesses a numeric quantity, the utility, to represent
                 each CDA's relative usefulness. Thus, design involves
                 selecting the CDA with the greatest utility.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Lim:1978:HSM
author: Raymond S. Lim
title: High-Speed Multiplication and Multiple Summand Addition
crossref: IEEE:1978:PSC
pages: 149--153
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lim.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Raymond S. Lim
rawtitle: High-Speed Multiplication and Multiple Summand Addition
abstract:
The problem of high-speed multiplication is considered from the viewpoint of summand generation and summand summation. The goal is to obtain at least a 2's-complement, 32-bit floating-point (sign plus 24-bit fraction) multiplication in 10 to 20 ns using ECL LSI packages. Summand generation is implemented by $ m times m $-bit multipliers. The optimum values for $m$ are 9, 13, 17, or 21. Summand summation is implemented by a row of $ (p, 2) $ column-summing counters. The $ (0, 2) $, $ (5, 2) $, and $ (7, 2) $ counters are optimum choices. These counters compress $p$ inputs into two outputs plus nonpropagating carry bits, where these bits are added to the next higher-order stage with at most two full adder delays.

rawabstract:
The problem of high-speed multiplication is considered from the viewpoint of summand generation and summand summation. The goal is to obtain at least a 2's-complement, 32-bit floating-point (sign plus 24-bit fraction) multiplication in 10 to 20 ns using ECL LSI packages. Summand generation is implemented by $ m \times m $-bit multipliers. The optimum values for $m$ are 9, 13, 17, or 21. Summand summation is implemented by a row of $ (p, 2) $ column-summing counters. The $ (0, 2) $, $ (5, 2) $, and $ (7, 2) $ counters are optimum choices. These counters compress $p$ inputs into two outputs plus nonpropagating carry bits, where these bits are added to the next higher-order stage with at most two full adder delays.

entry:
@InProceedings{Lim:1978:HSM,
  author =       "Raymond S. Lim",
  title =        "High-Speed Multiplication and Multiple Summand
                 Addition",
  crossref =     "IEEE:1978:PSC",
  pages =        "149--153",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lim.pdf",
  abstract =     "The problem of high-speed multiplication is considered
                 from the viewpoint of summand generation and summand
                 summation. The goal is to obtain at least a
                 2's-complement, 32-bit floating-point (sign plus 24-bit
                 fraction) multiplication in 10 to 20 ns using ECL LSI
                 packages. Summand generation is implemented by $ m
                 \times m $-bit multipliers. The optimum values for $m$
                 are 9, 13, 17, or 21. Summand summation is implemented
                 by a row of $ (p, 2) $ column-summing counters. The $
                 (0, 2) $, $ (5, 2) $, and $ (7, 2) $ counters are
                 optimum choices. These counters compress $p$ inputs
                 into two outputs plus nonpropagating carry bits, where
                 these bits are added to the next higher-order stage
                 with at most two full adder delays.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: article
filename: fparith.bib
label: Liu:1978:ECC
author: Chao-Kai Liu and Tse Lin Wang
title: Error-Correcting Codes in Binary-Coded-Decimal Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 11
pages: 977--984
month: nov
monthnumber: 11
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1674987
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Aug 07 17:26:15 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 17:26:15 ???
fjournal: IEEE Transactions on Computers
keywords: BCD arithmetic; decimal arithmetic
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Chao-Kai Liu and Tse Lin Wang
rawtitle: Error-Correcting Codes in Binary-Coded-Decimal Arithmetic
abstract:
Error-correcting coding schemes devised for binary arithmetic are not in general applicable to BCD arithmetic. In this paper, we investigate the new problem of using such coding schemes in BCD systems. We first discuss the general characteristics of arithmetic errors and define the arithmetic weight and distance in BCD systems. We show that the distance is a metric function. Number theory is used to construct a class of single-error-correcting codes for BCD arithmetic. It is shown that the generator of these codes possesses a very simple form and the structure of these codes can be analytically determined.

rawabstract:
Error-correcting coding schemes devised for binary arithmetic are not in general applicable to BCD arithmetic. In this paper, we investigate the new problem of using such coding schemes in BCD systems. We first discuss the general characteristics of arithmetic errors and define the arithmetic weight and distance in BCD systems. We show that the distance is a metric function. Number theory is used to construct a class of single-error-correcting codes for BCD arithmetic. It is shown that the generator of these codes possesses a very simple form and the structure of these codes can be analytically determined.

entry:
@Article{Liu:1978:ECC,
  author =       "Chao-Kai Liu and Tse Lin Wang",
  title =        "Error-Correcting Codes in Binary-Coded-Decimal
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "11",
  pages =        "977--984",
  month =        nov,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1674987",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 07 17:26:15 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Error-correcting coding schemes devised for binary
                 arithmetic are not in general applicable to BCD
                 arithmetic. In this paper, we investigate the new
                 problem of using such coding schemes in BCD systems. We
                 first discuss the general characteristics of arithmetic
                 errors and define the arithmetic weight and distance in
                 BCD systems. We show that the distance is a metric
                 function. Number theory is used to construct a class of
                 single-error-correcting codes for BCD arithmetic. It is
                 shown that the generator of these codes possesses a
                 very simple form and the structure of these codes can
                 be analytically determined.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "BCD arithmetic; decimal arithmetic",
}


bibtype: article
filename: fparith.bib
label: Logan:1978:FDP
author: Jonothan L. Logan and Samuel A. Goudsmit
title: The First Digit Phenomenon
journal: j-PROC-AMER-PHIL-SOC
volume: 122
number: 4
pages: 193--197
day: 18
month: aug
monthnumber: 8
year: 1978
CODEN: PAPCAA
ISSN: 0003-049X (print), 2326-9243 (electronic) OR 0003049X (print), 23269243 (electronic)
ISSNL: 0003-049X OR 0003049X
bibdate: Fri Mar 30 11:20:35 2007
bibtimestamp: 2007.03.30 11:20:35 ???
acknowledgement: ack-nhfb
authordates: Samuel A. Goudsmit (July 11, 1902--December 4, 1978)
journalURL: http://www.jstor.org/journal/procamerphilsoci
rawauthor: Jonothan L. Logan and Samuel A. Goudsmit
rawtitle: The First Digit Phenomenon
note:
This paper contains derivations of both Stigler's Law and Benford's Law, and receives strong criticism in cite Raimi:1985:FDP. This paper contains an important historical note that is recorded in entry cite Benford:1938:LAN.

URL:
http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C; http://www.jstor.org/stable/986530

abstract:
Forty years ago an article appeared in these Proceedings, which has since then attracted much attention of mathematicians and some physicists. It was written by Frank Benford, a physicist from the General Electric Company at Schenectady. He had examined a large number of numerical tables, the kind that are printed in almanacs, and in scientific and technical handbooks. He noticed a most unusual and unexpected property of many of these tables. Consider, for example, the numbers representing the populations of states or all the countries in the world, or their areas, their budgets, their numbers of hospital beds, etc. One would expect that on the average just as many of these entries would begin with the digit $1$ as with $2$ or $3$ or $4$, and so on. But Benford noticed that small values of the first digits occur far more often.

fjournal:
Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledge

remark:
In 1925, Samuel Goudsmit and George Uhlenbeck proposed the concept of electron spin, a critical step forward in the quantum mechanics of many-electron systems. Surprisingly, that work did not get them the Nobel Prize, but it did spur Wolfgang Pauli to present his Exclusion Principle in 1925, for which he received the 1945 Nobel Prize in Physics. After World War II, Goudsmit was the scientific head of the Alsos mission to capture German nuclear scientists. In the 1950s, he founded the journal Physical Review Letters. During the 1960s and 1970s, he was Editor-in-Chief of the main American physics journal, the Physical Review.

rawabstract:
Forty years ago an article appeared in these Proceedings, which has since then attracted much attention of mathematicians and some physicists. It was written by Frank Benford, a physicist from the General Electric Company at Schenectady. He had examined a large number of numerical tables, the kind that are printed in almanacs, and in scientific and technical handbooks. He noticed a most unusual and unexpected property of many of these tables. Consider, for example, the numbers representing the populations of states or all the countries in the world, or their areas, their budgets, their numbers of hospital beds, etc. One would expect that on the average just as many of these entries would begin with the digit $1$ as with $2$ or $3$ or $4$, and so on. But Benford noticed that small values of the first digits occur far more often.

rawnote:
This paper contains derivations of both Stigler's Law and Benford's Law, and receives strong criticism in \cite{Raimi:1985:FDP}. This paper contains an important historical note that is recorded in entry \cite{Benford:1938:LAN}.

entry:
@Article{Logan:1978:FDP,
  author =       "Jonothan L. Logan and Samuel A. Goudsmit",
  title =        "The First Digit Phenomenon",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "122",
  number =       "4",
  pages =        "193--197",
  day =          "18",
  month =        aug,
  year =         "1978",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Fri Mar 30 11:20:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper contains derivations of both Stigler's Law
                 and Benford's Law, and receives strong criticism in
                 \cite{Raimi:1985:FDP}. This paper contains an important
                 historical note that is recorded in entry
                 \cite{Benford:1938:LAN}.",
  URL =          "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
                 http://www.jstor.org/stable/986530",
  abstract =     "Forty years ago an article appeared in these
                 Proceedings, which has since then attracted much
                 attention of mathematicians and some physicists. It was
                 written by Frank Benford, a physicist from the General
                 Electric Company at Schenectady. He had examined a
                 large number of numerical tables, the kind that are
                 printed in almanacs, and in scientific and technical
                 handbooks. He noticed a most unusual and unexpected
                 property of many of these tables. Consider, for
                 example, the numbers representing the populations of
                 states or all the countries in the world, or their
                 areas, their budgets, their numbers of hospital beds,
                 etc. One would expect that on the average just as many
                 of these entries would begin with the digit $1$ as with
                 $2$ or $3$ or $4$, and so on. But Benford noticed that
                 small values of the first digits occur far more
                 often.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1978:BDS
author: David W. Matula
title: Basic Digit Sets for Radix Representation of the Integers
crossref: IEEE:1978:PSC
pages: 1--9
year: 1978
bibdate: Wed Nov 14 17:51:32 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:51:32 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula.pdf
keywords: ARITH-4; base; digit representation; finite and infinite precision; non-standard number
acknowledgement: ack-nhfb
rawauthor: David W. Matula
rawtitle: Basic Digit Sets for Radix Representation of the Integers
abstract:
Let $Z$ denote the set of integers. A digit set $ D in Z $ is basic for base $ beta in Z $ if the set of polynomials $ d_m beta ^m + d_m - 1 beta ^m - 1 + ldots + d_1 beta + d_0 | d_i in D $ contains a unique representation for every $ n in Z $. We give necessary and sufficient conditions for D to be basic for $ beta $. We exhibit efficient procedures for verifying that $D$ is basic for $S$, and for computing the representation of any $ n in Z $ when a representation exists. There exist $D$, $S$ with $D$ basic for $S$ where $ max |d| vert d in D > | beta | $, and more generally, an infinite class of basic digit sets is shown to exist for every base $S$ with $ beta geq 3 $. The natural extension to infinite precision radix representation using basic digit sets is considered and a summary of results is presented.

rawabstract:
Let $Z$ denote the set of integers. A digit set $ D \in Z $ is basic for base $ \beta \in Z $ if the set of polynomials $ \{ d_m \beta^m + d_{m - 1} \beta^{m - 1} + \ldots {} + d_1 \beta + d_0 | d_i \in D \} $ contains a unique representation for every $ n \in Z $. We give necessary and sufficient conditions for D to be basic for $ \beta $. We exhibit efficient procedures for verifying that $D$ is basic for $S$, and for computing the representation of any $ n \in Z $ when a representation exists. There exist $D$, $S$ with $D$ basic for $S$ where $ \max \{ |d| \vert d \in D \} > | \beta | $, and more generally, an infinite class of basic digit sets is shown to exist for every base $S$ with $ \beta \geq 3 $. The natural extension to infinite precision radix representation using basic digit sets is considered and a summary of results is presented.

entry:
@InProceedings{Matula:1978:BDS,
  author =       "David W. Matula",
  title =        "Basic Digit Sets for Radix Representation of the
                 Integers",
  crossref =     "IEEE:1978:PSC",
  pages =        "1--9",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:51:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula.pdf",
  abstract =     "Let $Z$ denote the set of integers. A digit set $ D
                 \in Z $ is basic for base $ \beta \in Z $ if the set of
                 polynomials $ \{ d_m \beta^m + d_{m - 1} \beta^{m - 1}
                 + \ldots {} + d_1 \beta + d_0 | d_i \in D \} $ contains
                 a unique representation for every $ n \in Z $. We give
                 necessary and sufficient conditions for D to be basic
                 for $ \beta $. We exhibit efficient procedures for
                 verifying that $D$ is basic for $S$, and for computing
                 the representation of any $ n \in Z $ when a
                 representation exists. There exist $D$, $S$ with $D$
                 basic for $S$ where $ \max \{ |d| \vert d \in D \} > |
                 \beta | $, and more generally, an infinite class of
                 basic digit sets is shown to exist for every base $S$
                 with $ \beta \geq 3 $. The natural extension to
                 infinite precision radix representation using basic
                 digit sets is considered and a summary of results is
                 presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; base; digit representation; finite and
                 infinite precision; non-standard number",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1978:FAF
author: David W. Matula and Peter Kornerup
title: A Feasibility Analysis of Fixed-Slash and Floating-Slash Number Systems
crossref: IEEE:1978:PSC
pages: {29--38}
year: 1978
bibdate: Wed Nov 14 17:52:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.14 17:52:07 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula_Kornerup.pdf
acknowledgement: ack-nhfb
rawauthor: David W. Matula and Peter Kornerup
rawtitle: A Feasibility Analysis of Fixed-Slash and Floating-Slash Number Systems
abstract:
Design and analysis of finite precision rational number systems based on fixed-slash and floating-slash representation is pursued. Natural formats for binary fixed-slash and binary floating-slash number representation in computer words are described. Compatibility with standard integer representation is obtained. Redundancy in the representation is shown to be minimal. Arithmetic register requirements are considered. Worst case and average case rounding errors are determined, and the concept of adaptive variable precision in the rounding is developed.

keywords:
adaptive variable precision; adjacent fractions; ARITH-4; binary numeric word format; Farey fractions; finite precision; fixed-slash numbers; floating-slash numbers; integer compatibility; mediant roundings; range of number system; rational arithmetic; redundancy; worst case and average case rounding error

rawabstract:
Design and analysis of finite precision rational number systems based on fixed-slash and floating-slash representation is pursued. Natural formats for binary fixed-slash and binary floating-slash number representation in computer words are described. Compatibility with standard integer representation is obtained. Redundancy in the representation is shown to be minimal. Arithmetic register requirements are considered. Worst case and average case rounding errors are determined, and the concept of adaptive variable precision in the rounding is developed.

entry:
@InProceedings{Matula:1978:FAF,
  author =       "David W. Matula and Peter Kornerup",
  title =        "A Feasibility Analysis of Fixed-Slash and
                 Floating-Slash Number Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "{29--38}",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:52:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula_Kornerup.pdf",
  abstract =     "Design and analysis of finite precision rational
                 number systems based on fixed-slash and floating-slash
                 representation is pursued. Natural formats for binary
                 fixed-slash and binary floating-slash number
                 representation in computer words are described.
                 Compatibility with standard integer representation is
                 obtained. Redundancy in the representation is shown to
                 be minimal. Arithmetic register requirements are
                 considered. Worst case and average case rounding errors
                 are determined, and the concept of adaptive variable
                 precision in the rounding is developed.",
  acknowledgement = ack-nhfb,
  keywords =     "adaptive variable precision; adjacent fractions;
                 ARITH-4; binary numeric word format; Farey fractions;
                 finite precision; fixed-slash numbers; floating-slash
                 numbers; integer compatibility; mediant roundings;
                 range of number system; rational arithmetic;
                 redundancy; worst case and average case rounding
                 error",
}


bibtype: article
filename: fparith.bib
label: McCrea:1978:CFP
author: P. G. McCrea and P. C. Maxwell and P. W. Baker
title: Comments on ``A Floating-Point Multiplexed DDA System''
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 12
pages: 1226--1226
month: dec
monthnumber: 12
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675033
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:33 MDT 2011
bibtimestamp: 2011.07.11 08:13:33 MDT
note: See cite Hannington:1976:FPM.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675033
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. G. McCrea and P. C. Maxwell and P. W. Baker
rawnote: See \cite{Hannington:1976:FPM}.
rawtitle: Comments on {``A Floating-Point Multiplexed DDA System''}
entry:
@Article{McCrea:1978:CFP,
  author =       "P. G. McCrea and P. C. Maxwell and P. W. Baker",
  title =        "Comments on {``A Floating-Point Multiplexed DDA
                 System''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "12",
  pages =        "1226--1226",
  month =        dec,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675033",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:33 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{Hannington:1976:FPM}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675033",
  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: Mitra:1978:ITD
author: S. K. Mitra and G. K. Sorknes
title: On the Implementation of a Two-Dimensional FIR Filter Using a Single Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 8
pages: 762--764
month: aug
monthnumber: 8
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675186
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:30 MDT 2011
bibtimestamp: 2011.07.11 08:13:30 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675186
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. K. Mitra and G. K. Sorknes
rawtitle: On the Implementation of a Two-Dimensional {FIR} Filter Using a Single Multiplier
entry:
@Article{Mitra:1978:ITD,
  author =       "S. K. Mitra and G. K. Sorknes",
  title =        "On the Implementation of a Two-Dimensional {FIR}
                 Filter Using a Single Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "8",
  pages =        "762--764",
  month =        aug,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675186",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:30 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=1675186",
  acknowledgement = 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: Morris:1978:DID
author: Robert Morris and Lorinda Cherry
title: DC --- An Interactive Desk Calculator
type: Technical Memorandum
number: 1056
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: 8
day: 15
month: nov
monthnumber: 11
year: 1978
bibdate: Tue Jun 06 08:07:45 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib
bibtimestamp: 2023.06.06 08:07:45 ???
remark: Available in PDF file of cite [pp. 399--406]Dolotta:1977:DPU.
acknowledgement: ack-nhfb
authordates: Lorinda L. Cherry (18 November 1944--February 2022); Robert Morris (25 July 1932--26 June 2011)
rawauthor: Robert Morris and Lorinda Cherry
rawtitle: {DC} --- An Interactive Desk Calculator
abstract:
DC is an arbitrary precision arithmetic package implemented on the UNIX time-sharing system in the form of an interactive desk calculator. It works like a stacking calculator using reverse Polish notation. Ordinarily DC operates on decimal integers, but one may specify an input base, output base, and a number of fractional digits to be maintained.

rawabstract:
DC is an arbitrary precision arithmetic package implemented on the UNIX time-sharing system in the form of an interactive desk calculator. It works like a stacking calculator using reverse Polish notation. Ordinarily DC operates on decimal integers, but one may specify an input base, output base, and a number of fractional digits to be maintained.

entry:
@TechReport{Morris:1978:DID,
  author =       "Robert Morris and Lorinda Cherry",
  title =        "{DC} --- An Interactive Desk Calculator",
  type =         "Technical Memorandum",
  number =       "1056",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "8",
  day =          "15",
  month =        nov,
  year =         "1978",
  bibdate =      "Tue Jun 06 08:07:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "DC is an arbitrary precision arithmetic package
                 implemented on the UNIX time-sharing system in the form
                 of an interactive desk calculator. It works like a
                 stacking calculator using reverse Polish notation.
                 Ordinarily DC operates on decimal integers, but one may
                 specify an input base, output base, and a number of
                 fractional digits to be maintained.",
  abstract-2 =   "DC is an interactive desk calculator program
                 implemented on the UNIX Time-Sharing System \ldots{}
                 arbitrary-precision integer arithmetic.",
  acknowledgement = ack-nhfb,
  author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
                 Robert Morris (25 July 1932--26 June 2011)",
  remark =       "Available in PDF file of \cite[pp.
                 399--406]{Dolotta:1977:DPU}.",
}


bibtype: article
filename: fparith.bib
label: Murphy:1978:SRP
author: T. R. Murphy and P. L. Rickard
title: Square-Root Procedure for Floating-Point Numbers
journal: j-IBM-TDB
volume: 21
number: 2
pages: 785
month: jul
monthnumber: 7
year: 1978
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:15:41 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 10:15:41 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: T. R. Murphy and P. L. Rickard
rawtitle: Square-Root Procedure for Floating-Point Numbers
entry:
@Article{Murphy:1978:SRP,
  author =       "T. R. Murphy and P. L. Rickard",
  title =        "Square-Root Procedure for Floating-Point Numbers",
  journal =      j-IBM-TDB,
  volume =       "21",
  number =       "2",
  pages =        "785",
  month =        jul,
  year =         "1978",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 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 =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Nussabaumer:1978:FMN
author: H. J. Nussabaumer
title: Fast Multipliers for Number Theoretic Transforms
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 8
pages: 764--765
month: aug
monthnumber: 8
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675187
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:30 MDT 2011
bibtimestamp: 2011.07.11 08:13:30 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675187
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. J. Nussabaumer
rawtitle: Fast Multipliers for Number Theoretic Transforms
entry:
@Article{Nussabaumer:1978:FMN,
  author =       "H. J. Nussabaumer",
  title =        "Fast Multipliers for Number Theoretic Transforms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "8",
  pages =        "764--765",
  month =        aug,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675187",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:30 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=1675187",
  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: OLeary:1978:DHS
author: G. P. O'Leary
title: The design of a high-speed arithmetic processor
crossref: COMPSAC:1978:CPC
pages: 175--176
year: 1978
bibdate: Wed Sep 07 22:19:45 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:19:45 ???
acknowledgement: ack-nj
rawauthor: G. P. O'Leary
rawtitle: The design of a high-speed arithmetic processor
entry:
@InProceedings{OLeary:1978:DHS,
  author =       "G. P. O'Leary",
  title =        "The design of a high-speed arithmetic processor",
  crossref =     "COMPSAC:1978:CPC",
  pages =        "175--176",
  year =         "1978",
  bibdate =      "Wed Sep 07 22:19:45 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Olver:1978:NAE
author: F. W. J. Olver
title: New Approach to Error Arithmetic
journal: j-SIAM-REVIEW
volume: 20
number: 3
pages: 632--632
year: 1978
CODEN: SIREAD
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: F. W. J. Olver
rawtitle: New Approach to Error Arithmetic
entry:
@Article{Olver:1978:NAE,
  author =       "F. W. J. Olver",
  title =        "New Approach to Error Arithmetic",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "3",
  pages =        "632--632",
  month =        "????",
  year =         "1978",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "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",
}


bibtype: article
filename: fparith.bib
label: Patel:1978:ASB
author: M. R. Patel and K. H. Bennett
title: Analysis of Speed of a Binary Divider Using a Variable Number of Shifts Per Cycle
journal: j-COMP-J
volume: 21
number: 3
pages: 246--252
month: aug
monthnumber: 8
year: 1978
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/21.3.246
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:48:03 MST 2012
bibtimestamp: 2012.12.04 14:48:03 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: M. R. Patel and K. H. Bennett
rawtitle: Analysis of Speed of a Binary Divider Using a Variable Number of Shifts Per Cycle
bibsource:
Compendex database; http://comjnl.oxfordjournals.org/content/21/3.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/; 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/21/3/246.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/246.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/247.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/248.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/249.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/250.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/251.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/252.tif

keywords:
analysis; computers, digital; cycle; digital arithmetic; discrete time; discrete time systems; finite state system model; ICL 2980; optimisation; optimum hardware configuration; Patel and Bennett (1976); speed of a binary divider; variable number of shifts per

entry:
@Article{Patel:1978:ASB,
  author =       "M. R. Patel and K. H. Bennett",
  title =        "Analysis of Speed of a Binary Divider Using a Variable
                 Number of Shifts Per Cycle",
  journal =      j-COMP-J,
  volume =       "21",
  number =       "3",
  pages =        "246--252",
  month =        aug,
  year =         "1978",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/21.3.246",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:03 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/21/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/;
                 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/21/3/246.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/246.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/247.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/248.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/249.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/250.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/251.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/252.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "721",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "analysis; computers, digital; cycle; digital
                 arithmetic; discrete time; discrete time systems;
                 finite state system model; ICL 2980; optimisation;
                 optimum hardware configuration; Patel and Bennett
                 (1976); speed of a binary divider; variable number of
                 shifts per",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: fparith.bib
label: Payne:1978:DPF
author: M. Payne and W. Strecker
title: Draft Proposal for Floating Point Standard
type: Technical report
institution: Digital Equipment Corporation
address: Maynard, MA, USA
pages: 246--252
day: 11
month: dec
monthnumber: 12
year: 1978
bibdate: Fri Nov 09 19:11:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:11:42 ???
acknowledgement: ack-nhfb
rawauthor: M. Payne and W. Strecker
rawtitle: Draft Proposal for Floating Point Standard
entry:
@TechReport{Payne:1978:DPF,
  author =       "M. Payne and W. Strecker",
  title =        "Draft Proposal for Floating Point Standard",
  type =         "Technical report",
  institution =  "Digital Equipment Corporation",
  address =      "Maynard, MA, USA",
  day =          "11",
  month =        dec,
  year =         "1978",
  bibdate =      "Fri Nov 09 19:11:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Preston:1978:NAT
author: F. S. Preston
title: A New Algorithm for the Tangent
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 2
pages: 167
month: feb
monthnumber: 2
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675052
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:16:10 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 10:16:10 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. S. Preston
rawtitle: A New Algorithm for the Tangent
entry:
@Article{Preston:1978:NAT,
  author =       "F. S. Preston",
  title =        "A New Algorithm for the Tangent",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "2",
  pages =        "167",
  month =        feb,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675052",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Ralston:1978:FCN
author: Anthony Ralston and Philip Rabinowitz
title: A first course in numerical analysis
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
edition: Second
pages: xix + 556
year: 1978
ISBN: 0-07-051158-6 OR 0070511586
ISBN13: 978-0-07-051158-3 OR 9780070511583
LCCN: QA297 .R3 1978
bibdate: Fri Aug 20 10:13:32 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 10:13:32 MDT
series: International series in pure and applied mathematics
remark: See also first edition cite Ralston:1965:FCN. Reprinted in cite Ralston:2001:FCN.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Anthony Ralston and Philip Rabinowitz
rawtitle: A first course in numerical analysis
entry:
@Book{Ralston:1978:FCN,
  author =       "Anthony Ralston and Philip Rabinowitz",
  title =        "A first course in numerical analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "xix + 556",
  year =         "1978",
  ISBN =         "0-07-051158-6",
  ISBN-13 =      "978-0-07-051158-3",
  LCCN =         "QA297 .R3 1978",
  bibdate =      "Fri Aug 20 10:13:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$19.50",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "See also first edition \cite{Ralston:1965:FCN}.
                 Reprinted in \cite{Ralston:2001:FCN}.",
  subject =      "Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Rashed:1978:LRI
author: Roshdi Rashed
journal: j-ARCH-HIST-EXACT-SCI
volume: 18
number: 3
pages: 191--243
month: sep
monthnumber: 9
year: 1978
CODEN: AHESAN
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 01A35
MRnumber: 0484970 (58 \#4829)
MRreviewer: H. L. L. Busard
bibdate: Fri Feb 4 21:50:14 MST 2011
bibtimestamp: 2011.02.04 21:50:14 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=18&issue=3&spage=191
fjournal: Archive for History of Exact Sciences
language: French
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: Roshd{\=\i} R{\=a}shed
title:
L'Extraction de la Racine $ n^rm scriptstyle igrave eme $ et l'Invention des Fractions Decimales (XI$^e$--XII$^e$ Siecles). (French) [The extraction of the n$^rm th$ root and the invention of decimal fractions (11$^rm th$--12$^rm th$ centuries)]

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=18&issue=3; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
{L}'Extraction de la Racine $ n^{\rm \scriptstyle i{\grave e}me} $ et {l'Invention} des Fractions D{\'e}cimales ({XI}$^e$--{XII}$^e$ Si{\`e}cles). ({French}) [{The} extraction of the n$^{{\rm th}}$ root and the invention of decimal fractions (11$^{{\rm th}}$--12$^{{\rm th}}$ centuries)]

entry:
@Article{Rashed:1978:LRI,
  author =       "Roshd{\=\i} R{\=a}shed",
  title =        "{L}'Extraction de la Racine $ n^{\rm \scriptstyle
                 i{\grave e}me} $ et {l'Invention} des Fractions
                 D{\'e}cimales ({XI}$^e$--{XII}$^e$ Si{\`e}cles).
                 ({French}) [{The} extraction of the n$^{{\rm th}}$ root
                 and the invention of decimal fractions (11$^{{\rm
                 th}}$--12$^{{\rm th}}$ centuries)]",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "18",
  number =       "3",
  pages =        "191--243",
  month =        sep,
  year =         "1978",
  CODEN =        "AHESAN",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A35",
  MRnumber =     "0484970 (58 \#4829)",
  MRreviewer =   "H. L. L. Busard",
  bibdate =      "Fri Feb 4 21:50:14 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=18&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=18&issue=3&spage=191",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  language =     "French",
  MRtitle =      "{L}'extraction de la racine {$n$}i{\`e}me et
                 l'invention des fractions d{\'e}cimales ({XIe--XIIe}
                 si{\`e}cles)",
  MRyear =       "1977/78",
}


bibtype: inproceedings
filename: fparith.bib
label: Reuter:1978:SEU
author: Eric K. Reuter and John P. Jeter and J. Wayne Anderson and Bruce D. Shriver
title: Some Experiments Using Interval Arithmetic
crossref: IEEE:1978:PSC
pages: 75--80
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Reuter.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Eric K. Reuter and John P. Jeter and J. Wayne Anderson and Bruce D. Shriver
rawtitle: Some Experiments Using Interval Arithmetic
abstract:
This paper reviews past experiences and discusses future work in the area of interval arithmetic at the University of Southwestern Louisiana (USL). Two versions of interval arithmetic were developed and implemented at USL. An interval data type declaration and the necessary mathematical functions for this data type were added to Fortran via the preprocessor Augment (4,5). In the first version the endpoints of the intervals were represented as single precision floating point numbers. In the other version, the endpoints were represented to 56 decimal digits. Production engineering programs were run as benchmarks (8). The accumulation of computational and algorithmic error could be observed as a widening of the intervals. The benchmarks were also run in normal single and double precision arithmetic. In some instances, the result obtained from a single or double precision calculation was not bounded by the corresponding interval result indicating some problem with the algorithm. The widening of an interval does not necessarily indicate a data sensitivity nor error in an algorithm. However, these large intervals can be used as indicator of no problems. As could be expected, the 56-decimal digit precision interval gave better results in terms of smaller intervals due to the increased amount of precision. The obvious problem with this version is that the amount of overhead required for its execution is high.

rawabstract:
This paper reviews past experiences and discusses future work in the area of interval arithmetic at the University of Southwestern Louisiana (USL). Two versions of interval arithmetic were developed and implemented at USL. An interval data type declaration and the necessary mathematical functions for this data type were added to Fortran via the preprocessor Augment (4,5). In the first version the endpoints of the intervals were represented as single precision floating point numbers. In the other version, the endpoints were represented to 56 decimal digits. Production engineering programs were run as benchmarks (8). The accumulation of computational and algorithmic error could be observed as a widening of the intervals. The benchmarks were also run in normal single and double precision arithmetic. In some instances, the result obtained from a single or double precision calculation was not bounded by the corresponding interval result indicating some problem with the algorithm. The widening of an interval does not necessarily indicate a data sensitivity nor error in an algorithm. However, these large intervals can be used as indicator of no problems. As could be expected, the 56-decimal digit precision interval gave better results in terms of smaller intervals due to the increased amount of precision. The obvious problem with this version is that the amount of overhead required for its execution is high.

entry:
@InProceedings{Reuter:1978:SEU,
  author =       "Eric K. Reuter and John P. Jeter and J. Wayne Anderson
                 and Bruce D. Shriver",
  title =        "Some Experiments Using Interval Arithmetic",
  crossref =     "IEEE:1978:PSC",
  pages =        "75--80",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Reuter.pdf",
  abstract =     "This paper reviews past experiences and discusses
                 future work in the area of interval arithmetic at the
                 University of Southwestern Louisiana (USL). Two
                 versions of interval arithmetic were developed and
                 implemented at USL. An interval data type declaration
                 and the necessary mathematical functions for this data
                 type were added to Fortran via the preprocessor Augment
                 (4,5). In the first version the endpoints of the
                 intervals were represented as single precision floating
                 point numbers. In the other version, the endpoints were
                 represented to 56 decimal digits. Production
                 engineering programs were run as benchmarks (8). The
                 accumulation of computational and algorithmic error
                 could be observed as a widening of the intervals. The
                 benchmarks were also run in normal single and double
                 precision arithmetic. In some instances, the result
                 obtained from a single or double precision calculation
                 was not bounded by the corresponding interval result
                 indicating some problem with the algorithm. The
                 widening of an interval does not necessarily indicate a
                 data sensitivity nor error in an algorithm. However,
                 these large intervals can be used as indicator of no
                 problems. As could be expected, the 56-decimal digit
                 precision interval gave better results in terms of
                 smaller intervals due to the increased amount of
                 precision. The obvious problem with this version is
                 that the amount of overhead required for its execution
                 is high.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: manual
filename: fparith.bib
label: Richardson:1978:ATB
author: Caryl Richardson and Jef Raskin
title: The Apple tutorial: based on the Apple II Basic programming manual
organization: Bell and Howell, Audio-Visual Products Division
address: Chicago, IL, USA
pages: vii + 157
year: 1978
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: Apple II (Computer) --- Programming.; BASIC (Computer program language)
acknowledgement: ack-nhfb
rawauthor: Caryl Richardson and Jef Raskin
rawtitle: The {Apple} tutorial: based on the {Apple} {II} Basic programming manual
remark:
Cover title: Floating point Basic tutorial manual. ``Reprinted with the permission of Apple Computer Inc.'' Companion volume: Bell and Howell floating point Basic programming reference manual.

entry:
@Manual{Richardson:1978:ATB,
  author =       "Caryl Richardson and Jef Raskin",
  title =        "The {Apple} tutorial: based on the {Apple} {II} Basic
                 programming manual",
  organization = "Bell and Howell, Audio-Visual Products Division",
  address =      "Chicago, IL, USA",
  pages =        "vii + 157",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming.; BASIC (Computer
                 program language)",
  remark =       "Cover title: Floating point Basic tutorial manual.
                 ``Reprinted with the permission of Apple Computer
                 Inc.'' Companion volume: Bell and Howell floating point
                 Basic programming reference manual.",
}


bibtype: article
filename: fparith.bib
label: Ruckdeschel:1978:FA
author: F. Ruckdeschel
title: Functional Approximations
journal: j-BYTE
volume: 3
number: 11
pages: 34--46
month: nov
monthnumber: 11
year: 1978
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Thu Sep 1 10:15:40 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 10:15:40 ???
fjournal: BYTE Magazine
acknowledgement: ack-nj
rawauthor: F. Ruckdeschel
rawtitle: Functional Approximations
entry:
@Article{Ruckdeschel:1978:FA,
  author =       "F. Ruckdeschel",
  title =        "Functional Approximations",
  journal =      j-BYTE,
  volume =       "3",
  number =       "11",
  pages =        "34--46",
  month =        nov,
  year =         "1978",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 1 10:15:40 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 =     "BYTE Magazine",
}


bibtype: article
filename: fparith.bib
label: Russell:1978:CCS
author: Richard M. Russell
title: The Cray-1 Computer System
journal: j-CACM
volume: 21
number: 1
pages: 63--72
month: jan
monthnumber: 1
year: 1978
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Dec 08 13:08:43 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:08:43 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Richard M. Russell
rawtitle: The {Cray-1} Computer System
keywords:
grecommended91, existing classic architecture, maeder biblio: parallel hardware and devices, implementation, ginsberg biblio: bhibbard enm, jlb

remark:
The original paper describing the Cray-1. This paper is reproduced in Kuhn and Padua's (1981, IEEE) survey ``Tutorial on Parallel Processing.'' Also reproduced in ``Computer Structures: Principles and Examples'' by Daniel P. Siewiorek, C. Gordon Bell, and Allen Newell, McGraw-Hill, 1982, pp. 743-752. Reproduced in Dharma P. Agrawal's (ed.) ``Advanced Computer Architecture,'' IEEE, 1986, pp. 15--24. Literature search yields: 00712248 E. I. Monthly No: EI7804023850 E. I. Yearly No: EI78014612 Title: Cray-1 Computer System. Author: Russell, Richard M. Corporate Source: Cray Res Inc, Minneapolis, Minn Source: Communications of the ACM v 21 n 1 Jan 1978 p 63--72 Publication Year: 1978 CODEN: CACMA2 ISSN: 0001-0782 Language: ENGLISH Journal Announcement: 7804 Abstract: The CRAY-1 is described, the evolution of its architecture is discussed, and an account is given of some of the problems that were overcome during its manufacture. The CRAY-1 is the only computer to have been built to date that satisfies ERDA's Class VI requirement (a computer capable of processing from 20 to 60 million floating point operations per second). The CRAY-1's Fortran compiler (CFT) is designed to give the scientific user immediate access to the benefits of the CRAY-1's vector processing architecture. An optimizing compiler, CFT, ``vectorizes'' innermost DO loops. Compatible with the ANSI 1966 Fortran Standard and with many commonly supported Fortran extensions, CFT does not require any source program modifications or the use of additional nonstandard Fortran statements to achieve vectorization. 6 refs. Descriptors: *COMPUTER ARCHITECTURE; COMPUTER SYSTEMS, DIGITAL Classification Codes: 722 (Computer Hardware); 723 (Computer Software) 72 (COMPUTERS & DATA PROCESSING)

entry:
@Article{Russell:1978:CCS,
  author =       "Richard M. Russell",
  title =        "The {Cray-1} Computer System",
  journal =      j-CACM,
  volume =       "21",
  number =       "1",
  pages =        "63--72",
  month =        jan,
  year =         "1978",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Dec 08 13:08:43 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "grecommended91, existing classic architecture, maeder
                 biblio: parallel hardware and devices, implementation,
                 ginsberg biblio: bhibbard enm, j\-lb",
  remark =       "The original paper describing the Cray-1. This paper
                 is reproduced in Kuhn and Padua's (1981, IEEE) survey
                 ``Tutorial on Parallel Processing.'' Also reproduced in
                 ``Computer Structures: Principles and Examples'' by
                 Daniel P. Siewiorek, C. Gordon Bell, and Allen Newell,
                 McGraw-Hill, 1982, pp. 743-752. Reproduced in Dharma P.
                 Agrawal's (ed.) ``Advanced Computer Architecture,''
                 IEEE, 1986, pp. 15--24. Literature search yields:
                 00712248 E. I. Monthly No: EI7804023850 E. I. Yearly
                 No: EI78014612 Title: Cray-1 Computer System. Author:
                 Russell, Richard M. Corporate Source: Cray Res Inc,
                 Minneapolis, Minn Source: Communications of the ACM v
                 21 n 1 Jan 1978 p 63--72 Publication Year: 1978 CODEN:
                 CACMA2 ISSN: 0001-0782 Language: ENGLISH Journal
                 Announcement: 7804 Abstract: The CRAY-1 is described,
                 the evolution of its architecture is discussed, and an
                 account is given of some of the problems that were
                 overcome during its manufacture. The CRAY-1 is the only
                 computer to have been built to date that satisfies
                 ERDA's Class VI requirement (a computer capable of
                 processing from 20 to 60 million floating point
                 operations per second). The CRAY-1's Fortran compiler
                 (CFT) is designed to give the scientific user immediate
                 access to the benefits of the CRAY-1's vector
                 processing architecture. An optimizing compiler, CFT,
                 ``vectorizes'' innermost DO loops. Compatible with the
                 ANSI 1966 Fortran Standard and with many commonly
                 supported Fortran extensions, CFT does not require any
                 source program modifications or the use of additional
                 nonstandard Fortran statements to achieve
                 vectorization. 6 refs. Descriptors: *COMPUTER
                 ARCHITECTURE; COMPUTER SYSTEMS, DIGITAL Classification
                 Codes: 722 (Computer Hardware); 723 (Computer Software)
                 72 (COMPUTERS \& DATA PROCESSING)",
}


bibtype: book
filename: fparith.bib
label: Schmid:1978:EDS
author: Hermann Schmid
publisher: pub-OLDENBOURG
address: pub-OLDENBOURG:adr
pages: 275
year: 1978
ISBN: 3-486-20211-1 OR 3486202111
ISBN13: 978-3-486-20211-3 OR 9783486202113
bibdate: Fri Sep 16 16:30:39 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:39 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: Hermann Schmid
title:
Elektronische Dezimalrechner, Schaltungen und Verfahren toenglish Electronic Decimal Computers, Wiring and Methods endtoenglish 

rawtitle:
{Elektronische Dezimalrechner, Schaltungen und Verfahren} \toenglish {Electronic Decimal Computers, Wiring and Methods} \endtoenglish

entry:
@Book{Schmid:1978:EDS,
  author =       "Hermann Schmid",
  title =        "{Elektronische Dezimalrechner, Schaltungen und
                 Verfahren} \toenglish {Electronic Decimal Computers,
                 Wiring and Methods} \endtoenglish",
  publisher =    pub-OLDENBOURG,
  address =      pub-OLDENBOURG:adr,
  pages =        "275",
  year =         "1978",
  ISBN =         "3-486-20211-1",
  ISBN-13 =      "978-3-486-20211-3",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Schreiber:1978:TMF
author: F. A. Schreiber and R. Stefanelli
title: Two Methods for Fast Binary-BCD Conversion
crossref: IEEE:1978:PSC
pages: 200--207
year: 1978
bibdate: Sat Nov 12 21:58:26 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.12 21:58:26 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Schreiber.pdf
keywords: ARITH-4
acknowledgement: ack-nj
rawauthor: F. A. Schreiber and R. Stefanelli
rawtitle: Two Methods for Fast Binary-{BCD} Conversion
abstract:
Two methods for performing binary--BCD conversion of positive integers are discussed. The principle which underlies both methods in the repeated division by five and then by two, obtained the first by means of subtractions performed from left to right, the second by shifting bits before next subtraction.par It is shown that these methods work in a time which is linear with the length in bit of the number to be converted.par A ROM solution is proposed and its complexity is compared with that of other methods.

rawabstract:
Two methods for performing binary--BCD conversion of positive integers are discussed. The principle which underlies both methods in the repeated division by five and then by two, obtained the first by means of subtractions performed from left to right, the second by shifting bits before next subtraction.\par It is shown that these methods work in a time which is linear with the length in bit of the number to be converted.\par A ROM solution is proposed and its complexity is compared with that of other methods.

entry:
@InProceedings{Schreiber:1978:TMF,
  author =       "F. A. Schreiber and R. Stefanelli",
  title =        "Two Methods for Fast Binary-{BCD} Conversion",
  crossref =     "IEEE:1978:PSC",
  pages =        "200--207",
  year =         "1978",
  bibdate =      "Sat Nov 12 21:58:26 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/arith4/papers/ARITH4_Schreiber.pdf",
  abstract =     "Two methods for performing binary--BCD conversion of
                 positive integers are discussed. The principle which
                 underlies both methods in the repeated division by five
                 and then by two, obtained the first by means of
                 subtractions performed from left to right, the second
                 by shifting bits before next subtraction.\par

                 It is shown that these methods work in a time which is
                 linear with the length in bit of the number to be
                 converted.\par

                 A ROM solution is proposed and its complexity is
                 compared with that of other methods.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4",
}


bibtype: book
filename: fparith.bib
label: Seck:1978:WSA
editor: Friedrich Seck
volume: 25
publisher: Mohr
address: Tubingen, West Germany
pages: 422
year: 1978
ISBN: 3-16-939772-9 OR 3169397729
ISBN13: 978-3-16-939772-3 OR 9783169397723
LCCN: QB36.S312 W54
bibdate: Sat Jul 27 11:00:08 MDT 2013
bibtimestamp: 2013.07.27 11:00:08 MDT
series: Contubernium
language: German
remark: Includes texts in Latin.
subject: Schickard, Wilhelm; Astronomers; Germany; Biography; Middle East specialists
acknowledgement: ack-nhfb
subjectdates: 1592--1635
raweditor: Friedrich Seck
title:
Wilhelm Schickard, 1592--1635: Astronom, Geograph, Orientalist, Erfinder der Rechenmaschine. (German) [Wilhelm Schickard, 1592--1635: Astronomer, Geographer, Orientalist, Inventor of the calculator]

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/scicontext.bib; z3950.loc.gov:7090/Voyager

rawtitle:
{Wilhelm Schickard, 1592--1635: Astronom, Geograph, Orientalist, Erfinder der Rechenmaschine}. ({German}) [{Wilhelm Schickard}, 1592--1635: Astronomer, Geographer, Orientalist, Inventor of the calculator]

entry:
@Book{Seck:1978:WSA,
  editor =       "Friedrich Seck",
  title =        "{Wilhelm Schickard, 1592--1635: Astronom, Geograph,
                 Orientalist, Erfinder der Rechenmaschine}. ({German})
                 [{Wilhelm Schickard}, 1592--1635: Astronomer,
                 Geographer, Orientalist, Inventor of the calculator]",
  volume =       "25",
  publisher =    "Mohr",
  address =      "T{\"u}bingen, West Germany",
  pages =        "422",
  year =         "1978",
  ISBN =         "3-16-939772-9",
  ISBN-13 =      "978-3-16-939772-3",
  LCCN =         "QB36.S312 W54",
  bibdate =      "Sat Jul 27 11:00:08 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Contubernium",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "Includes texts in Latin.",
  subject =      "Schickard, Wilhelm; Astronomers; Germany; Biography;
                 Middle East specialists",
  subject-dates = "1592--1635",
}


bibtype: article
filename: fparith.bib
label: Shen:1978:CSA
author: D. T. Shen and A. Weinberger
title: 4-2 carry-save adder implementation using send circuits
journal: j-IBM-TDB
volume: 20
number: 9
pages: ??--??
month: feb
monthnumber: 2
year: 1978
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Mon Dec 24 10:18:16 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 10:18:16 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nhfb
rawauthor: D. T. Shen and A. Weinberger
rawtitle: 4-2 carry-save adder implementation using send circuits
entry:
@Article{Shen:1978:CSA,
  author =       "D. T. Shen and A. Weinberger",
  title =        "4-2 carry-save adder implementation using send
                 circuits",
  journal =      j-IBM-TDB,
  volume =       "20",
  number =       "9",
  pages =        "??--??",
  month =        feb,
  year =         "1978",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Mon Dec 24 10:18:16 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: inproceedings
filename: fparith.bib
label: Slekys:1978:MBI
author: Arunas G. Slekys and Algirdas Avizienis
title: A Modified Bi-Imaginary Number Systems
crossref: IEEE:1978:PSC
pages: 48--55
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Slekys.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Arunas G. Slekys and Algirdas Avi{\v{z}}ienis
rawtitle: A Modified Bi-Imaginary Number Systems
abstract:
In this paper the properties of $p$-imaginary number systems are reviewed and a modified bi-imaginary number system is introduced as a special case with $ p = 2 $. Major properties, including conversion of integer and floating point operands represented in a radix $ + p $ system, range, sign and zero tests, and shifting are discussed. The ability to represent the operands as vectors of radix-2 digits suggests advantages in implementing machine-usable arithmetic algorithms.

rawabstract:
In this paper the properties of $p$-imaginary number systems are reviewed and a modified bi-imaginary number system is introduced as a special case with $ p = 2 $. Major properties, including conversion of integer and floating point operands represented in a radix $ + p $ system, range, sign and zero tests, and shifting are discussed. The ability to represent the operands as vectors of radix-2 digits suggests advantages in implementing machine-usable arithmetic algorithms.

entry:
@InProceedings{Slekys:1978:MBI,
  author =       "Arunas G. Slekys and Algirdas Avi{\v{z}}ienis",
  title =        "A Modified Bi-Imaginary Number Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "48--55",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Slekys.pdf",
  abstract =     "In this paper the properties of $p$-imaginary number
                 systems are reviewed and a modified bi-imaginary number
                 system is introduced as a special case with $ p = 2 $.
                 Major properties, including conversion of integer and
                 floating point operands represented in a radix $ + p $
                 system, range, sign and zero tests, and shifting are
                 discussed. The ability to represent the operands as
                 vectors of radix-2 digits suggests advantages in
                 implementing machine-usable arithmetic algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: article
filename: fparith.bib
label: Sripad:1978:QEF
author: A. Sripad and D. Snyder
title: Quantization errors in floating-point arithmetic
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 26
number: 5
pages: 456--463
month: oct
monthnumber: 10
year: 1978
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. Sripad and D. Snyder
rawtitle: Quantization errors in floating-point arithmetic
entry:
@Article{Sripad:1978:QEF,
  author =       "A. Sripad and D. Snyder",
  title =        "Quantization errors in floating-point arithmetic",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "26",
  number =       "5",
  pages =        "456--463",
  month =        oct,
  year =         "1978",
  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 =      "In this paper, the quantization of the mantissa in a
                 normalized floating-point number is investigated. A
                 necessary and sufficient condition is given for the
                 mantissa to have a reciprocal probability density. A
                 model to represent a floating-point quantity \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Svoboda:1978:ACF
author: Antonin Svoboda
title: Arithmetic Circuit Fault Detection by Modular Encoding
crossref: IEEE:1978:PSC
pages: 208--219
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Svoboda.pdf
keywords: ARITH-4; decimal arithmetic
acknowledgement: ack-nhfb
rawauthor: Antonin Svoboda
rawtitle: Arithmetic Circuit Fault Detection by Modular Encoding
abstract:
Design principles of self checking digital circuits are in the focus of the general interest and many papers exist treating that subject. The use of special data encoding techniques, suitable algorithms of arithmetic, special hardware elements have been proposed long ago. The purpose of this paper is to show that the design can produce rather simple self checking circuit when the design principles are chosen which collaborate harmoniously:par (1) decimal numerical system is usedpar (2) decimal digit $ d in 0, 1, ldots , 9 $ is represented in the Diamond Code by the 5-bit binary number $ f = 3 d + 2 $ par (3) decimal digit' addition algorithm introduced here is simple and effective so that 10 decimal digits can be added in parallelpar (4) implementation of the addition algorithm by conventional Full Adders results in a single fault detecting circuit.par The design of a decimal adder for 10 decimal numbers, each with 10 digits. is described here as an illustration. It shows the way how to design other decimal arithmetic circuits which are single fault detecting, for instance a multiplier (derived from the adder for 10 decimal numbers).

rawabstract:
Design principles of self checking digital circuits are in the focus of the general interest and many papers exist treating that subject. The use of special data encoding techniques, suitable algorithms of arithmetic, special hardware elements have been proposed long ago. The purpose of this paper is to show that the design can produce rather simple self checking circuit when the design principles are chosen which collaborate harmoniously:\par (1) decimal numerical system is used\par (2) decimal digit $ d \in \{ 0, 1, \ldots {}, 9 \} $ is represented in the Diamond Code by the 5-bit binary number $ f = 3 d + 2 $ \par (3) decimal digit' addition algorithm introduced here is simple and effective so that 10 decimal digits can be added in parallel\par (4) implementation of the addition algorithm by conventional Full Adders results in a single fault detecting circuit.\par The design of a decimal adder for 10 decimal numbers, each with 10 digits. is described here as an illustration. It shows the way how to design other decimal arithmetic circuits which are single fault detecting, for instance a multiplier (derived from the adder for 10 decimal numbers).

entry:
@InProceedings{Svoboda:1978:ACF,
  author =       "Antonin Svoboda",
  title =        "Arithmetic Circuit Fault Detection by Modular
                 Encoding",
  crossref =     "IEEE:1978:PSC",
  pages =        "208--219",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Svoboda.pdf",
  abstract =     "Design principles of self checking digital circuits
                 are in the focus of the general interest and many
                 papers exist treating that subject. The use of special
                 data encoding techniques, suitable algorithms of
                 arithmetic, special hardware elements have been
                 proposed long ago. The purpose of this paper is to show
                 that the design can produce rather simple self checking
                 circuit when the design principles are chosen which
                 collaborate harmoniously:\par

                 (1) decimal numerical system is used\par

                 (2) decimal digit $ d \in \{ 0, 1, \ldots {}, 9 \} $ is
                 represented in the Diamond Code by the 5-bit binary
                 number $ f = 3 d + 2 $ \par

                 (3) decimal digit' addition algorithm introduced here
                 is simple and effective so that 10 decimal digits can
                 be added in parallel\par

                 (4) implementation of the addition algorithm by
                 conventional Full Adders results in a single fault
                 detecting circuit.\par

                 The design of a decimal adder for 10 decimal numbers,
                 each with 10 digits. is described here as an
                 illustration. It shows the way how to design other
                 decimal arithmetic circuits which are single fault
                 detecting, for instance a multiplier (derived from the
                 adder for 10 decimal numbers).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; decimal arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Swartzlander:1978:MAS
author: E. E. Swartzlander, Jr.
title: Merged Arithmetic for Signal Processing
crossref: IEEE:1978:PSC
pages: 239--244
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Swartzlander.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: E. E. {Swartzlander, Jr.}
rawtitle: Merged Arithmetic for Signal Processing
abstract:
The concept of merged arithmetic is introduced and applied to signal processing. The basic idea involves synthesizing a composite arithmetic function (e.g., a complex multiply) directly instead of decomposing it into multiply and add operations as is conventional practice. This approach results in a simpler design which is also faster.

rawabstract:
The concept of merged arithmetic is introduced and applied to signal processing. The basic idea involves synthesizing a composite arithmetic function (e.g., a complex multiply) directly instead of decomposing it into multiply and add operations as is conventional practice. This approach results in a simpler design which is also faster.

entry:
@InProceedings{Swartzlander:1978:MAS,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "Merged Arithmetic for Signal Processing",
  crossref =     "IEEE:1978:PSC",
  pages =        "239--244",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Swartzlander.pdf",
  abstract =     "The concept of merged arithmetic is introduced and
                 applied to signal processing. The basic idea involves
                 synthesizing a composite arithmetic function (e.g., a
                 complex multiply) directly instead of decomposing it
                 into multiply and add operations as is conventional
                 practice. This approach results in a simpler design
                 which is also faster.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: inproceedings
filename: fparith.bib
label: Tan:1978:TIH
author: Kwang G. Tan
title: The theory and implementation of high-radix division
crossref: IEEE:1978:PSC
pages: 154--163
year: 1978
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 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Tan.pdf
keywords: ARITH-4
acknowledgement: ack-sfo
rawauthor: Kwang G. Tan
rawtitle: The theory and implementation of high-radix division
abstract:
This report derives the theory of high-radix division in terms of the properties of the overlapped regions of the P-D plot. The minimum precision requirements in quotient selection are discussed. The methods of implementations in hardware and in read-only memory are explored.

rawabstract:
This report derives the theory of high-radix division in terms of the properties of the overlapped regions of the P-D plot. The minimum precision requirements in quotient selection are discussed. The methods of implementations in hardware and in read-only memory are explored.

entry:
@InProceedings{Tan:1978:TIH,
  author =       "Kwang G. Tan",
  title =        "The theory and implementation of high-radix division",
  crossref =     "IEEE:1978:PSC",
  pages =        "154--163",
  year =         "1978",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Tan.pdf",
  abstract =     "This report derives the theory of high-radix division
                 in terms of the properties of the overlapped regions of
                 the P-D plot. The minimum precision requirements in
                 quotient selection are discussed. The methods of
                 implementations in hardware and in read-only memory are
                 explored.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: article
filename: fparith.bib
label: Trivedi:1978:CUC
author: K. S. Trivedi
title: Corrections to ``On the Use of Continued Fractions for Digital Computer Arithmetic''
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 3
pages: 288--288
month: mar
monthnumber: 3
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675093
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:27 MDT 2011
bibtimestamp: 2011.07.11 08:13:27 MDT
note: See cite Trivedi:1977:UCF.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675093
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. S. Trivedi
rawnote: See \cite{Trivedi:1977:UCF}.
rawtitle: Corrections to {``On the Use of Continued Fractions for Digital Computer Arithmetic''}
entry:
@Article{Trivedi:1978:CUC,
  author =       "K. S. Trivedi",
  title =        "Corrections to {``On the Use of Continued Fractions
                 for Digital Computer Arithmetic''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "3",
  pages =        "288--288",
  month =        mar,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675093",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:27 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{Trivedi:1977:UCF}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675093",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


