# bibtab

bibtype: article
filename: fparith.bib
label: Daumas:1995:MRR
author: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
journal: j-J-UCS
volume: 1
number: 3
pages: 162--175
day: 28
month: mar
monthnumber: 3
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
MRclass: 68M07 (65D20 68Q20)
MRnumber: 97b:68012
bibdate: Wed May 28 19:32:35 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.28 19:32:35 MDT
URL: http://www.iicm.edu/jucs_1_3/modular_range_reduction
fjournal: J.UCS: Journal of Universal Computer Science
keywords: range reduction
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
title:
Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions

rawtitle:
Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions

entry:
@Article{Daumas:1995:MRR,
  author =       "Marc Daumas and Christophe Mazenc and Xavier Merrheim
                 and Jean-Michel Muller",
  title =        "Modular range reduction: a new algorithm for fast and
                 accurate computation of the elementary functions",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "162--175",
  day =          "28",
  month =        mar,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (65D20 68Q20)",
  MRnumber =     "97b:68012",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iicm.edu/jucs_1_3/modular_range_reduction",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
  keywords =     "range reduction",
}


bibtype: article
filename: fparith.bib
label: Demmel:1995:CSB
author: James W. Demmel and Inderjit Dhillon and Huan Ren
journal: j-ELECTRON-TRANS-NUMER-ANAL
volume: 3
pages: 116--149
year: 1995
ISSN: 1068-9613 (print), 1097-4067 (electronic) OR 10689613 (print), 10974067 (electronic)
ISSNL: 1068-9613 OR 10689613
bibdate: Mon Sep 6 12:28:29 MDT 2010
bibsource: http://etna.mcs.kent.edu/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.09.06 12:28:29 MDT
URL: http://etna.mcs.kent.edu/vol.3.1995/pp116-149.dir/pp116-149.pdf
fjournal: Electronic Transactions on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://etna.mcs.kent.edu/
rawauthor: James W. Demmel and Inderjit Dhillon and Huan Ren
title:
On the correctness of some bisection-like parallel eigenvalue algorithms in floating point arithmetic

rawtitle:
On the correctness of some bisection-like parallel eigenvalue algorithms in floating point arithmetic

entry:
@Article{Demmel:1995:CSB,
  author =       "James W. Demmel and Inderjit Dhillon and Huan Ren",
  title =        "On the correctness of some bisection-like parallel
                 eigenvalue algorithms in floating point arithmetic",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "3",
  pages =        "116--149",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  bibdate =      "Mon Sep 6 12:28:29 MDT 2010",
  bibsource =    "http://etna.mcs.kent.edu/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://etna.mcs.kent.edu/vol.3.1995/pp116-149.dir/pp116-149.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}


bibtype: article
filename: fparith.bib
label: DiClaudio:1995:FCR
author: E. D. Di Claudio and F. Piazza and G. Orlandi
title: Fast combinatorial RNS processors for DSP applications
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 5
pages: 624--633
month: may
monthnumber: 5
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.381948
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:27 MDT 2011
bibtimestamp: 2011.07.06 08:01:27 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=381948
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. D. {Di Claudio} and F. Piazza and G. Orlandi
rawtitle: Fast combinatorial {RNS} processors for {DSP} applications
entry:
@Article{DiClaudio:1995:FCR,
  author =       "E. D. {Di Claudio} and F. Piazza and G. Orlandi",
  title =        "Fast combinatorial {RNS} processors for {DSP}
                 applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "5",
  pages =        "624--633",
  month =        may,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.381948",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=381948",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Doman:1995:SAP
author: B. G. S. Doman and C. J. Pursglove and W. M. Coen
title: A Set of Ada Packages for High Precision Calculations
journal: j-TOMS
volume: 21
number: 4
pages: 416--431
month: dec
monthnumber: 12
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/212066.212087
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Nov 14 09:57:55 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.11.14 09:57:55 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p416-doman/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: B. G. S. Doman and C. J. Pursglove and W. M. Coen
rawtitle: A Set of {Ada} Packages for High Precision Calculations
keywords:
accuracy; Ada; arithmetic elementary-function evaluation; floating-point; multiple-precision portable software

subject:
G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; portability

entry:
@Article{Doman:1995:SAP,
  author =       "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
  title =        "A Set of {Ada} Packages for High Precision
                 Calculations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "416--431",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212087",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:55 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p416-doman/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accuracy; Ada; arithmetic elementary-function
                 evaluation; floating-point; multiple-precision portable
                 software",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic; G.1.2 [Numerical Analysis]: Approximation
                 -- elementary function approximation; G.4 [Mathematics
                 of Computing]: Mathematical Software -- algorithm
                 analysis; efficiency; portability",
}


bibtype: article
filename: fparith.bib
label: Doran:1995:SCD
author: R. W. Doran
title: Special Cases of Division
journal: j-J-UCS
volume: 1
number: 3
pages: 176--194
day: 28
month: mar
monthnumber: 3
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
MRclass: 68M07 (68Q20)
MRnumber: 97b:68013
bibdate: Wed May 28 19:32:35 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.28 19:32:35 MDT
URL: http://www.iicm.edu/jucs_1_3/special_cases_of_division
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: R. W. Doran
rawtitle: Special Cases of Division
entry:
@Article{Doran:1995:SCD,
  author =       "R. W. Doran",
  title =        "Special Cases of Division",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "176--194",
  day =          "28",
  month =        mar,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (68Q20)",
  MRnumber =     "97b:68013",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iicm.edu/jucs_1_3/special_cases_of_division",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: inproceedings
filename: fparith.bib
label: Ercegovac:1995:SDC
author: Milos D. Ercegovac and Tomas Lang
title: Sign Detection and Comparison Networks with a Small Number of Transitions
crossref: Knowles:1995:PSC
pages: 59--66
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ercegovac.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang
rawtitle: Sign Detection and Comparison Networks with a Small Number of Transitions
entry:
@InProceedings{Ercegovac:1995:SDC,
  author =       "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang",
  title =        "Sign Detection and Comparison Networks with a Small
                 Number of Transitions",
  crossref =     "Knowles:1995:PSC",
  pages =        "59--66",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ercegovac.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Espelid:1995:FPS
author: T. O. Espelid
title: On Floating-Point Summation
journal: j-SIAM-REVIEW
volume: 37
number: 4
pages: 603--607
month: dec
monthnumber: 12
year: 1995
CODEN: SIREAD
DOI: https://doi.org/10.1137/1037130
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 65Gxx (65Bxx)
MRnumber: 1 368 391
bibdate: Sat Mar 29 09:55:35 MDT 2014
bibtimestamp: 2014.03.29 09:55:35 MDT
URL: http://epubs.siam.org/27303.htm
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliation: Univ of Bergen
affiliationaddress: Bergen, Norway
corpsource: Department of Inf., Bergen University, Norway
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: December 1995
treatment: T Theoretical or Mathematical
rawauthor: T. O. Espelid
rawtitle: On Floating-Point Summation
bibsource:
Compendex database; http://epubs.siam.org/toc/siread/37/4; http://www.siam.org/journals/sirev/sirev374.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

abstract:
In this paper we focus on some general error analysis results in floating-point summation. We emphasize analysis that is useful from both a scientific and a teaching point of view.

keywords:
accurate floating-point summation; algorithm sum; algorithms; binary summation tree; digital arithmetic; error analysis; floating-point arithmetic; floating-point summation; number theory; numerical analysis; ordering; root of the tree; rounding errors; roundoff errors; set theory; trees (mathematics)

rawabstract:
In this paper we focus on some general error analysis results in floating-point summation. We emphasize analysis that is useful from both a scientific and a teaching point of view.

entry:
@Article{Espelid:1995:FPS,
  author =       "T. O. Espelid",
  title =        "On Floating-Point Summation",
  journal =      j-SIAM-REVIEW,
  volume =       "37",
  number =       "4",
  pages =        "603--607",
  month =        dec,
  year =         "1995",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1037130",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65Gxx (65Bxx)",
  MRnumber =     "1 368 391",
  bibdate =      "Sat Mar 29 09:55:35 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/37/4;
                 http://www.siam.org/journals/sirev/sirev374.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/27303.htm",
  abstract =     "In this paper we focus on some general error analysis
                 results in floating-point summation. We emphasize
                 analysis that is useful from both a scientific and a
                 teaching point of view.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Bergen",
  affiliationaddress = "Bergen, Norway",
  classification = "721.1; 921.4; 921.6; C4110 (Error analysis in
                 numerical methods); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Inf., Bergen University, Norway",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "accurate floating-point summation; algorithm sum;
                 algorithms; binary summation tree; digital arithmetic;
                 error analysis; floating-point arithmetic;
                 floating-point summation; number theory; numerical
                 analysis; ordering; root of the tree; rounding errors;
                 roundoff errors; set theory; trees (mathematics)",
  onlinedate =   "December 1995",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Fateman:1995:FFP
author: Richard J. Fateman and Kevin A. Broughan and Diane K. Willcock and Duane Rettig
title: Fast Floating Point Processing in Common Lisp
journal: j-TOMS
volume: 21
number: 1
pages: 26--62
month: mar
monthnumber: 3
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/200979.200989
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:20:50 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.03.09 10:20:50 ???
note: See remark cite Reid:1996:RFF.
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p26-fateman/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Richard J. Fateman and Kevin A. Broughan and Diane K. Willcock and Duane Rettig
rawnote: See remark \cite{Reid:1996:RFF}.
rawtitle: Fast Floating Point Processing in {Common Lisp}
keywords:
C programming language; Common Lisp; compiler optimization; floating-point arithmetic; Fortran; Lisp; numerical algorithms; symbolic computation

subject:
D.3.4 [Programming Languages]: Processors --- compilers; interpreters; optimization; G.4 [Mathematics of Computing]: Mathematical Software --- efficiency; portability

entry:
@Article{Fateman:1995:FFP,
  author =       "Richard J. Fateman and Kevin A. Broughan and Diane K.
                 Willcock and Duane Rettig",
  title =        "Fast Floating Point Processing in {Common Lisp}",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "26--62",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200989",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:20:50 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark \cite{Reid:1996:RFF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p26-fateman/",
  acknowledgement = ack-nhfb # " and " # ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C programming language; Common Lisp; compiler
                 optimization; floating-point arithmetic; Fortran; Lisp;
                 numerical algorithms; symbolic computation",
  subject =      "D.3.4 [Programming Languages]: Processors ---
                 compilers; interpreters; optimization; G.4 [Mathematics
                 of Computing]: Mathematical Software --- efficiency;
                 portability",
}


bibtype: inproceedings
filename: fparith.bib
label: Ferguson:1995:ECS
author: Warren E. Ferguson, Jr.
title: Exact Computation of a Sum or Difference with Applications to Argument Reduction
crossref: Knowles:1995:PSC
pages: 216--221
year: 1995
DOI: https://doi.org/10.1109/ARITH.1995.465355
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ferguson.pdf
keywords: accurate floating-point summation; ARITH-12; range reduction
acknowledgement: ack-nhfb
rawauthor: Warren E. {Ferguson, Jr.}
rawtitle: Exact Computation of a Sum or Difference with Applications to Argument Reduction
abstract:
Results are presented that identify when the computed value of a sum or difference is exact. The accuracy of an argument reduction algorithm is analyzed using these results. This analysis demonstrates that catastrophic cancellation does not occur in this algorithm's computation of the reduced argument.

rawabstract:
Results are presented that identify when the computed value of a sum or difference is exact. The accuracy of an argument reduction algorithm is analyzed using these results. This analysis demonstrates that catastrophic cancellation does not occur in this algorithm's computation of the reduced argument.

entry:
@InProceedings{Ferguson:1995:ECS,
  author =       "Warren E. {Ferguson, Jr.}",
  title =        "Exact Computation of a Sum or Difference with
                 Applications to Argument Reduction",
  crossref =     "Knowles:1995:PSC",
  pages =        "216--221",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/ARITH.1995.465355",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ferguson.pdf",
  abstract =     "Results are presented that identify when the computed
                 value of a sum or difference is exact. The accuracy of
                 an argument reduction algorithm is analyzed using these
                 results. This analysis demonstrates that catastrophic
                 cancellation does not occur in this algorithm's
                 computation of the reduced argument.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; ARITH-12; range
                 reduction",
}


bibtype: article
filename: fparith.bib
label: Figueroa:1995:WDR
author: Samuel A. Figueroa
title: When is Double Rounding Innocuous?
journal: j-SIGNUM
volume: 30
number: 3
pages: 21--26
month: jul
monthnumber: 7
year: 1995
CODEN: SNEWD6
DOI: https://doi.org/10.1145/221332.221334
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:26 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:26 MDT
URL: http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.pdf
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Samuel A. Figueroa
rawtitle: When is Double Rounding Innocuous?
abstract:
Double rounding is the phenomenon that occurs when the result of an operation is rounded to fit some intermediate destination, and then again when delivered to its final destination. This can be a common occurrence when using some floating-point arithmetic engines which lack single precision registers: results of operations are typically rounded to fit in a register, whose width may be double precision or wider, before being stored in some memory location possibly in a format narrower than that of the registers. Examples of such floating-point arithmetic engines include Intel's x87 series and IBM's POWER architecture. (Implementations of the latter are found in some IBM workstations.)

rawabstract:
Double rounding is the phenomenon that occurs when the result of an operation is rounded to fit some intermediate destination, and then again when delivered to its final destination. This can be a common occurrence when using some floating-point arithmetic engines which lack single precision registers: results of operations are typically rounded to fit in a register, whose width may be double precision or wider, before being stored in some memory location possibly in a format narrower than that of the registers. Examples of such floating-point arithmetic engines include Intel's x87 series and IBM's POWER architecture. (Implementations of the latter are found in some IBM workstations.)

entry:
@Article{Figueroa:1995:WDR,
  author =       "Samuel A. Figueroa",
  title =        "When is Double Rounding Innocuous?",
  journal =      j-SIGNUM,
  volume =       "30",
  number =       "3",
  pages =        "21--26",
  month =        jul,
  year =         "1995",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/221332.221334",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:26 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.pdf",
  abstract =     "Double rounding is the phenomenon that occurs when the
                 result of an operation is rounded to fit some
                 intermediate destination, and then again when delivered
                 to its final destination. This can be a common
                 occurrence when using some floating-point arithmetic
                 engines which lack single precision registers: results
                 of operations are typically rounded to fit in a
                 register, whose width may be double precision or wider,
                 before being stored in some memory location possibly in
                 a format narrower than that of the registers. Examples
                 of such floating-point arithmetic engines include
                 Intel's x87 series and IBM's POWER architecture.
                 (Implementations of the latter are found in some IBM
                 workstations.)",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: techreport
filename: fparith.bib
label: Flynn:1995:ADA
author: Michael J. Flynn and Stuart F. Oberman
title: An analysis of division algorithms and implementations
type: Report
number: CSL-TR-95-675
institution: Stanford University
address: Stanford, CA, USA
pages: 58
month: jul
monthnumber: 7
year: 1995
bibdate: Wed Dec 13 08:55:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.13 08:55:25 ???
URL: https://searchworks.stanford.edu/view/4639530
acknowledgement: ack-nhfb
rawauthor: Michael J. Flynn and Stuart F. Oberman
rawtitle: An analysis of division algorithms and implementations
abstract:
Floating-point division is generally regarded as a low frequency, high latency operation in typical floating-point applications. However, the increasing emphasis on high performance graphics and the industry-wide usage of performance benchmarks forces processor designers to pay close attention to all aspects of floating-point computation. Many algorithms are suitable for implementing division in hardware. This paper presents four major classes of algorithms in a unified framework, namely digit recurrence, functional iteration, very high radix, and variable latency. Digit recurrence algorithms, the most common of which is SRT, use subtraction as the fundamental operator, and they converge to a quotient linearly. Division by functional iteration converges to a quotient quadratically using multiplication. Very high radix division algorithms are similar to digit recurrence algorithms, but they incorporate multiplication to reduce the latency. Variable latency division algorithms reduce the average latency to form the quotient. These algorithms are explained and compared in this work. It is found that for low-cost implementations where chip area must be minimized, digit recurrence algorithms are suitable. An implementation of division by functional iteration can provide the lowest latency for typical multiplier latencies. Variable latency algorithms show promise for simultaneously minimizing average latency while also minimizing area.

rawabstract:
Floating-point division is generally regarded as a low frequency, high latency operation in typical floating-point applications. However, the increasing emphasis on high performance graphics and the industry-wide usage of performance benchmarks forces processor designers to pay close attention to all aspects of floating-point computation. Many algorithms are suitable for implementing division in hardware. This paper presents four major classes of algorithms in a unified framework, namely digit recurrence, functional iteration, very high radix, and variable latency. Digit recurrence algorithms, the most common of which is SRT, use subtraction as the fundamental operator, and they converge to a quotient linearly. Division by functional iteration converges to a quotient quadratically using multiplication. Very high radix division algorithms are similar to digit recurrence algorithms, but they incorporate multiplication to reduce the latency. Variable latency division algorithms reduce the average latency to form the quotient. These algorithms are explained and compared in this work. It is found that for low-cost implementations where chip area must be minimized, digit recurrence algorithms are suitable. An implementation of division by functional iteration can provide the lowest latency for typical multiplier latencies. Variable latency algorithms show promise for simultaneously minimizing average latency while also minimizing area.

entry:
@TechReport{Flynn:1995:ADA,
  author =       "Michael J. Flynn and Stuart F. Oberman",
  title =        "An analysis of division algorithms and
                 implementations",
  type =         "Report",
  number =       "CSL-TR-95-675",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "58",
  month =        jul,
  year =         "1995",
  bibdate =      "Wed Dec 13 08:55:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://searchworks.stanford.edu/view/4639530",
  abstract =     "Floating-point division is generally regarded as a low
                 frequency, high latency operation in typical
                 floating-point applications. However, the increasing
                 emphasis on high performance graphics and the
                 industry-wide usage of performance benchmarks forces
                 processor designers to pay close attention to all
                 aspects of floating-point computation. Many algorithms
                 are suitable for implementing division in hardware.
                 This paper presents four major classes of algorithms in
                 a unified framework, namely digit recurrence,
                 functional iteration, very high radix, and variable
                 latency. Digit recurrence algorithms, the most common
                 of which is SRT, use subtraction as the fundamental
                 operator, and they converge to a quotient linearly.
                 Division by functional iteration converges to a
                 quotient quadratically using multiplication. Very high
                 radix division algorithms are similar to digit
                 recurrence algorithms, but they incorporate
                 multiplication to reduce the latency. Variable latency
                 division algorithms reduce the average latency to form
                 the quotient. These algorithms are explained and
                 compared in this work. It is found that for low-cost
                 implementations where chip area must be minimized,
                 digit recurrence algorithms are suitable. An
                 implementation of division by functional iteration can
                 provide the lowest latency for typical multiplier
                 latencies. Variable latency algorithms show promise for
                 simultaneously minimizing average latency while also
                 minimizing area.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Flynn:1995:SPT
author: M. J. Flynn and K. Nowka and G. Bewick and E. Schwarz and N. Quach
title: The SNAP Project: Towards Sub-Nanosecond Arithmetic
crossref: Knowles:1995:PSC
pages: 75--83
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: M. J. Flynn and K. Nowka and G. Bewick and E. Schwarz and N. Quach
rawtitle: The {SNAP} Project: Towards Sub-Nanosecond Arithmetic
URL:
ftp://arith.stanford.edu/tr/snap_arith12.ps.Z; http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Flynn.pdf

entry:
@InProceedings{Flynn:1995:SPT,
  author =       "M. J. Flynn and K. Nowka and G. Bewick and E. Schwarz
                 and N. Quach",
  title =        "The {SNAP} Project: Towards Sub-Nanosecond
                 Arithmetic",
  crossref =     "Knowles:1995:PSC",
  pages =        "75--83",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/snap_arith12.ps.Z;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Flynn.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: inproceedings
filename: fparith.bib
label: Freeman:1995:CAD
author: S. Freeman and M. O'Donnell
booktitle: 1995 International Conference on Acoustics, Speech, and Signal Processing
title: A complex arithmetic digital signal processor using CORDIC rotators
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 3191--3194 (vol. 5)
year: 1995
DOI: https://doi.org/10.1109/ICASSP.1995.479563
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: S. Freeman and M. O'Donnell
rawbooktitle: {1995 International Conference on Acoustics, Speech, and Signal Processing}
rawtitle: A complex arithmetic digital signal processor using {CORDIC} rotators
keywords:
Adders; Clocks; Digital arithmetic; Digital signal processors; Process design; Random access memory; Read only memory; Registers; Signal design; Signal processing

entry:
@InProceedings{Freeman:1995:CAD,
  author =       "S. Freeman and M. O'Donnell",
  booktitle =    "{1995 International Conference on Acoustics, Speech,
                 and Signal Processing}",
  title =        "A complex arithmetic digital signal processor using
                 {CORDIC} rotators",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3191--3194 (vol. 5)",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/ICASSP.1995.479563",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Clocks; Digital arithmetic; Digital signal
                 processors; Process design; Random access memory; Read
                 only memory; Registers; Signal design; Signal
                 processing",
}


bibtype: article
filename: fparith.bib
label: Fried:1995:PON
author: Stephen S. Fried
title: Pentium Optimizations and Numeric Performance
journal: j-DDJ
volume: 20
number: 1
pages: 18--20, 22, 26--29
month: jan
monthnumber: 1
year: 1995
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Sep 05 07:21:01 1996
bibtimestamp: 1996.09.05 07:21:01 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
affiliation: Microway, Kingston, MA, USA
rawauthor: Stephen S. Fried
rawtitle: {Pentium} Optimizations and Numeric Performance
abstract:
The Pentium is the first member of the Intel x86 family that requires RISC-style instruction scheduling to achieve its full potential. Steve analyzes what this means in terms of Pentium floating-point performance and how you can get full throughput from a Pentium.

keywords:
Compilers; Floating-point performance; Full throughput; Intel x86 family; Numeric performance; Optimizations; Pentium; RISC-style instruction scheduling; Tools

thesaurus:
Floating point arithmetic; Microprocessor chips; Optimisation; Performance evaluation; Program compilers; Reduced instruction set computing

rawabstract:
The Pentium is the first member of the Intel x86 family that requires RISC-style instruction scheduling to achieve its full potential. Steve analyzes what this means in terms of Pentium floating-point performance and how you can get full throughput from a Pentium.

entry:
@Article{Fried:1995:PON,
  author =       "Stephen S. Fried",
  title =        "{Pentium} Optimizations and Numeric Performance",
  journal =      j-DDJ,
  volume =       "20",
  number =       "1",
  pages =        "18--20, 22, 26--29",
  month =        jan,
  year =         "1995",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 05 07:21:01 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "The Pentium is the first member of the Intel x86
                 family that requires RISC-style instruction scheduling
                 to achieve its full potential. Steve analyzes what this
                 means in terms of Pentium floating-point performance
                 and how you can get full throughput from a Pentium.",
  acknowledgement = ack-nhfb,
  affiliation =  "Microway, Kingston, MA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods); C5470 (Performance evaluation and
                 testing); C6150C (Compilers, interpreters and other
                 processors)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "Compilers; Floating-point performance; Full
                 throughput; Intel x86 family; Numeric performance;
                 Optimizations; Pentium; RISC-style instruction
                 scheduling; Tools",
  thesaurus =    "Floating point arithmetic; Microprocessor chips;
                 Optimisation; Performance evaluation; Program
                 compilers; Reduced instruction set computing",
}


bibtype: phdthesis
filename: fparith.bib
label: Gluss:1995:DIA
author: Robert Joseph Gluss
title: Design and implementation of an asynchronous radix-$4$ pre-scaling floating-point divider
type: Thesis (M.S.)
school: Department of Electrical and Computer Engineering, University of California, Davis
address: Davis, CA, USA
pages: 18--20, 22, 26--29
year: 1995
LCCN: LD781.D5j 1995 G587
bibdate: Thu Oct 24 14:19:35 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 14:19:35 MDT
keywords: dissertations, academic -- University of California, Davis -- Electrical and Computer Engineering
acknowledgement: ack-nhfb
rawauthor: Robert Joseph Gluss
rawtitle: Design and implementation of an asynchronous radix-$4$ pre-scaling floating-point divider
entry:
@PhdThesis{Gluss:1995:DIA,
  author =       "Robert Joseph Gluss",
  title =        "Design and implementation of an asynchronous radix-$4$
                 pre-scaling floating-point divider",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical and Computer Engineering,
                 University of California, Davis",
  address =      "Davis, CA, USA",
  year =         "1995",
  LCCN =         "LD781.D5j 1995 G587",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations, academic -- University of California,
                 Davis -- Electrical and Computer Engineering",
}


bibtype: inproceedings
filename: fparith.bib
label: Greenley:1995:UNG
title: UltraSPARC: the next generation superscalar 64-bit SPARC
crossref: IEEE:1995:DPC
pages: 442--451
month: mar
monthnumber: 3
year: 1995
DOI: https://doi.org/10.1109/CMPCON.1995.512421
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawtitle: {UltraSPARC}: the next generation superscalar 64-bit {SPARC}
author:
D. Greenley and J. Bauman and D. Chang and Dennis Chen and R. Eltejaein and P. Ferolito and P. Fu and Robert B. Garner and D. Greenhill and H. Grewal and Kalon Holdbrook and B. Kim and Leslie Kohn and H. Kwan and M. Levitt and Guillermo Maturana and D. Mrazek and Chitresh Narasimhaiah and Kevin Normoyle and N. Parveen and P. Patel and A. Prabhu and Marc Tremblay and Michelle Wong and L. Yang and Krishna Yarlagadda and Robert K. Yu and Robert Yung and Gregory B. Zyner

abstract:
UltraSPARC is the first microprocessor from Sun Microsystems' SPARC Technology Business to implement the new 64-bit SPARC V9 architecture. ULtraSPARC is equipped with unique multimedia capabilities and is capable of 4-way superscalar instruction dispatch, with an emphasis on maximal system efficiency and throughput in the execution of complex, memory-intensive applications. UltraSPARC maintains a strict binary compatibility with the thousands of existing 32-bit applications developed for other SPARC processors. This paper describes the feature set and operation of UltraSPARC.

rawabstract:
UltraSPARC is the first microprocessor from Sun Microsystems' SPARC Technology Business to implement the new 64-bit SPARC V9 architecture. ULtraSPARC is equipped with unique multimedia capabilities and is capable of 4-way superscalar instruction dispatch, with an emphasis on maximal system efficiency and throughput in the execution of complex, memory-intensive applications. UltraSPARC maintains a strict binary compatibility with the thousands of existing 32-bit applications developed for other SPARC processors. This paper describes the feature set and operation of UltraSPARC.

rawauthor:
D. Greenley and J. Bauman and D. Chang and Dennis Chen and R. Eltejaein and P. Ferolito and P. Fu and Robert B. Garner and D. Greenhill and H. Grewal and Kalon Holdbrook and B. Kim and Leslie Kohn and H. Kwan and M. Levitt and Guillermo Maturana and D. Mrazek and Chitresh Narasimhaiah and Kevin Normoyle and N. Parveen and P. Patel and A. Prabhu and Marc Tremblay and Michelle Wong and L. Yang and Krishna Yarlagadda and Robert K. Yu and Robert Yung and Gregory B. Zyner

entry:
@InProceedings{Greenley:1995:UNG,
  author =       "D. Greenley and J. Bauman and D. Chang and Dennis Chen
                 and R. Eltejaein and P. Ferolito and P. Fu and Robert
                 B. Garner and D. Greenhill and H. Grewal and Kalon
                 Holdbrook and B. Kim and Leslie Kohn and H. Kwan and M.
                 Levitt and Guillermo Maturana and D. Mrazek and
                 Chitresh Narasimhaiah and Kevin Normoyle and N. Parveen
                 and P. Patel and A. Prabhu and Marc Tremblay and
                 Michelle Wong and L. Yang and Krishna Yarlagadda and
                 Robert K. Yu and Robert Yung and Gregory B. Zyner",
  title =        "{UltraSPARC}: the next generation superscalar 64-bit
                 {SPARC}",
  crossref =     "IEEE:1995:DPC",
  pages =        "442--451",
  month =        mar,
  year =         "1995",
  DOI =          "https://doi.org/10.1109/CMPCON.1995.512421",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "UltraSPARC is the first microprocessor from Sun
                 Microsystems' SPARC Technology Business to implement
                 the new 64-bit SPARC V9 architecture. ULtraSPARC is
                 equipped with unique multimedia capabilities and is
                 capable of 4-way superscalar instruction dispatch, with
                 an emphasis on maximal system efficiency and throughput
                 in the execution of complex, memory-intensive
                 applications. UltraSPARC maintains a strict binary
                 compatibility with the thousands of existing 32-bit
                 applications developed for other SPARC processors. This
                 paper describes the feature set and operation of
                 UltraSPARC.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Halfhill:1995:TBP
author: Tom R. Halfhill
journal: j-BYTE
volume: 20
number: 3
pages: 163--??
month: mar
monthnumber: 3
year: 1995
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Tue Jan 2 10:01:41 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.01.02 10:01:41 MST
fjournal: BYTE Magazine
acknowledgement: ack-nhfb
rawauthor: Tom R. Halfhill
title:
The Truth Behind the Pentium Bug: How often do the five empty cells in the Pentium's FPU lookup table spell miscalculation?

rawtitle:
The Truth Behind the {Pentium} Bug: How often do the five empty cells in the {Pentium}'s {FPU} lookup table spell miscalculation?

entry:
@Article{Halfhill:1995:TBP,
  author =       "Tom R. Halfhill",
  title =        "The Truth Behind the {Pentium} Bug: How often do the
                 five empty cells in the {Pentium}'s {FPU} lookup table
                 spell miscalculation?",
  journal =      j-BYTE,
  volume =       "20",
  number =       "3",
  pages =        "163--??",
  month =        mar,
  year =         "1995",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Tue Jan 2 10:01:41 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
}


bibtype: inproceedings
filename: fparith.bib
label: Hamano:1995:DCA
author: Takafumi Hamano and Naofumi Takagi and Shuzo Yajima and Franco P. Preparata
title: $ O(n) $-Depth Circuit Algorithm for Modular Exponentiation
crossref: Knowles:1995:PSC
pages: 188--192
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hamano.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Takafumi Hamano and Naofumi Takagi and Shuzo Yajima and Franco P. Preparata
rawtitle: {$ O(n) $}-Depth Circuit Algorithm for Modular Exponentiation
entry:
@InProceedings{Hamano:1995:DCA,
  author =       "Takafumi Hamano and Naofumi Takagi and Shuzo Yajima
                 and Franco P. Preparata",
  title =        "{$ O(n) $}-Depth Circuit Algorithm for Modular
                 Exponentiation",
  crossref =     "Knowles:1995:PSC",
  pages =        "188--192",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hamano.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Harrison:1995:FPV
author: J. Harrison
title: Floating Point Verification in HOL
journal: j-LECT-NOTES-COMP-SCI
number: 971
pages: 186--??
year: 1995
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
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
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: J. Harrison
rawtitle: Floating Point Verification in {HOL}
entry:
@Article{Harrison:1995:FPV,
  author =       "J. Harrison",
  title =        "Floating Point Verification in {HOL}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "??",
  number =       "971",
  pages =        "186--??",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Hassler:1995:FET
author: Hannes Hassler and Naofumi Takagi
title: Function Evaluation by Table Look-up and Addition
crossref: Knowles:1995:PSC
pages: 10--16
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hassler.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Hannes Hassler and Naofumi Takagi
rawtitle: Function Evaluation by Table Look-up and Addition
entry:
@InProceedings{Hassler:1995:FET,
  author =       "Hannes Hassler and Naofumi Takagi",
  title =        "Function Evaluation by Table Look-up and Addition",
  crossref =     "Knowles:1995:PSC",
  pages =        "10--16",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hassler.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: techreport
filename: fparith.bib
label: Hauser:1995:HFE
author: John R. Hauser
title: Handling floating-point exceptions in numeric programs
type: Report
number: UCB/CSD 95-870
institution: Computer Science Division (EECS), University of California
address: Berkeley, CA, USA
pages: 31
month: mar
monthnumber: 3
year: 1995
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: John R. Hauser
rawtitle: Handling floating-point exceptions in numeric programs
entry:
@TechReport{Hauser:1995:HFE,
  author =       "John R. Hauser",
  title =        "Handling floating-point exceptions in numeric
                 programs",
  type =         "Report",
  number =       "UCB/CSD 95-870",
  institution =  "Computer Science Division (EECS), University of
                 California",
  address =      "Berkeley, CA, USA",
  pages =        "31",
  month =        mar,
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Helsley:1995:SZL
author: Harold David Helsley
title: A study of zero-input limit cycles in floating-point digital signal processors
type: Thesis (M.S.)
school: University of Tennessee, Knoxville
address: Knoxville, TN, USA
pages: vii + 65
year: 1995
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: Limit cycles.; Signal processing --- Digital techniques.
acknowledgement: ack-nhfb
rawauthor: Harold David Helsley
rawtitle: A study of zero-input limit cycles in floating-point digital signal processors
entry:
@MastersThesis{Helsley:1995:SZL,
  author =       "Harold David Helsley",
  title =        "A study of zero-input limit cycles in floating-point
                 digital signal processors",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vii + 65",
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Limit cycles.; Signal processing --- Digital
                 techniques.",
}


bibtype: inproceedings
filename: fparith.bib
label: Hiasat:1995:HSDa
author: A. A. Hiasat and H. S. Abdel-Aty-Zohdy
booktitle: IEEE International Symposium on Circuits and Systems, ISCAS '95, 3 May 1995
title: A high-speed division algorithm for residue number system
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1996--1999
year: 1995
DOI: https://doi.org/10.1109/ISCAS.1995.523813
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. A. Hiasat and H. S. Abdel-Aty-Zohdy
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, {ISCAS '95}, 3 May 1995
rawtitle: A high-speed division algorithm for residue number system
entry:
@InProceedings{Hiasat:1995:HSDa,
  author =       "A. A. Hiasat and H. S. Abdel-Aty-Zohdy",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '95}, 3 May 1995",
  title =        "A high-speed division algorithm for residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1996--1999",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1995.523813",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for one of the longstanding problems
                 in residue number system, namely division, is
                 presented. The algorithm is very simple. It approaches
                 the paper-and-pencil division procedure where the
                 quotient is selected to guarantee a non- \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Hiasat:1995:HSDb
author: A. A. Hiasat and H. S. Abdel-Aty-Zohdy
booktitle: IEEE International Symposium on Circuits and Systems, ISCAS '95, 3 May 1995
title: A high-speed division algorithm for residue number system
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1996--1999
year: 1995
DOI: https://doi.org/10.1109/ISCAS.1995.523813
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. A. Hiasat and H. S. Abdel-Aty-Zohdy
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, {ISCAS '95}, 3 May 1995
rawtitle: A high-speed division algorithm for residue number system
entry:
@InProceedings{Hiasat:1995:HSDb,
  author =       "A. A. Hiasat and H. S. Abdel-Aty-Zohdy",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '95}, 3 May 1995",
  title =        "A high-speed division algorithm for residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1996--1999",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1995.523813",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for one of the longstanding problems
                 in residue number system, namely division, is
                 presented. The algorithm is very simple. It approaches
                 the paper-and-pencil division procedure where the
                 quotient is selected to guarantee a non- \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Hitz:1995:IDR
author: Markus A. Hitz and Erich Kaltofen
title: Integer division in residue number systems
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 8
pages: 983--989
month: aug
monthnumber: 8
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.403714
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:29 MDT 2011
bibtimestamp: 2011.07.06 08:01:29 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Markus A. Hitz and Erich Kaltofen
rawtitle: Integer division in residue number systems
URL:
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9076; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403714

entry:
@Article{Hitz:1995:IDR,
  author =       "Markus A. Hitz and Erich Kaltofen",
  title =        "Integer division in residue number systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "8",
  pages =        "983--989",
  month =        aug,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.403714",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9076;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403714",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This contribution to the ongoing discussion of
                 division algorithm for residue number systems (RNS) is
                 based on Newton iteration for computing the reciprocal.
                 An extended RNS with twice the number of moduli
                 provides the range required for \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Ho:1995:CFF
author: H. Ho and V. Szwarc and L. Desormeaux
booktitle: Proceedings of the Eighth Annual IEEE International ASIC Conference and Exhibit, 1995
title: A comparison of FIR filter implementations based on two's complement and residue number arithmetic
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 35--38
year: 1995
DOI: https://doi.org/10.1109/ASIC.1995.580676
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: H. Ho and V. Szwarc and L. Desormeaux
rawbooktitle: Proceedings of the Eighth Annual {IEEE} International {ASIC} Conference and Exhibit, 1995
rawtitle:
A comparison of {FIR} filter implementations based on two's complement and residue number arithmetic

entry:
@InProceedings{Ho:1995:CFF,
  author =       "H. Ho and V. Szwarc and L. Desormeaux",
  booktitle =    "Proceedings of the Eighth Annual {IEEE} International
                 {ASIC} Conference and Exhibit, 1995",
  title =        "A comparison of {FIR} filter implementations based on
                 two's complement and residue number arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "35--38",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASIC.1995.580676",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Two FIR filter designs based on residue number
                 arithmetic (RNA) are presented and compared with a
                 conventional design based on two's complement
                 arithmetic (TCA). For the RNA based designs the
                 arithmetic operations are implemented by means of small
                 \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Ho:1995:FPI
author: Lei Ho
title: Floating point implementation for Motorola HC6811C: GNU C cross-compiler
type: Master's Thesis
school: Department of Electrical Engineering, Ryerson Polytechnic University
address: Toronto, Ontario, Canada
pages: 35--38
year: 1995
bibdate: Mon Apr 18 06:29:41 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.18 06:29:41 ???
acknowledgement: ack-nhfb
rawauthor: Lei Ho
rawtitle: Floating point implementation for {Motorola HC6811C}: {GNU C} cross-compiler
entry:
@MastersThesis{Ho:1995:FPI,
  author =       "Lei Ho",
  title =        "Floating point implementation for {Motorola HC6811C}:
                 {GNU C} cross-compiler",
  type =         "{Master}'s Thesis",
  school =       "Department of Electrical Engineering, Ryerson
                 Polytechnic University",
  address =      "Toronto, Ontario, Canada",
  year =         "1995",
  bibdate =      "Mon Apr 18 06:29:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Check thesis type?? Ryerson library catalog does not
                 specify.",
}


bibtype: article
filename: fparith.bib
label: Hobson:1995:EMR
author: R. F. Hobson and M. W. Fraser
title: An efficient maximum-redundancy radix-$8$ SRT division and square-root method
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 30
number: 1
pages: 29--38
month: jan
monthnumber: 1
year: 1995
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
affiliation: Sch. of Computer Science, Simon Fraser University, Burnaby, BC, Canada
rawauthor: R. F. Hobson and M. W. Fraser
rawtitle: An efficient maximum-redundancy radix-$8$ {SRT} division and square-root method
abstract:
A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.

keywords:
1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE floating point algorithm; Integrated control path; Maximally redundant digit set; Maximum-redundancy radix-8 SRT algorithm; Multiplication; Parallel iterative multiplier; Partial remainder production; Redundant partial-remainder; Square-root method; Table lookup

thesaurus:
Adders; CMOS digital integrated circuits; Digital arithmetic; Dividing circuits; Floating point arithmetic; Multiplying circuits

rawabstract:
A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.

entry:
@Article{Hobson:1995:EMR,
  author =       "R. F. Hobson and M. W. Fraser",
  title =        "An efficient maximum-redundancy radix-$8$ {SRT}
                 division and square-root method",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "1",
  pages =        "29--38",
  month =        jan,
  year =         "1995",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the next quotient or
                 square-root digit by the divisor or square-root value.
                 A separate (parallel) full precision iterative
                 multiplier is used for partial remainder production.
                 Strategic details of a radix-8 implementation are
                 discussed. It is shown that a maximally redundant digit
                 set is a viable choice for high performance in this
                 case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Computer Science, Simon Fraser University,
                 Burnaby, BC, Canada",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
                 floating point algorithm; Integrated control path;
                 Maximally redundant digit set; Maximum-redundancy
                 radix-8 SRT algorithm; Multiplication; Parallel
                 iterative multiplier; Partial remainder production;
                 Redundant partial-remainder; Square-root method; Table
                 lookup",
  numericalindex = "Size 1.2E-06 m",
  summary =      "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the \ldots{}",
  thesaurus =    "Adders; CMOS digital integrated circuits; Digital
                 arithmetic; Dividing circuits; Floating point
                 arithmetic; Multiplying circuits",
}


bibtype: inproceedings
filename: fparith.bib
label: Houelle:1995:AFL
author: A. Houelle and H. Mehrez and N. Vaucher and L. Montalvo and A. Guyot
title: Application of Fast Layout Synthesis Environment to Dividers Evaluation
crossref: Knowles:1995:PSC
pages: 67--74
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Houelle.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: A. Houelle and H. Mehrez and N. Vaucher and L. Montalvo and A. Guyot
rawtitle: Application of Fast Layout Synthesis Environment to Dividers Evaluation
entry:
@InProceedings{Houelle:1995:AFL,
  author =       "A. Houelle and H. Mehrez and N. Vaucher and L.
                 Montalvo and A. Guyot",
  title =        "Application of Fast Layout Synthesis Environment to
                 Dividers Evaluation",
  crossref =     "Knowles:1995:PSC",
  pages =        "67--74",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Houelle.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: techreport
filename: fparith.bib
label: Hough:1995:EPD
author: David Hough
title: Effects of Pentium Division Flaw and its Software Workaround
type: Report
institution: Sun Microsystems
address: Mountain View, CA 94043, USA
pages: 22
day: 28
month: feb
monthnumber: 2
year: 1995
bibdate: Mon Dec 16 11:29:48 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2024.12.16 11:29:48 ???
URL: https://www.validlab.com/reports/pentium/
keywords: Pentium divide flaw
acknowledgement: ack-nhfb
rawauthor: David Hough
rawtitle: Effects of {Pentium} Division Flaw and its Software Workaround
abstract:
The infamous Intel Pentium floating-point division flaw is seldom visible in the results of realistic technical applications, nor does it perceptibly affect performance. But some programs skillfully designed to look for arithmetic flaws can find it. In contrast, the expected harmless differences between 486 and Pentium elementary transcendental functions, due to the improved approximations in the latter, are often evident in ordinary applications.par Intel and Cygnus published a recommended compiler workaround that reduces the effect of the Pentium division flaw to at most one unit per division, in the least significant bit of extended precision. Intel has also modified its math library product libm.a to avoid the division flaw. The compiler and libm workarounds do not affect results of CPU chips other than flawed Pentium chips.par The two modifications to the compiler and libm avoid any severe effects of the Pentium flaw, but sometimes cause harmlessly different results in realistic technical applications. The modifications degrade performance of flawed CPUs by a median of 1%, and SPECfp92 ratios by about 9%.

rawabstract:
The infamous Intel Pentium floating-point division flaw is seldom visible in the results of realistic technical applications, nor does it perceptibly affect performance. But some programs skillfully designed to look for arithmetic flaws can find it. In contrast, the expected harmless differences between 486 and Pentium elementary transcendental functions, due to the improved approximations in the latter, are often evident in ordinary applications.\par Intel and Cygnus published a recommended compiler workaround that reduces the effect of the Pentium division flaw to at most one unit per division, in the least significant bit of extended precision. Intel has also modified its math library product libm.a to avoid the division flaw. The compiler and libm workarounds do not affect results of CPU chips other than flawed Pentium chips.\par The two modifications to the compiler and libm avoid any severe effects of the Pentium flaw, but sometimes cause harmlessly different results in realistic technical applications. The modifications degrade performance of flawed CPUs by a median of 1\%, and SPECfp92 ratios by about 9\%.

entry:
@TechReport{Hough:1995:EPD,
  author =       "David Hough",
  title =        "Effects of {Pentium} Division Flaw and its Software
                 Workaround",
  type =         "Report",
  institution =  "Sun Microsystems",
  address =      "Mountain View, CA 94043, USA",
  pages =        "22",
  day =          "28",
  month =        feb,
  year =         "1995",
  bibdate =      "Mon Dec 16 11:29:48 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.validlab.com/reports/pentium/",
  abstract =     "The infamous Intel Pentium floating-point division
                 flaw is seldom visible in the results of realistic
                 technical applications, nor does it perceptibly affect
                 performance. But some programs skillfully designed to
                 look for arithmetic flaws can find it. In contrast, the
                 expected harmless differences between 486 and Pentium
                 elementary transcendental functions, due to the
                 improved approximations in the latter, are often
                 evident in ordinary applications.\par

                 Intel and Cygnus published a recommended compiler
                 workaround that reduces the effect of the Pentium
                 division flaw to at most one unit per division, in the
                 least significant bit of extended precision. Intel has
                 also modified its math library product libm.a to avoid
                 the division flaw. The compiler and libm workarounds do
                 not affect results of CPU chips other than flawed
                 Pentium chips.\par

                 The two modifications to the compiler and libm avoid
                 any severe effects of the Pentium flaw, but sometimes
                 cause harmlessly different results in realistic
                 technical applications. The modifications degrade
                 performance of flawed CPUs by a median of 1\%, and
                 SPECfp92 ratios by about 9\%.",
  acknowledgement = ack-nhfb,
  keywords =     "Pentium divide flaw",
}


bibtype: techreport
filename: fparith.bib
label: Hough:1995:UVP
author: David Hough
title: UCBTEST vs. Pentium
type: Report
institution: Sun Microsystems
address: Mountain View, CA 94043, USA
pages: 3
day: 5
month: mar
monthnumber: 3
year: 1995
bibdate: Mon Dec 16 11:40:24 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2024.12.16 11:40:24 ???
URL: https://www.validlab.com/reports/testing.pdf
keywords: Pentium divide flaw
acknowledgement: ack-nhfb
rawauthor: David Hough
rawtitle: {UCBTEST} vs. {Pentium}
abstract:
University of California research into systematic verification of computer arithmetic has been put into a form in which anybody could in principle test any computer arithmetic.par So it's exceedingly unlikely that another microprocessor will come to market with bugs that UCBTEST software might detect, or with uninitialized entries in a divider's PLA. But to avoid the situation of generals always fighting the last war, what can be done to detect, or better prevent, the next arithmetic flaw

rawabstract:
University of California research into systematic verification of computer arithmetic has been put into a form in which anybody could in principle test any computer arithmetic.\par So it's exceedingly unlikely that another microprocessor will come to market with bugs that UCBTEST software might detect, or with uninitialized entries in a divider's PLA. But to avoid the situation of generals always fighting the last war, what can be done to detect, or better prevent, the next arithmetic flaw

entry:
@TechReport{Hough:1995:UVP,
  author =       "David Hough",
  title =        "{UCBTEST} vs. {Pentium}",
  type =         "Report",
  institution =  "Sun Microsystems",
  address =      "Mountain View, CA 94043, USA",
  pages =        "3",
  day =          "5",
  month =        mar,
  year =         "1995",
  bibdate =      "Mon Dec 16 11:40:24 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.validlab.com/reports/testing.pdf",
  abstract =     "University of California research into systematic
                 verification of computer arithmetic has been put into a
                 form in which anybody could in principle test any
                 computer arithmetic.\par

                 So it's exceedingly unlikely that another
                 microprocessor will come to market with bugs that
                 UCBTEST software might detect, or with uninitialized
                 entries in a divider's PLA. But to avoid the situation
                 of generals always fighting the last war, what can be
                 done to detect, or better prevent, the next arithmetic
                 flaw",
  acknowledgement = ack-nhfb,
  keywords =     "Pentium divide flaw",
}


bibtype: inproceedings
filename: fparith.bib
label: Hunt:1995:APF
author: D. Hunt
title: Advanced performance features of the 64-bit PA-8000
crossref: IEEE:1995:DPC
pages: 123--128
month: mar
monthnumber: 3
year: 1995
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: D. Hunt
rawtitle: Advanced performance features of the 64-bit {PA-8000}
entry:
@InProceedings{Hunt:1995:APF,
  author =       "D. Hunt",
  title =        "Advanced performance features of the 64-bit
                 {PA-8000}",
  crossref =     "IEEE:1995:DPC",
  pages =        "123--128",
  month =        mar,
  year =         "1995",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Ito:1995:EIAa
author: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
title: Efficient Initial Approximation Methods for Division and Square Using a Multiply-Add Unit
type: SIG Notes
number: 95-HPC-55-10
institution: IPSJ
pages: 73--80
month: mar
monthnumber: 3
year: 1995
bibdate: Wed Dec 13 10:53:57 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.13 10:53:57 ???
acknowledgement: ack-nhfb
rawauthor: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
rawtitle: Efficient Initial Approximation Methods for Division and Square Using a Multiply-Add Unit
remark:
I cannot find this online, so institution and address are uncertain. Is this a journal article or technical report?

entry:
@TechReport{Ito:1995:EIAa,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Efficient Initial Approximation Methods for Division
                 and Square Using a Multiply-Add Unit",
  type =         "SIG Notes",
  number =       "95-HPC-55-10",
  institution =  "IPSJ",
  address =      "????",
  pages =        "73--80",
  month =        mar,
  year =         "1995",
  bibdate =      "Wed Dec 13 10:53:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "I cannot find this online, so institution and address
                 are uncertain. Is this a journal article or technical
                 report?",
}


bibtype: inproceedings
filename: fparith.bib
label: Ito:1995:EIAb
author: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
title: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
crossref: Knowles:1995:PSC
pages: 2--9
month: jul
monthnumber: 7
year: 1995
DOI: https://doi.org/10.1109/arith.1995.465383
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ito.pdf
keywords: ARITH-12
acknowledgement: ack-sfo
rawauthor: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
rawtitle: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
entry:
@InProceedings{Ito:1995:EIAb,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Efficient Initial Approximation and Fast Converging
                 Methods for Division and Square Root",
  crossref =     "Knowles:1995:PSC",
  pages =        "2--9",
  month =        jul,
  year =         "1995",
  DOI =          "https://doi.org/10.1109/arith.1995.465383",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ito.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "Efficient initial approximations and fast converging
                 algorithms are important to achieve the desired
                 precision faster at lower hardware cost in
                 multiplicative division and square root. In this paper,
                 a new initial approximation method for division,
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Jain:1995:HSD
author: V. K. Jain and L. Lin
title: High-Speed Double Precision Computation of Nonlinear Functions
crossref: Knowles:1995:PSC
pages: 107--114
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: V. K. Jain and L. Lin
rawtitle: High-Speed Double Precision Computation of Nonlinear Functions
entry:
@InProceedings{Jain:1995:HSD,
  author =       "V. K. Jain and L. Lin",
  title =        "High-Speed Double Precision Computation of Nonlinear
                 Functions",
  crossref =     "Knowles:1995:PSC",
  pages =        "107--114",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Jang:1995:OSA
author: Ju-Wook Jang and Viktor K. Prasanna
title: An Optimal Sorting Algorithm on Reconfigurable Mesh
journal: j-J-PAR-DIST-COMP
volume: 25
number: 1
pages: 31--41
day: 15
month: feb
monthnumber: 2
year: 1995
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1995.1027
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:18:56 MST 2000
bibtimestamp: 2000.03.09 09:18:56 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: University of Southern California, Los Angeles, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: T Theoretical or Mathematical
rawauthor: Ju-Wook Jang and Viktor K. Prasanna
rawtitle: An Optimal Sorting Algorithm on Reconfigurable Mesh
URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production/pdf

keywords:
architectures; arithmetic; bit model; computational complexity; constant time; constant time algorithm; lower bound; optimal sorting algorithm; parallel; parallel algorithms; problems; reconfigurable architecture; reconfigurable architectures; reconfigurable mesh; sorting; VLSI

entry:
@Article{Jang:1995:OSA,
  author =       "Ju-Wook Jang and Viktor K. Prasanna",
  title =        "An Optimal Sorting Algorithm on Reconfigurable Mesh",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "25",
  number =       "1",
  pages =        "31--41",
  day =          "15",
  month =        feb,
  year =         "1995",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1995.1027",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:56 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C4240P (Parallel programming and algorithm theory);
                 C5220P (Parallel architecture); C6130 (Data handling
                 techniques)",
  corpsource =   "University of Southern California, Los Angeles, CA,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "architectures; arithmetic; bit model; computational
                 complexity; constant time; constant time algorithm;
                 lower bound; optimal sorting algorithm; parallel;
                 parallel algorithms; problems; reconfigurable
                 architecture; reconfigurable architectures;
                 reconfigurable mesh; sorting; VLSI",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: unpublished
filename: fparith.bib
label: Kahan:1995:TSD
author: W. Kahan
title: A Test for SRT Division
pages: 31--41
year: 1995
bibdate: Mon Apr 25 05:50:41 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.25 05:50:41 ???
note: Lecture notes
URL: http://www.cs.berkeley.edu/~wkahan/srtest
keywords: floating-point testing
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Lecture notes
rawtitle: A Test for {SRT} Division
entry:
@Unpublished{Kahan:1995:TSD,
  author =       "W. Kahan",
  title =        "A Test for {SRT} Division",
  year =         "1995",
  bibdate =      "Mon Apr 25 05:50:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture notes",
  URL =          "http://www.cs.berkeley.edu/~wkahan/srtest",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1995:USP
author: Students of Prof.W.Kahan
pages: 31--41
day: 12
month: mar
monthnumber: 3
year: 1995
bibdate: Wed May 26 07:29:55 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.05.26 07:29:55 ???
URL: http://www.netlib.org/fp/ucbtest.tgz
keywords: floating-point testing
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: {Students of Prof.W.Kahan}
title:
UCBTEST: a suite of programs for testing certain difficult cases of IEEE 754 floating-point arithmetic

remark:
From the source code, students and authors credited are (in alphabetical order) M. Alemi, D. Feenberg, Warren Ferguson David G. Hough, David Gay, W. J. Cody, R. Karpkinski, Z. A. Liu, S. Ma, Stephen Moshier, M. Mueller, K. C. Ng, D. Priest, T. Quarles, T. Sumner, G. Taylor, B. Toy, W. Waite, and B. Wichmann.

rawtitle:
{UCBTEST}: a suite of programs for testing certain difficult cases of {IEEE 754} floating-point arithmetic

entry:
@Misc{Kahan:1995:USP,
  author =       "{Students of Prof.W.Kahan}",
  title =        "{UCBTEST}: a suite of programs for testing certain
                 difficult cases of {IEEE 754} floating-point
                 arithmetic",
  howpublished = "World-Wide Web document",
  day =          "12",
  month =        mar,
  year =         "1995",
  bibdate =      "Wed May 26 07:29:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/fp/ucbtest.tgz",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
  remark =       "From the source code, students and authors credited
                 are (in alphabetical order) M. Alemi, D. Feenberg,
                 Warren Ferguson David G. Hough, David Gay, W. J. Cody,
                 R. Karpkinski, Z. A. Liu, S. Ma, Stephen Moshier, M.
                 Mueller, K. C. Ng, D. Priest, T. Quarles, T. Sumner, G.
                 Taylor, B. Toy, W. Waite, and B. Wichmann.",
}


bibtype: article
filename: fparith.bib
label: Kaliski:1995:MIA
author: Burton S. Kaliski, Jr.
title: The Montgomery inverse and its applications
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 8
pages: 1064--1065
month: aug
monthnumber: 8
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.403725
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:29 MDT 2011
bibtimestamp: 2011.07.06 08:01:29 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403725
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Burton S. {Kaliski, Jr.}
rawtitle: The {Montgomery} inverse and its applications
abstract:
The Montgomery inverse of $b$ modulo $a$ is $ b^-1 2^n bmod a $, where $n$ is the number of bits in $a$. The right-shifting binary algorithm for modular inversion is shown naturally to compute the new inverse in fewer operations than the ordinary modular inverse. The new inverse facilitates recent work by Koc on modular exponentiation and has other applications in cryptography

rawabstract:
The Montgomery inverse of $b$ modulo $a$ is $ b^{-1} 2^n \bmod a $, where $n$ is the number of bits in $a$. The right-shifting binary algorithm for modular inversion is shown naturally to compute the new inverse in fewer operations than the ordinary modular inverse. The new inverse facilitates recent work by Ko{\c{c}} on modular exponentiation and has other applications in cryptography

entry:
@Article{Kaliski:1995:MIA,
  author =       "Burton S. {Kaliski, Jr.}",
  title =        "The {Montgomery} inverse and its applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "8",
  pages =        "1064--1065",
  month =        aug,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.403725",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403725",
  abstract =     "The Montgomery inverse of $b$ modulo $a$ is $ b^{-1}
                 2^n \bmod a $, where $n$ is the number of bits in $a$.
                 The right-shifting binary algorithm for modular
                 inversion is shown naturally to compute the new inverse
                 in fewer operations than the ordinary modular inverse.
                 The new inverse facilitates recent work by Ko{\c{c}} on
                 modular exponentiation and has other applications in
                 cryptography",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: Kalliojarvi:1995:FWL
author: Kari Kalliojarvi
volume: 159
type: Avhandling (doktorgrad)
school: Tampereen teknillinen korkeakoulu
address: Tampere, Finland
pages: vii + 71 + 68
year: 1995
ISBN: 951-722-330-7 OR 9517223307
ISBN13: 978-951-722-330-0 OR 9789517223300
bibdate: Thu May 09 08:21:36 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:21:36 ???
series: Julkaisuja
acknowledgement: ack-nhfb
rawauthor: Kari Kallioj{\"a}rvi
title:
Finite word length effects in floating-point and block-floating-point digital signal processing systems

rawtitle:
Finite word length effects in floating-point and block-floating-point digital signal processing systems

entry:
@PhdThesis{Kalliojarvi:1995:FWL,
  author =       "Kari Kallioj{\"a}rvi",
  title =        "Finite word length effects in floating-point and
                 block-floating-point digital signal processing
                 systems",
  volume =       "159",
  type =         "Avhandling (doktorgrad)",
  school =       "Tampereen teknillinen korkeakoulu",
  address =      "Tampere, Finland",
  pages =        "vii + 71 + 68",
  year =         "1995",
  ISBN =         "951-722-330-7",
  ISBN-13 =      "978-951-722-330-0",
  bibdate =      "Thu May 09 08:21:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Julkaisuja",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ke:1995:SFQ
author: Qing Ke and M. J. Feldman
title: Single Flux Quantum Circuits Using the Residue Number System
journal: j-IEEE-TRANS-APPL-SUPERCOND
volume: 5
number: 2
pages: 2988--2991
month: jun
monthnumber: 6
year: 1995
CODEN: ITASE9
DOI: https://doi.org/10.1109/77.403220
ISSN: 1051-8223 (print), 1558-2515 (electronic) OR 10518223 (print), 15582515 (electronic)
ISSNL: 1051-8223 OR 10518223
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9069
fjournal: IEEE Transactions on Applied Superconductivity
keywords: residue arithmetic; residue number system (RNS)
acknowledgement: ack-nhfb
rawauthor: Qing Ke and M. J. Feldman
rawtitle: Single Flux Quantum Circuits Using the Residue Number System
entry:
@Article{Ke:1995:SFQ,
  author =       "Qing Ke and M. J. Feldman",
  title =        "Single Flux Quantum Circuits Using the Residue Number
                 System",
  journal =      j-IEEE-TRANS-APPL-SUPERCOND,
  volume =       "5",
  number =       "2",
  pages =        "2988--2991",
  month =        jun,
  year =         "1995",
  CODEN =        "ITASE9",
  DOI =          "https://doi.org/10.1109/77.403220",
  ISSN =         "1051-8223 (print), 1558-2515 (electronic)",
  ISSN-L =       "1051-8223",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9069",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Applied Superconductivity",
  keywords =     "residue arithmetic; residue number system (RNS)",
  summary =      "We have designed and developed superconducting single
                 flux quantum (SFQ) digital signal processing circuits
                 using the residue number system (RNS). RNS arithmetic
                 is a complete alternative to binary arithmetic for
                 performing digital computations, \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kistermann:1995:RWS
author: Friedrich Wilhelm Kistermann
crossref: Seck:1995:GWS
pages: 241--272
year: 1995
bibdate: Sat Jul 27 12:43:03 2013
bibtimestamp: 2013.07.27 12:43:03 ???
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich Wilhelm Kistermann
title:
Die Rechentechnik um 1600 und Wilhelm Schickards Rechenmaschine. (German) [The calculating technique of 1600 and Wilhelm Schickard's calculator]

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

rawtitle:
{Die Rechentechnik um 1600 und Wilhelm Schickards Rechenmaschine}. ({German}) [{The} calculating technique of 1600 and {Wilhelm Schickard}'s calculator]

entry:
@InProceedings{Kistermann:1995:RWS,
  author =       "Friedrich Wilhelm Kistermann",
  title =        "{Die Rechentechnik um 1600 und Wilhelm Schickards
                 Rechenmaschine}. ({German}) [{The} calculating
                 technique of 1600 and {Wilhelm Schickard}'s
                 calculator]",
  crossref =     "Seck:1995:GWS",
  pages =        "241--272",
  year =         "1995",
  bibdate =      "Sat Jul 27 12:43:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: inproceedings
filename: fparith.bib
label: Knowles:1995:FSC
author: Simon Knowles and William H. McAllister
title: Foreword: 12th Symposium on Computer Arithmetic, Assembly Rooms, Bath, England, July 19--21, 1995
crossref: Knowles:1995:PSC
pages: ix--x
year: 1995
bibdate: Sat Nov 17 12:02:52 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 12:02:52 ???
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Simon Knowles and William H. McAllister
rawtitle: Foreword: {12th Symposium on Computer Arithmetic, Assembly Rooms, Bath, England, July 19--21, 1995}
URL:
http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_contents.pdf; http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_foreword.pdf; http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_preface.pdf

entry:
@InProceedings{Knowles:1995:FSC,
  author =       "Simon Knowles and William H. McAllister",
  title =        "Foreword: {12th Symposium on Computer Arithmetic,
                 Assembly Rooms, Bath, England, July 19--21, 1995}",
  crossref =     "Knowles:1995:PSC",
  pages =        "ix--x",
  year =         "1995",
  bibdate =      "Sat Nov 17 12:02:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Koko:1995:FP
author: Boma Koko
title: Floating Point
journal: j-COMPUT-AIDED-ENG
volume: 14
number: 10
pages: 132--??
year: 1995
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
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
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawauthor: Boma Koko
rawtitle: Floating Point
entry:
@Article{Koko:1995:FP,
  author =       "Boma Koko",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "14",
  number =       "10",
  pages =        "132--??",
  year =         "1995",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Kubota:1995:DRE
author: K. Kubota
journal: Transactions of the Japan Society for Industrial and Applied Mathematics
volume: 5
number: 1
pages: 37--46
year: 1995
ISSN: 0917-2246 OR 09172246
bibdate: Thu Dec 14 11:25:18 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.14 11:25:18 MST
language: Japanese
acknowledgement: ack-nhfb
affiliation: Fac. of Sci. and Eng., Chuo University, Tokyo, Japan
thesaurus: Error analysis; Floating point arithmetic; Probability; Random processes
rawauthor: K. Kubota
title:
On distribution of rounding errors generated in additions and subtractions of floating-point numbers

abstract:
Analyzing the behaviour of rounding errors generated in additions and subtractions of floating-point numbers and regarding them as random variables, we propose a slightly strange model for their distribution. The model gives distributions which approximate the observed generated relative errors more precisely than the uniform distribution which is usually adopted in probabilistic analysis of rounding errors.

keywords:
Additions; Distribution; Floating-point numbers; Probabilistic analysis; Random variables; Relative errors; Rounding errors; Subtractions; Uniform distribution

rawabstract:
Analyzing the behaviour of rounding errors generated in additions and subtractions of floating-point numbers and regarding them as random variables, we propose a slightly strange model for their distribution. The model gives distributions which approximate the observed generated relative errors more precisely than the uniform distribution which is usually adopted in probabilistic analysis of rounding errors.

rawtitle:
On distribution of rounding errors generated in additions and subtractions of floating-point numbers

entry:
@Article{Kubota:1995:DRE,
  author =       "K. Kubota",
  title =        "On distribution of rounding errors generated in
                 additions and subtractions of floating-point numbers",
  journal =      "Transactions of the Japan Society for Industrial and
                 Applied Mathematics",
  volume =       "5",
  number =       "1",
  pages =        "37--46",
  month =        "????",
  year =         "1995",
  ISSN =         "0917-2246",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Analyzing the behaviour of rounding errors generated
                 in additions and subtractions of floating-point numbers
                 and regarding them as random variables, we propose a
                 slightly strange model for their distribution. The
                 model gives distributions which approximate the
                 observed generated relative errors more precisely than
                 the uniform distribution which is usually adopted in
                 probabilistic analysis of rounding errors.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fac. of Sci. and Eng., Chuo University, Tokyo, Japan",
  classification = "C1140 (Probability and statistics); C4110 (Error
                 analysis in numerical methods); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Additions; Distribution; Floating-point numbers;
                 Probabilistic analysis; Random variables; Relative
                 errors; Rounding errors; Subtractions; Uniform
                 distribution",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Error analysis; Floating point arithmetic;
                 Probability; Random processes",
}


bibtype: inproceedings
filename: fparith.bib
label: Kwan:1995:CII
author: Hercule Kwan and Robert Leonard Nelson, Jr. and Earl E. Swartzlander, Jr.
title: Cascaded Implementation of an Iterative Inverse-Square-Root Algorithm, with Overflow Lookahead
crossref: Knowles:1995:PSC
pages: 115--122
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Kwan.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Hercule Kwan and Robert Leonard {Nelson, Jr.} and Earl E. {Swartzlander, Jr.}
rawtitle: Cascaded Implementation of an Iterative Inverse-Square-Root Algorithm, with Overflow Lookahead
entry:
@InProceedings{Kwan:1995:CII,
  author =       "Hercule Kwan and Robert Leonard {Nelson, Jr.} and Earl
                 E. {Swartzlander, Jr.}",
  title =        "Cascaded Implementation of an Iterative
                 Inverse-Square-Root Algorithm, with Overflow
                 Lookahead",
  crossref =     "Knowles:1995:PSC",
  pages =        "115--122",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Kwan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "We present an unconventional method of computing the
                 inverse of the square root. It implements the
                 equivalent of two iterations of a well-known
                 multiplicative method to obtain 24-bit mantissa
                 accuracy. We implement each ``iteration'' as a
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lang:1995:VHR
author: Tomas Lang and Paolo Montuschi
title: Very-High Radix Combined Division and Square Root with Prescaling and Selection by Rounding
crossref: Knowles:1995:PSC
pages: 124--131
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lang.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Paolo Montuschi
rawtitle: Very-High Radix Combined Division and Square Root with Prescaling and Selection by Rounding
entry:
@InProceedings{Lang:1995:VHR,
  author =       "Tom{\'a}s Lang and Paolo Montuschi",
  title =        "Very-High Radix Combined Division and Square Root with
                 Prescaling and Selection by Rounding",
  crossref =     "Knowles:1995:PSC",
  pages =        "124--131",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "An algorithm for square root with prescaling is
                 developed and combined with a similar scheme for
                 division. An implementation is described, evaluated and
                 compared with other combined div/sqrt \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Leeser:1995:VSR
author: M. Leeser and J. O'Leary
title: Verification of a subtractive radix-$2$ square root algorithm and implementation
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 526--531
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. Leeser and J. O'Leary
rawtitle: Verification of a subtractive radix-$2$ square root algorithm and implementation
booktitle:
Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors, ICCD '95

rawbooktitle:
Proceedings of the {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors, {ICCD '95}

entry:
@InProceedings{Leeser:1995:VSR,
  author =       "M. Leeser and J. O'Leary",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors,
                 {ICCD '95}",
  title =        "Verification of a subtractive radix-$2$ square root
                 algorithm and implementation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "526--531",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Many modern microprocessors implement floating point
                 square root hardware using subtractive algorithms. Such
                 processors include the HP PA7200, the MIPS R4400, and
                 the Intel Pentium. The Intel Pentium division bug
                 highlights the importance of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Lehmann:1995:SLE
author: N. Joachim Lehmann
crossref: Seck:1995:GWS
pages: 273--286
year: 1995
bibdate: Sat Jul 27 12:46:37 2013
bibtimestamp: 2013.07.27 12:46:37 ???
language: German
acknowledgement: ack-nhfb
rawauthor: N. Joachim Lehmann
title:
Schickard und Leibniz als Erfinder von rechenmaschinen. (German) [Schickard and Leibniz, the inventors of calculators]

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

rawtitle:
{Schickard und Leibniz als Erfinder von rechenmaschinen}. ({German}) [{Schickard} and {Leibniz}, the inventors of calculators]

entry:
@InProceedings{Lehmann:1995:SLE,
  author =       "N. Joachim Lehmann",
  title =        "{Schickard und Leibniz als Erfinder von
                 rechenmaschinen}. ({German}) [{Schickard} and
                 {Leibniz}, the inventors of calculators]",
  crossref =     "Seck:1995:GWS",
  pages =        "273--286",
  year =         "1995",
  bibdate =      "Sat Jul 27 12:46:37 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Liu:1995:SRV
author: S.-I. Liu
title: Square-rooting and vector summation circuits using current conveyors
volume: 142
number: 4
pages: 223--226
month: aug
monthnumber: 8
year: 1995
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: S.-I. Liu
rawtitle: Square-rooting and vector summation circuits using current conveyors
journal:
IEE Proceedings on Circuits, Devices and Systems [see also IEE Proceedings G- Circuits, Devices and Systems]

entry:
@Article{Liu:1995:SRV,
  author =       "S.-I. Liu",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "142",
  number =       "4",
  pages =        "223--226",
  month =        aug,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  summary =      "New analogue squaring, square-rooting and vector
                 summation circuits using current conveyors (CCIIs) are
                 presented. They consist of MOS transistors biased in
                 the triode region, a buffered unity-gain inverting
                 amplifier, resistors and CCIIs. A general \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Louie:1995:VPS
author: Marianne E. Louie and Milos D. Ercegovac
title: A Variable-Precision Square Root Implementation for Field Programmable Gate Arrays
journal: j-J-SUPERCOMPUTING
volume: 9
number: 3
pages: 315--336
month: sep
monthnumber: 9
year: 1995
CODEN: JOSUED
DOI: https://doi.org/10.1007/BF01212874
ISSN: 0920-8542 (print), 1573-0484 (electronic) OR 09208542 (print), 15730484 (electronic)
ISSNL: 0920-8542 OR 09208542
bibdate: Wed Jul 6 11:13:09 MDT 2005
bibtimestamp: 2005.07.06 11:13:09 MDT
fjournal: The Journal of Supercomputing
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, California University, Los Angeles, CA, USA
corpsource: Department of Computer Science, California University, Los Angeles, CA, USA
journalURL: http://link.springer.com/journal/11227
treatment: P Practical
rawauthor: Marianne E. Louie and Milo{\v{s}} D. Ercegovac
rawtitle: A Variable-Precision Square Root Implementation for Field Programmable Gate Arrays
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3; http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315; http://www.wkap.nl/oasis.htm/95692

keywords:
digital arithmetic; field programmable gate arrays; square root; square root implementation; variable-precision; Xilinx XC4010

entry:
@Article{Louie:1995:VPS,
  author =       "Marianne E. Louie and Milo{\v{s}} D. Ercegovac",
  title =        "A Variable-Precision Square Root Implementation for
                 Field Programmable Gate Arrays",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "9",
  number =       "3",
  pages =        "315--336",
  month =        sep,
  year =         "1995",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/BF01212874",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 11:13:09 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3;
                 http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315;
                 http://www.wkap.nl/oasis.htm/95692",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  classification = "C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  keywords =     "digital arithmetic; field programmable gate arrays;
                 square root; square root implementation;
                 variable-precision; Xilinx XC4010",
  treatment =    "P Practical",
}


bibtype: techreport
filename: fparith.bib
label: Lozier:1995:EBL
author: Daniel W. Lozier and P. R. Turner
title: Error-Bounding in Level-Index Computer Arithmetic
type: Internal Report
number: NISTIR-5724
institution: National Bureau of Standards
address: Gaithersburg, MD, USA
pages: 315--336
year: 1995
bibdate: Tue Nov 05 15:20:28 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.11.05 15:20:28 ???
URL: https://www.nist.gov/publications/error-bounding-level-index-computer-arithmetic
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier and P. R. Turner
rawtitle: Error-Bounding in Level-Index Computer Arithmetic
entry:
@TechReport{Lozier:1995:EBL,
  author =       "Daniel W. Lozier and P. R. Turner",
  title =        "Error-Bounding in Level-Index Computer Arithmetic",
  type =         "Internal Report",
  number =       "NISTIR-5724",
  institution =  "National Bureau of Standards",
  address =      "Gaithersburg, MD, USA",
  year =         "1995",
  bibdate =      "Tue Nov 05 15:20:28 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nist.gov/publications/error-bounding-level-index-computer-arithmetic",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Lynch:1995:HRL
author: Thomas Lynch and Michael J. Schulte
title: A High Radix On-line Arithmetic for Credible and Accurate Computing
journal: j-J-UCS
volume: 1
number: 7
pages: 439--453
day: 28
month: jul
monthnumber: 7
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
MRclass: 68M07
MRnumber: 1 403 706
bibdate: Wed May 28 19:32:35 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.28 19:32:35 MDT
URL: http://www.jucs.org/a_high_radix_online_arithmetic
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: Thomas Lynch and Michael J. Schulte
rawtitle: A High Radix On-line Arithmetic for Credible and Accurate Computing
entry:
@Article{Lynch:1995:HRL,
  author =       "Thomas Lynch and Michael J. Schulte",
  title =        "A High Radix On-line Arithmetic for Credible and
                 Accurate Computing",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "7",
  pages =        "439--453",
  day =          "28",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07",
  MRnumber =     "1 403 706",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/a_high_radix_online_arithmetic",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: inproceedings
filename: fparith.bib
label: Lynch:1995:KTF
author: Tom Lynch and Ahmed Ahmed and Mike Schulte and Tom Callaway and Robert Tisdale
title: The K5 Transcendental Functions
crossref: Knowles:1995:PSC
pages: 163--171
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Tom Lynch and Ahmed Ahmed and Mike Schulte and Tom Callaway and Robert Tisdale
rawtitle: The {K5} Transcendental Functions
URL:
http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf; http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lynch.pdf

entry:
@InProceedings{Lynch:1995:KTF,
  author =       "Tom Lynch and Ahmed Ahmed and Mike Schulte and Tom
                 Callaway and Robert Tisdale",
  title =        "The {K5} Transcendental Functions",
  crossref =     "Knowles:1995:PSC",
  pages =        "163--171",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lynch.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: inproceedings
filename: fparith.bib
label: Lyu:1995:RBB
author: Chung Nan Lyu and David W. Matula
title: Redundant Binary Booth Recoding
crossref: Knowles:1995:PSC
pages: 50--58
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Chung.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Chung Nan Lyu and David W. Matula
rawtitle: Redundant Binary {Booth} Recoding
entry:
@InProceedings{Lyu:1995:RBB,
  author =       "Chung Nan Lyu and David W. Matula",
  title =        "Redundant Binary {Booth} Recoding",
  crossref =     "Knowles:1995:PSC",
  pages =        "50--58",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Chung.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Mandelbaum:1995:DUL
author: D. M. Mandelbaum
title: Division using a logarithmic-exponential transform to form a short reciprocal
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 11
pages: 1326--1330
month: nov
monthnumber: 11
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.475129
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:30 MDT 2011
bibtimestamp: 2011.07.06 08:01:30 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475129
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. M. Mandelbaum
rawtitle: Division using a logarithmic-exponential transform to form a short reciprocal
entry:
@Article{Mandelbaum:1995:DUL,
  author =       "D. M. Mandelbaum",
  title =        "Division using a logarithmic-exponential transform to
                 form a short reciprocal",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1326--1330",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475129",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475129",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Martel:1995:DSO
author: Charles Martel and Vojin Oklobdzija and R. Ravi and Paul F. Stelling
title: Design Strategies for Optimal Multiplier Circuits
crossref: Knowles:1995:PSC
pages: 42--49
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Martel.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Charles Martel and Vojin Oklobdzija and R. Ravi and Paul F. Stelling
rawtitle: Design Strategies for Optimal Multiplier Circuits
entry:
@InProceedings{Martel:1995:DSO,
  author =       "Charles Martel and Vojin Oklobdzija and R. Ravi and
                 Paul F. Stelling",
  title =        "Design Strategies for Optimal Multiplier Circuits",
  crossref =     "Knowles:1995:PSC",
  pages =        "42--49",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Martel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: inproceedings
filename: fparith.bib
label: Matsubara:1995:NBS
author: Gensoh Matsubara and Nobuhiro Ide and Haruyuki Tago and Seigo Suzuki and Nobuyuki Goto
title: 30-ns 55-b Shared Radix $2$ Division and Square Root Using a Self-Timed Circuit
crossref: Knowles:1995:PSC
pages: 98--105
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Matsubara.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Gensoh Matsubara and Nobuhiro Ide and Haruyuki Tago and Seigo Suzuki and Nobuyuki Goto
rawtitle: 30-ns 55-b Shared Radix $2$ Division and Square Root Using a Self-Timed Circuit
entry:
@InProceedings{Matsubara:1995:NBS,
  author =       "Gensoh Matsubara and Nobuhiro Ide and Haruyuki Tago
                 and Seigo Suzuki and Nobuyuki Goto",
  title =        "30-ns 55-b Shared Radix $2$ Division and Square Root
                 Using a Self-Timed Circuit",
  crossref =     "Knowles:1995:PSC",
  pages =        "98--105",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Matsubara.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "A shared radix 2 division and square root
                 implementation using a self-timed circuit is presented.
                 The same execution time for division and square root is
                 achieved by using an on-the-fly digit decoding and a
                 root multiple generation technique. Most \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Meissner:1995:EAD
author: Loren P. Meissner
journal: j-FORTRAN-FORUM
volume: 14
number: 3
pages: 1--3
month: sep
monthnumber: 9
year: 1995
ISSN: 1061-7264 (print), 1931-1311 (electronic) OR 10617264 (print), 19311311 (electronic)
ISSNL: 1061-7264 OR 10617264
bibdate: Thu Feb 07 06:54:12 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.07 06:54:12 ???
fjournal: ACM Fortran Forum
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/toc.cfm?id=J286
issue: 43
rawauthor: Loren P. Meissner
title:
From the Editor: Allocatable Dummy Argument Arrays; How Should Fortran Standards Describe Arithmetic? Are External Procedures Obsolete?; When are Local Variables Initialized in F77 and F90?

rawtitle:
From the {Editor}: Allocatable Dummy Argument Arrays; How Should {Fortran Standards} Describe Arithmetic? {Are} External Procedures Obsolete?; {When} are Local Variables Initialized in {F77} and {F90}?

entry:
@Article{Meissner:1995:EAD,
  author =       "Loren P. Meissner",
  title =        "From the {Editor}: Allocatable Dummy Argument Arrays;
                 How Should {Fortran Standards} Describe Arithmetic?
                 {Are} External Procedures Obsolete?; {When} are Local
                 Variables Initialized in {F77} and {F90}?",
  journal =      j-FORTRAN-FORUM,
  volume =       "14",
  number =       "3",
  pages =        "1--3",
  month =        sep,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Thu Feb 07 06:54:12 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "43",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}


bibtype: article
filename: fparith.bib
label: Metafas:1995:FAC
author: D. E. Metafas and C. E. Goutis
title: A Floating-Point Advanced CORDIC Processor
journal: j-J-VLSI-SIGNAL-PROC
volume: 10
number: 1
pages: 53--65
month: jun
monthnumber: 6
year: 1995
CODEN: JVSPED
DOI: https://doi.org/10.1007/BF02407026
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Journal of VLSI Signal Processing
acknowledgement: ack-nhfb
rawauthor: D. E. Metafas and C. E. Goutis
rawtitle: A Floating-Point Advanced {CORDIC} Processor
abstract:
In this paper, a novel architecture of a floating-point digital signal processor is presented. It introduces a single hardware structure with a full set of elementary arithmetic functions which includes sin, cos, tan, arctanh, circular rotation and vectoring, sinh, cosh, tanh, arctanh, hyperbolic rotation and vectoring, square root, logarithm, exponential as well as addition, multiplication and division. The architecture of the processor is based on the COordinate Rotation DIgital Computer (CORDIC) and the Convergence Computing Method (CCM) algorithms for computing arithmetic functions and it is fully parallel and pipelined. Its advanced functionality is achieved without significant increase in hardware, in comparison to ordinary CORDIC processor, and makes it an ideal processing element in high speed multiprocessor applications, e.g. real time Digital Signal Processing (DSP) and computer graphics.

rawabstract:
In this paper, a novel architecture of a floating-point digital signal processor is presented. It introduces a single hardware structure with a full set of elementary arithmetic functions which includes sin, cos, tan, arctanh, circular rotation and vectoring, sinh, cosh, tanh, arctanh, hyperbolic rotation and vectoring, square root, logarithm, exponential as well as addition, multiplication and division. The architecture of the processor is based on the COordinate Rotation DIgital Computer (CORDIC) and the Convergence Computing Method (CCM) algorithms for computing arithmetic functions and it is fully parallel and pipelined. Its advanced functionality is achieved without significant increase in hardware, in comparison to ordinary CORDIC processor, and makes it an ideal processing element in high speed multiprocessor applications, e.g. real time Digital Signal Processing (DSP) and computer graphics.

entry:
@Article{Metafas:1995:FAC,
  author =       "D. E. Metafas and C. E. Goutis",
  title =        "A Floating-Point Advanced {CORDIC} Processor",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "10",
  number =       "1",
  pages =        "53--65",
  month =        jun,
  year =         "1995",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/BF02407026",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, a novel architecture of a
                 floating-point digital signal processor is presented.
                 It introduces a single hardware structure with a full
                 set of elementary arithmetic functions which includes
                 sin, cos, tan, arctanh, circular rotation and
                 vectoring, sinh, cosh, tanh, arctanh, hyperbolic
                 rotation and vectoring, square root, logarithm,
                 exponential as well as addition, multiplication and
                 division. The architecture of the processor is based on
                 the COordinate Rotation DIgital Computer (CORDIC) and
                 the Convergence Computing Method (CCM) algorithms for
                 computing arithmetic functions and it is fully parallel
                 and pipelined. Its advanced functionality is achieved
                 without significant increase in hardware, in comparison
                 to ordinary CORDIC processor, and makes it an ideal
                 processing element in high speed multiprocessor
                 applications, e.g. real time Digital Signal Processing
                 (DSP) and computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}


bibtype: inproceedings
filename: fparith.bib
label: Michelucci:1995:ARD
author: D. Michelucci
title: An $ epsilon $ Arithmetic for Removing Degeneracies
crossref: Knowles:1995:PSC
pages: 230--238
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Michelucci.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: D. Michelucci
rawtitle: An $ \epsilon $ Arithmetic for Removing Degeneracies
entry:
@InProceedings{Michelucci:1995:ARD,
  author =       "D. Michelucci",
  title =        "An $ \epsilon $ Arithmetic for Removing Degeneracies",
  crossref =     "Knowles:1995:PSC",
  pages =        "230--238",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Michelucci.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: techreport
filename: fparith.bib
label: Miner:1995:DIF
author: Paul S. Miner
title: Defining the IEEE-854 floating-point standard in PVS
number: 110167
address: Hampton, VA, USA
year: 1995
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: NASA technical memorandum
keywords: Floating point arithmetic.; Formalism.; Prototypes.; Proving.
acknowledgement: ack-nhfb
rawauthor: Paul S. Miner
rawtitle: Defining the {IEEE-854} floating-point standard in {PVS}
institution:
National Aeronautics and Space Administration, Langley Research Center; National Technical Information Service, distributor

remark:
Distributed to depository libraries in microfiche. Shipping list no.: 96-0033-M. Microfiche. [Washington, D.C.: National Aeronautics and Space Administration, 1995] 1 microfiche.

entry:
@TechReport{Miner:1995:DIF,
  author =       "Paul S. Miner",
  title =        "Defining the {IEEE-854} floating-point standard in
                 {PVS}",
  number =       "110167",
  institution =  "National Aeronautics and Space Administration, Langley
                 Research Center; National Technical Information
                 Service, distributor",
  address =      "Hampton, VA, USA",
  pages =        "????",
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "NASA technical memorandum",
  acknowledgement = ack-nhfb,
  alttitle =     "Defining the IEEE 854 floating point standard in PVS
                 Defining the IEEE eight hundred fifty-four floating
                 point standard in PVS",
  govtdocnumber = "NAS 1.15:110167 0830-D (MF)",
  keywords =     "Floating point arithmetic.; Formalism.; Prototypes.;
                 Proving.",
  remark =       "Distributed to depository libraries in microfiche.
                 Shipping list no.: 96-0033-M. Microfiche. [Washington,
                 D.C.: National Aeronautics and Space Administration,
                 1995] 1 microfiche.",
}


bibtype: techreport
filename: fparith.bib
label: Moler:1995:CCT
author: Cleve B. Moler
type: Technical note
institution: inst-MATHWORKS
address: inst-MATHWORKS:adr
month: Winter
year: 1995
bibdate: Thu Oct 24 07:16:21 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.24 07:16:21 ???
URL: http://www.mathworks.com/company/newsletter/pdf/win95cleve.pdf
keywords: Matlab; Pentium FDIV divide flaw
acknowledgement: ack-nhfb
rawauthor: Cleve B. Moler
title:
Cleve's Corner: a Tale of Two Numbers: With the Pentium, there is a very small chance of making a very large error

rawtitle:
{Cleve}'s Corner: a Tale of Two Numbers: {With} the {Pentium}, there is a very small chance of making a very large error

entry:
@TechReport{Moler:1995:CCT,
  author =       "Cleve B. Moler",
  title =        "{Cleve}'s Corner: a Tale of Two Numbers: {With} the
                 {Pentium}, there is a very small chance of making a
                 very large error",
  type =         "Technical note",
  institution =  inst-MATHWORKS,
  address =      inst-MATHWORKS:adr,
  month =        "Winter",
  year =         "1995",
  bibdate =      "Thu Oct 24 07:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathworks.com/company/newsletter/pdf/win95cleve.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab; Pentium FDIV divide flaw",
}


bibtype: article
filename: fparith.bib
label: Moler:1995:TTN
author: Cleve B. Moler
title: A tale of two numbers
journal: j-SIAM-NEWS
volume: 28
number: 1
pages: 16--16
day: 1
month: jan
monthnumber: 1
year: 1995
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Wed Nov 13 07:16:43 1996
bibtimestamp: 1996.11.13 07:16:43 ???
note: Discusses the Intel Pentium chip divide flaw.
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: https://sinews.siam.org/
rawauthor: Cleve B. Moler
rawnote: Discusses the Intel Pentium chip divide flaw.
rawtitle: A tale of two numbers
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Moler:1995:TTN,
  author =       "Cleve B. Moler",
  title =        "A tale of two numbers",
  journal =      j-SIAM-NEWS,
  volume =       "28",
  number =       "1",
  pages =        "16--16",
  day =          "1",
  month =        jan,
  year =         "1995",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Wed Nov 13 07:16:43 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses the Intel Pentium chip divide flaw.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}


bibtype: article
filename: fparith.bib
label: Montuschi:1995:RRI
author: P. Montuschi and L. Ciminiera
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 1
pages: 144--146
month: jan
monthnumber: 1
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.368000
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:25 MDT 2011
bibtimestamp: 2011.07.06 08:01:25 MDT
note: See cite Montuschi:1993:RIT.
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=368000
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and L. Ciminiera
rawnote: See \cite{Montuschi:1993:RIT}.
title:
A remark on ``Reducing iteration time when result digit is zero for radix-$2$ SRT division and square root with redundant remainders''

rawtitle:
A remark on {``Reducing iteration time when result digit is zero for radix-$2$ SRT division and square root with redundant remainders''}

entry:
@Article{Montuschi:1995:RRI,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "A remark on {``Reducing iteration time when result
                 digit is zero for radix-$2$ SRT division and square
                 root with redundant remainders''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "144--146",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.368000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Montuschi:1993:RIT}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=368000",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "In a previous paper by P. Montuschi and L. Ciminiera
                 (ibid., vol. 42, no.2 p239-246, Feb 1993), an
                 architecture for shared radix 2 division and square
                 root has been presented whose main characteristic is
                 the ability to avoid any addition/subtraction,
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Muller:1995:SLN
author: Jean-Michel Muller and Arnaud Tisserand and Alexandre Scherbyna
title: Semi-Logarithmic Number Systems
crossref: Knowles:1995:PSC
pages: 201--207
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Muller.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller and Arnaud Tisserand and Alexandre Scherbyna
rawtitle: Semi-Logarithmic Number Systems
entry:
@InProceedings{Muller:1995:SLN,
  author =       "Jean-Michel Muller and Arnaud Tisserand and Alexandre
                 Scherbyna",
  title =        "Semi-Logarithmic Number Systems",
  crossref =     "Knowles:1995:PSC",
  pages =        "201--207",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Muller.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Nielsen:1995:MFD
author: Asger Munk Nielsen and Peter Kornerup
title: MSB-First Digit Serial Arithmetic
journal: j-J-UCS
volume: 1
number: 7
pages: 527--547
day: 28
month: jul
monthnumber: 7
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
MRclass: 68Mxx
MRnumber: 1 403 711
bibdate: Wed May 28 19:32:35 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.28 19:32:35 MDT
URL: http://www.jucs.org/jucs_1_7/msb_first_digit_serial
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: Asger Munk Nielsen and Peter Kornerup
rawtitle: {MSB}-First Digit Serial Arithmetic
entry:
@Article{Nielsen:1995:MFD,
  author =       "Asger Munk Nielsen and Peter Kornerup",
  title =        "{MSB}-First Digit Serial Arithmetic",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "7",
  pages =        "527--547",
  day =          "28",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68Mxx",
  MRnumber =     "1 403 711",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_1_7/msb_first_digit_serial",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: phdthesis
filename: fparith.bib
label: Nowka:1995:HPC
author: Kevin Nowka
title: High Performance CMOS VLSI System Design Using Wave Pipelining
type: Thesis (Ph.D.)
school: Department of Electrical Engineering, Stanford University
address: Stanford, CA, USA
month: sep
monthnumber: 9
year: 1995
bibdate: Mon Dec 24 11:03:54 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 11:03:54 ???
acknowledgement: ack-nhfb
rawauthor: Kevin Nowka
rawtitle: High Performance {CMOS} {VLSI} System Design Using Wave Pipelining
entry:
@PhdThesis{Nowka:1995:HPC,
  author =       "Kevin Nowka",
  title =        "High Performance {CMOS} {VLSI} System Design Using
                 Wave Pipelining",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        sep,
  year =         "1995",
  bibdate =      "Mon Dec 24 11:03:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Oberman:1995:DRC
author: S. F. Oberman and M. J. Flynn
title: On division and reciprocal caches
type: Technical Report
number: CSL-TR-95-666
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
month: apr
monthnumber: 4
year: 1995
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: S. F. Oberman and M. J. Flynn
rawtitle: On division and reciprocal caches
entry:
@TechReport{Oberman:1995:DRC,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "On division and reciprocal caches",
  type =         "Technical Report",
  number =       "CSL-TR-95-666",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        apr,
  year =         "1995",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: OGara:1995:SET
journal: j-FORTRAN-FORUM
volume: 14
number: 1
pages: 11--28
month: mar
monthnumber: 3
year: 1995
ISSN: 1061-7264 (print), 1931-1311 (electronic) OR 10617264 (print), 19311311 (electronic)
ISSNL: 1061-7264 OR 10617264
bibdate: Thu Feb 07 06:54:12 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.07 06:54:12 ???
fjournal: ACM Fortran Forum
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/toc.cfm?id=J286
issue: 41
author:
Linda O'Gara and Jeanne Adams and Walt Brainerd and Vic Kelson and Craig Dedo and Keith Bierman and Jerry Wagener and Richard Maine and Leonard J. Moss and James H. Billen and Robert Corbett and Dick Hendrickson and Jamie Shiers and David Levine and David L. Epstein and John Reid and Lawrie Schonfelder and Kurt W. Hirchert and Jens Helmers and William Behrman and A. C. Marshall and William B. Clodius

title:
Some Email threads: Is Fortran 90 Succeeding?; Fortran Market Acceptance; Fortran--C Interoperability; Fortran Preprocessors or Conditional Compilation: Is Standardization Needed?; Floating Point Subsets of Enable; Pointers to Procedures, or Procedure Names as Variables; Standard Linear Algebra and Advanced Math Functions Modules; Re: Allocatable arrays in structures; Restricted Module Visibility

rawauthor:
Linda O'Gara and Jeanne Adams and Walt Brainerd and Vic Kelson and Craig Dedo and Keith Bierman and Jerry Wagener and Richard Maine and Leonard J. Moss and James H. Billen and Robert Corbett and Dick Hendrickson and Jamie Shiers and David Levine and David L. Epstein and John Reid and Lawrie Schonfelder and Kurt W. Hirchert and Jens Helmers and William Behrman and A. C. Marshall and William B. Clodius

rawtitle:
Some Email threads: Is {Fortran 90} Succeeding?; {Fortran} Market Acceptance; {Fortran--C} Interoperability; {Fortran} Preprocessors or Conditional Compilation: Is Standardization Needed?; Floating Point Subsets of Enable; Pointers to Procedures, or Procedure Names as Variables; Standard Linear Algebra and Advanced Math Functions Modules; Re: Allocatable arrays in structures; Restricted Module Visibility

entry:
@Article{OGara:1995:SET,
  author =       "Linda O'Gara and Jeanne Adams and Walt Brainerd and
                 Vic Kelson and Craig Dedo and Keith Bierman and Jerry
                 Wagener and Richard Maine and Leonard J. Moss and James
                 H. Billen and Robert Corbett and Dick Hendrickson and
                 Jamie Shiers and David Levine and David L. Epstein and
                 John Reid and Lawrie Schonfelder and Kurt W. Hirchert
                 and Jens Helmers and William Behrman and A. C. Marshall
                 and William B. Clodius",
  title =        "Some Email threads: Is {Fortran 90} Succeeding?;
                 {Fortran} Market Acceptance; {Fortran--C}
                 Interoperability; {Fortran} Preprocessors or
                 Conditional Compilation: Is Standardization Needed?;
                 Floating Point Subsets of Enable; Pointers to
                 Procedures, or Procedure Names as Variables; Standard
                 Linear Algebra and Advanced Math Functions Modules; Re:
                 Allocatable arrays in structures; Restricted Module
                 Visibility",
  journal =      j-FORTRAN-FORUM,
  volume =       "14",
  number =       "1",
  pages =        "11--28",
  month =        mar,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Thu Feb 07 06:54:12 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "41",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}


bibtype: inproceedings
filename: fparith.bib
label: Ohi:1995:RCN
author: Y. Ohi and T. Aoki and T. Higuchi
title: Redundant Complex Number Systems
crossref: IEEE:1995:ISM
pages: 14--??
year: 1995
DOI: https://doi.org/10.1109/ISMVL.1995.513504
bibdate: Sat Aug 22 08:43:14 MDT 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2009.08.22 08:43:14 MDT
acknowledgement: ack-nhfb
rawauthor: Y. Ohi and T. Aoki and T. Higuchi
rawtitle: Redundant Complex Number Systems
abstract:
This paper presents redundant complex number systems (RCNSs)-new complex number representations for high-speed arithmetic circuits. RCNS is a positional number system that has a complex radix $ r_j $ and a digit set $ - alpha , ldots , 0, ldots , alpha $, where $ r geq 2 $ and $ [(r^2 - 1) / 2] < alpha leq r^2 - 1 $. The use of complex radix $ r_j $ allows additions and multiplications of complex numbers to be done without treating real part and imaginary part separately. Also the redundancy in the number representation enables carry-free addition as well as binary-tree multiple-operand addition. This paper discusses the basic arithmetic algorithms of RCNSs and their implementations.

rawabstract:
This paper presents redundant complex number systems (RCNSs)-new complex number representations for high-speed arithmetic circuits. RCNS is a positional number system that has a complex radix $ r_j $ and a digit set $ \{ - \alpha, \ldots {}, 0, \ldots {}, \alpha \} $, where $ r \geq 2 $ and $ [(r^2 - 1) / 2] < \alpha \leq r^2 - 1 $. The use of complex radix $ r_j $ allows additions and multiplications of complex numbers to be done without treating real part and imaginary part separately. Also the redundancy in the number representation enables carry-free addition as well as binary-tree multiple-operand addition. This paper discusses the basic arithmetic algorithms of RCNSs and their implementations.

entry:
@InProceedings{Ohi:1995:RCN,
  author =       "Y. Ohi and T. Aoki and T. Higuchi",
  title =        "Redundant Complex Number Systems",
  crossref =     "IEEE:1995:ISM",
  pages =        "14--??",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/ISMVL.1995.513504",
  bibdate =      "Sat Aug 22 08:43:14 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents redundant complex number systems
                 (RCNSs)-new complex number representations for
                 high-speed arithmetic circuits. RCNS is a positional
                 number system that has a complex radix $ r_j $ and a
                 digit set $ \{ - \alpha, \ldots {}, 0, \ldots {},
                 \alpha \} $, where $ r \geq 2 $ and $ [(r^2 - 1) / 2] <
                 \alpha \leq r^2 - 1 $. The use of complex radix $ r_j $
                 allows additions and multiplications of complex numbers
                 to be done without treating real part and imaginary
                 part separately. Also the redundancy in the number
                 representation enables carry-free addition as well as
                 binary-tree multiple-operand addition. This paper
                 discusses the basic arithmetic algorithms of RCNSs and
                 their implementations.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ohkubo:1995:CBM
author: N. Ohkubo and M. Suzuki and T. Shinbo and T. Yamanaka and A. Shimizu and K. Sasaki and Y. Nakagome
title: A 4.4ns CMOS $ 54 times 54 $-b multiplier using pass-transistor multiplexor
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: SC-30
number: 3
pages: 251--257
month: mar
monthnumber: 3
year: 1995
CODEN: IJSCBC
DOI: https://doi.org/10.1109/4.364439
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Mon Dec 24 10:23:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 10:23:37 ???
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: N. Ohkubo and M. Suzuki and T. Shinbo and T. Yamanaka and A. Shimizu and K. Sasaki and Y. Nakagome
rawtitle: A 4.4ns {CMOS} $ 54 \times 54 $-b multiplier using pass-transistor multiplexor
entry:
@Article{Ohkubo:1995:CBM,
  author =       "N. Ohkubo and M. Suzuki and T. Shinbo and T. Yamanaka
                 and A. Shimizu and K. Sasaki and Y. Nakagome",
  title =        "A 4.4ns {CMOS} $ 54 \times 54 $-b multiplier using
                 pass-transistor multiplexor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-30",
  number =       "3",
  pages =        "251--257",
  month =        mar,
  year =         "1995",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.364439",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Mon Dec 24 10:23:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  xxpages =      "294--305",
}


bibtype: article
filename: fparith.bib
label: OLeary:1995:NRI
author: J. O'Leary and M. Leeser and J. Hickey and M. Aagaard
title: Non-Restoring Integer Square Root: a Case Study in Design by Principled Optimization
journal: j-LECT-NOTES-COMP-SCI
volume: 901
pages: 52--??
year: 1995
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat May 11 13:45:32 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.05.11 13:45:32 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: J. O'Leary and M. Leeser and J. Hickey and M. Aagaard
rawtitle: Non-Restoring Integer Square Root: a Case Study in Design by Principled Optimization
entry:
@Article{OLeary:1995:NRI,
  author =       "J. O'Leary and M. Leeser and J. Hickey and M.
                 Aagaard",
  title =        "Non-Restoring Integer Square Root: a Case Study in
                 Design by Principled Optimization",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "901",
  pages =        "52--??",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat May 11 13:45:32 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Orup:1995:SQD
author: Holger Orup
title: Simplifying Quotient Determination in High-Radix Modular Multiplication
crossref: Knowles:1995:PSC
pages: 193--200
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Orup.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Holger Orup
rawtitle: Simplifying Quotient Determination in High-Radix Modular Multiplication
entry:
@InProceedings{Orup:1995:SQD,
  author =       "Holger Orup",
  title =        "Simplifying Quotient Determination in High-Radix
                 Modular Multiplication",
  crossref =     "Knowles:1995:PSC",
  pages =        "193--200",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Orup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: inproceedings
filename: fparith.bib
label: Owens:1995:RNC
author: Robert M. Owens and Raminder S. Bajwa and Mary Jane Irwin
title: Reducing the Number of Counters Needed for Integer Multiplication
crossref: Knowles:1995:PSC
pages: 38--41
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Owens.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Robert M. Owens and Raminder S. Bajwa and Mary Jane Irwin
rawtitle: Reducing the Number of Counters Needed for Integer Multiplication
entry:
@InProceedings{Owens:1995:RNC,
  author =       "Robert M. Owens and Raminder S. Bajwa and Mary Jane
                 Irwin",
  title =        "Reducing the Number of Counters Needed for Integer
                 Multiplication",
  crossref =     "Knowles:1995:PSC",
  pages =        "38--41",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Owens.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Parker:1995:MUP
author: M. G. Parker and M. Benaissa
title: $ mathrm GF(p^m) $ multiplication using polynomial residue number systems
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 42
number: 11
pages: 718--721
month: nov
monthnumber: 11
year: 1995
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.475249
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=10018
fjournal: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: M. G. Parker and M. Benaissa
rawtitle: {$ \mathrm {GF}(p^m) $} multiplication using polynomial residue number systems
entry:
@Article{Parker:1995:MUP,
  author =       "M. G. Parker and M. Benaissa",
  title =        "{$ \mathrm {GF}(p^m) $} multiplication using
                 polynomial residue number systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "42",
  number =       "11",
  pages =        "718--721",
  month =        nov,
  year =         "1995",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.475249",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=10018",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "$\mathrm{GF}(p^m)$ multiplication is computed in two
                 stages. First, the polynomial product is computed
                 modulus: a highly factorizable degree S polynomial,
                 $M(x)$, with $S \geq 2m - 1$. This enables the product
                 to be computed using a polynomial residue number
                 system. \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Popova:1995:FCI
author: E. Popova
title: On a Formally Correct Implementation of IEEE Computer Arithmetic
journal: j-J-UCS
volume: 1
number: 7
pages: 560--??
day: 28
month: jul
monthnumber: 7
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
bibdate: Wed May 28 19:32:35 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.28 19:32:35 MDT
URL: http://www.iicm.edu/jucs_1_7/on_a_formally_correct
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: E. Popova
rawtitle: On a Formally Correct Implementation of {IEEE} Computer Arithmetic
entry:
@Article{Popova:1995:FCI,
  author =       "E. Popova",
  title =        "On a Formally Correct Implementation of {IEEE}
                 Computer Arithmetic",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "7",
  pages =        "560--??",
  day =          "28",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iicm.edu/jucs_1_7/on_a_formally_correct",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: article
filename: fparith.bib
label: Posch:1995:MRRa
author: Karl C. Posch and Reinhard Posch
title: Modulo Reduction in Residue Number Systems
journal: j-IEEE-TRANS-PAR-DIST-SYS
volume: 6
number: 5
pages: 449--454
month: may
monthnumber: 5
year: 1995
CODEN: ITDSEO
DOI: https://doi.org/10.1109/71.382314
ISSN: 1045-9219 (print), 1558-2183 (electronic) OR 10459219 (print), 15582183 (electronic)
ISSNL: 1045-9219 OR 10459219
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666
fjournal: IEEE Transactions on Parallel and Distributed Systems
acknowledgement: ack-nhfb
corpsource: Inst. for Appl. Inf. Process., Graz University of Technol., Austria
journalURL: http://www.computer.org/tpds/archives.htm
journalabr: IEEE Trans Parallel Distrib Syst
treatment: T Theoretical or Mathematical
rawauthor: Karl C. Posch and Reinhard Posch
rawtitle: Modulo Reduction in Residue Number Systems
keywords:
Approximation theory; Carry free operations; complexity; computational complexity; Computational complexity; Computer arithmetic; Computer hardware; Cryptography; cryptography; Digital arithmetic; Distributed computer systems; distributed systems; extremely long; integer arithmetic; Iterative methods; Long integer arithmetic; Modulo reduction; modulo reduction; number systems; Number theory; Parallel algorithms; parallel algorithms; parallel implementations; Parallel processing systems; residue arithmetic; Residue number systems; residue number systems

entry:
@Article{Posch:1995:MRRa,
  author =       "Karl C. Posch and Reinhard Posch",
  title =        "Modulo Reduction in Residue Number Systems",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "6",
  number =       "5",
  pages =        "449--454",
  month =        may,
  year =         "1995",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.382314",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666",
  acknowledgement = ack-nhfb,
  classification = "721.1; 722.4; 723.1; 723.2; 921.6; C4240C
                 (Computational complexity); C4240P (Parallel
                 programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C6110P (Parallel programming)",
  corpsource =   "Inst. for Appl. Inf. Process., Graz University of
                 Technol., Austria",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Approximation theory; Carry free operations;
                 complexity; computational complexity; Computational
                 complexity; Computer arithmetic; Computer hardware;
                 Cryptography; cryptography; Digital arithmetic;
                 Distributed computer systems; distributed systems;
                 extremely long; integer arithmetic; Iterative methods;
                 Long integer arithmetic; Modulo reduction; modulo
                 reduction; number systems; Number theory; Parallel
                 algorithms; parallel algorithms; parallel
                 implementations; Parallel processing systems; residue
                 arithmetic; Residue number systems; residue number
                 systems",
  summary =      "Residue number systems provide a good means for
                 extremely long integer arithmetic. Their carry-free
                 operations make parallel implementations feasible. Some
                 applications involving very long integers, such as
                 public key encryption, rely heavily on \ldots{}",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Posch:1995:MRRb
author: K. C. Posch and R. Posch
title: Modulo reduction in residue number systems
journal: j-IEEE-TRANS-PAR-DIST-SYS
volume: 6
number: 5
pages: 449--454
month: may
monthnumber: 5
year: 1995
CODEN: ITDSEO
DOI: https://doi.org/10.1109/71.382314
ISSN: 1045-9219 (print), 1558-2183 (electronic) OR 10459219 (print), 15582183 (electronic)
ISSNL: 1045-9219 OR 10459219
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666
fjournal: IEEE Transactions on Parallel and Distributed Systems
acknowledgement: ack-nhfb
affiliation: Graz Univ of Technology
affiliationaddress: Graz, Austria
corpsource: Inst. for Appl. Inf. Process., Graz University of Technol., Austria
journalURL: http://www.computer.org/tpds/archives.htm
journalabr: IEEE Trans Parallel Distrib Syst
treatment: T Theoretical or Mathematical
rawauthor: K. C. Posch and R. Posch
rawtitle: Modulo reduction in residue number systems
keywords:
Approximation theory; Carry free operations; complexity; computational complexity; Computational complexity; Computer arithmetic; Computer hardware; Cryptography; cryptography; Digital arithmetic; Distributed computer systems; distributed systems; extremely long; integer arithmetic; Iterative methods; Long integer arithmetic; Modulo reduction; modulo reduction; number systems; Number theory; Parallel algorithms; parallel algorithms; parallel implementations; Parallel processing systems; residue; Residue number systems; residue number systems

entry:
@Article{Posch:1995:MRRb,
  author =       "K. C. Posch and R. Posch",
  title =        "Modulo reduction in residue number systems",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "6",
  number =       "5",
  pages =        "449--454",
  month =        may,
  year =         "1995",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.382314",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666",
  acknowledgement = ack-nhfb,
  affiliation =  "Graz Univ of Technology",
  affiliationaddress = "Graz, Austria",
  classification = "721.1; 722.4; 723.1; 723.2; 921.6; C4240C
                 (Computational complexity); C4240P (Parallel
                 programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C6110P (Parallel programming)",
  corpsource =   "Inst. for Appl. Inf. Process., Graz University of
                 Technol., Austria",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Approximation theory; Carry free operations;
                 complexity; computational complexity; Computational
                 complexity; Computer arithmetic; Computer hardware;
                 Cryptography; cryptography; Digital arithmetic;
                 Distributed computer systems; distributed systems;
                 extremely long; integer arithmetic; Iterative methods;
                 Long integer arithmetic; Modulo reduction; modulo
                 reduction; number systems; Number theory; Parallel
                 algorithms; parallel algorithms; parallel
                 implementations; Parallel processing systems; residue;
                 Residue number systems; residue number systems",
  summary =      "Residue number systems provide a good means for
                 extremely long integer arithmetic. Their carry-free
                 operations make parallel implementations feasible. Some
                 applications involving very long integers, such as
                 public key encryption, rely heavily on \ldots{}",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Prabhu:1995:MRD
author: J. A. Prabhu and G. B. Zyner
title: 167 MHz Radix-$8$ Divide and Square Root Using Overlapped Radix-$2$ Stages
crossref: Knowles:1995:PSC
pages: 155--162
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: J. A. Prabhu and G. B. Zyner
rawtitle: {167 MHz} Radix-$8$ Divide and Square Root Using Overlapped Radix-$2$ Stages
entry:
@InProceedings{Prabhu:1995:MRD,
  author =       "J. A. Prabhu and G. B. Zyner",
  title =        "{167 MHz} Radix-$8$ Divide and Square Root Using
                 Overlapped Radix-$2$ Stages",
  crossref =     "Knowles:1995:PSC",
  pages =        "155--162",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "UltraSPARC's IEEE-754 compliant floating point divide
                 and square root implementation is presented. Three
                 overlapping stages of SRT radix-$2$ quotient selection
                 logic enable an effective radix-$8$ calculation at 167
                 MHz while only a single radix-$2$ \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Prabhu:1995:MRF
author: J. Arjun Prabhu and Gregory B. Zyner
title: 167 MHz Radix-8 floating point divide and square root using overlapped radix-2 stages
crossref: Knowles:1995:PSC
pages: 155--162
month: jul
monthnumber: 7
year: 1995
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/arith12/papers/ARITH12_Prabhu.pdf
keywords: ARITH-12; UltraSPARC
acknowledgement: ack-sfo
rawauthor: J. Arjun Prabhu and Gregory B. Zyner
rawtitle: 167 {MHz} Radix-8 floating point divide and square root using overlapped radix-2 stages
entry:
@InProceedings{Prabhu:1995:MRF,
  author =       "J. Arjun Prabhu and Gregory B. Zyner",
  title =        "167 {MHz} Radix-8 floating point divide and square
                 root using overlapped radix-2 stages",
  crossref =     "Knowles:1995:PSC",
  month =        jul,
  year =         "1995",
  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/arith12/papers/ARITH12_Prabhu.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12; UltraSPARC",
}


bibtype: article
filename: fparith.bib
label: Pratt:1995:APB
author: V. Pratt
title: Anatomy of the Pentium Bug
journal: j-LECT-NOTES-COMP-SCI
volume: 915
pages: 97--107
year: 1995
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat May 11 13:45:32 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.05.11 13:45:32 MDT
URL: ftp://boole.stanford.edu/pub/FDIV/anapent.ps.gz
fjournal: Lecture Notes in Computer Science
keywords: Intel Pentium divide flaw; Thomas R. Nicely
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: V. Pratt
rawtitle: Anatomy of the {Pentium} Bug
entry:
@Article{Pratt:1995:APB,
  author =       "V. Pratt",
  title =        "Anatomy of the {Pentium} Bug",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "915",
  pages =        "97--107",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat May 11 13:45:32 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://boole.stanford.edu/pub/FDIV/anapent.ps.gz",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
}


bibtype: article
filename: fparith.bib
label: Price:1995:PFF
author: Dick Price
title: Pentium FDIV Flaw --- Lessons Learned
journal: j-IEEE-MICRO
volume: 15
number: 2
pages: 88, 86--87
month: mar
monthnumber: 3
year: 1995
CODEN: IEMIDZ
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; Science Citation Index database (1980--2000)
bibtimestamp: 2000.12.14 06:08:58 MST
URL: https://ieeexplore.ieee.org/iel1/40/8521/00372360.pdf
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
thesaurus: Computer testing; Floating point arithmetic; Integrated circuit testing
treatment: G General Review
rawauthor: Dick Price
rawtitle: {Pentium FDIV} Flaw --- Lessons Learned
abstract:
As the tidal wave of publicity surrounding the Pentium floating-point divide bug subsides, questions about the controversy's lasting impact linger. Intel's competitors may rejoice at the industry giant's technical and public relations missteps, but they too must worry about damage done to customer confidence, shuddering at the prospect of taking a similar public pratfall. And consumers, justified or not, have new reliability worries with every new product release. Intel recently adopted a `no questions asked' replacement policy for defective Pentium chips, reversing its earlier stance. As part of a new commitment to openness, Intel has posted a variety of documents on its World Wide Web home page (http://www.intel.com) describing the flaw, analysing its severity, and providing replacement procedures. Industry observers have pointed to the benefits that will come from Intel's woes: more openness by manufacturers, better understanding among consumers of the problems facing chip makers, and greater emphasis on testing. For chip makers and computer users alike, it remains then to calculate the lessons learned.

keywords:
Chip makers; chip makers; circuit testing; computer testing; Defective Pentium chips; defective Pentium chips; floating point arithmetic; integrated; Intel; Intel Pentium divide flaw; Pentium floating-point divide bug; reliability; Reliability; replacement procedures; Replacement procedures; Thomas R. Nicely

classcodes:
B1265F (Microprocessors and microcomputers); C5130 (Microprocessor chips); C5470 (Performance evaluation and testing); C5230 (Digital arithmetic methods)

rawabstract:
As the tidal wave of publicity surrounding the Pentium floating-point divide bug subsides, questions about the controversy's lasting impact linger. Intel's competitors may rejoice at the industry giant's technical and public relations missteps, but they too must worry about damage done to customer confidence, shuddering at the prospect of taking a similar public pratfall. And consumers, justified or not, have new reliability worries with every new product release. Intel recently adopted a `no questions asked' replacement policy for defective Pentium chips, reversing its earlier stance. As part of a new commitment to openness, Intel has posted a variety of documents on its World Wide Web home page (http://www.intel.com) describing the flaw, analysing its severity, and providing replacement procedures. Industry observers have pointed to the benefits that will come from Intel's woes: more openness by manufacturers, better understanding among consumers of the problems facing chip makers, and greater emphasis on testing. For chip makers and computer users alike, it remains then to calculate the lessons learned.

entry:
@Article{Price:1995:PFF,
  author =       "Dick Price",
  title =        "{Pentium FDIV} Flaw --- Lessons Learned",
  journal =      j-IEEE-MICRO,
  volume =       "15",
  number =       "2",
  pages =        "88, 86--87",
  month =        mar # "\slash " # apr,
  year =         "1995",
  CODEN =        "IEMIDZ",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  URL =          "https://ieeexplore.ieee.org/iel1/40/8521/00372360.pdf",
  abstract =     "As the tidal wave of publicity surrounding the Pentium
                 floating-point divide bug subsides, questions about the
                 controversy's lasting impact linger. Intel's
                 competitors may rejoice at the industry giant's
                 technical and public relations missteps, but they too
                 must worry about damage done to customer confidence,
                 shuddering at the prospect of taking a similar public
                 pratfall. And consumers, justified or not, have new
                 reliability worries with every new product release.
                 Intel recently adopted a `no questions asked'
                 replacement policy for defective Pentium chips,
                 reversing its earlier stance. As part of a new
                 commitment to openness, Intel has posted a variety of
                 documents on its World Wide Web home page
                 (http://www.intel.com) describing the flaw, analysing
                 its severity, and providing replacement procedures.
                 Industry observers have pointed to the benefits that
                 will come from Intel's woes: more openness by
                 manufacturers, better understanding among consumers of
                 the problems facing chip makers, and greater emphasis
                 on testing. For chip makers and computer users alike,
                 it remains then to calculate the lessons learned.",
  acknowledgement = ack-nhfb,
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5470 (Performance evaluation
                 and testing); C5230 (Digital arithmetic methods)",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods); C5470 (Performance evaluation and testing)",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "Chip makers; chip makers; circuit testing; computer
                 testing; Defective Pentium chips; defective Pentium
                 chips; floating point arithmetic; integrated; Intel;
                 Intel Pentium divide flaw; Pentium floating-point
                 divide bug; reliability; Reliability; replacement
                 procedures; Replacement procedures; Thomas R. Nicely",
  thesaurus =    "Computer testing; Floating point arithmetic;
                 Integrated circuit testing",
  treatment =    "G General Review",
}


bibtype: article
filename: fparith.bib
label: Rogers:1995:UMP
author: John Rogers
title: Using the Multiple Precision Library
journal: j-DDJ
volume: 20
number: 1
pages: 36, 38, 40, 42, 86, 88--89
month: jan
monthnumber: 1
year: 1995
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
thesaurus: C language; Software libraries; Software portability; Subroutines; Unix
rawauthor: John Rogers
rawtitle: Using the Multiple Precision Library
abstract:
Although most implementations of C boast 32-bit integer arithmetic, many applications are beginning to require higher precision. However, even the IEEE double-precision floating-point format only gives 15 digits of precision. What is needed is a way to deal with multiple-precision integers, independent of the machine's word size. The multiple precision (MP) integer library available with UNIX V7, UNIX SVR4, 4.3BSD, and other versions of UNIX provide infinite precision signed integer operations for C programs. I have also ported the GMP library to Windows NT. In this article, I describe how to use the scantily documented MP routines, along with providing sample code, portability information, some MP helpers, and a few other hints.

keywords:
4.3BSD; C; C programs; GMP library; IEEE double-precision floating-point format; Infinite precision signed integer operations; Integer arithmetic; MP routines; Multiple precision library; Multiple-precision integers; Portability; UNIX; UNIX SVR4; UNIX V7; Windows NT; Word size

rawabstract:
Although most implementations of C boast 32-bit integer arithmetic, many applications are beginning to require higher precision. However, even the IEEE double-precision floating-point format only gives 15 digits of precision. What is needed is a way to deal with multiple-precision integers, independent of the machine's word size. The multiple precision (MP) integer library available with UNIX V7, UNIX SVR4, 4.3BSD, and other versions of UNIX provide infinite precision signed integer operations for C programs. I have also ported the GMP library to Windows NT. In this article, I describe how to use the scantily documented MP routines, along with providing sample code, portability information, some MP helpers, and a few other hints.

entry:
@Article{Rogers:1995:UMP,
  author =       "John Rogers",
  title =        "Using the Multiple Precision Library",
  journal =      j-DDJ,
  volume =       "20",
  number =       "1",
  pages =        "36, 38, 40, 42, 86, 88--89",
  month =        jan,
  year =         "1995",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "Although most implementations of C boast 32-bit
                 integer arithmetic, many applications are beginning to
                 require higher precision. However, even the IEEE
                 double-precision floating-point format only gives 15
                 digits of precision. What is needed is a way to deal
                 with multiple-precision integers, independent of the
                 machine's word size. The multiple precision (MP)
                 integer library available with UNIX V7, UNIX SVR4,
                 4.3BSD, and other versions of UNIX provide infinite
                 precision signed integer operations for C programs. I
                 have also ported the GMP library to Windows NT. In this
                 article, I describe how to use the scantily documented
                 MP routines, along with providing sample code,
                 portability information, some MP helpers, and a few
                 other hints.",
  acknowledgement = ack-nhfb,
  classification = "C6110B (Software engineering techniques); C6140D
                 (High level languages)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "4.3BSD; C; C programs; GMP library; IEEE
                 double-precision floating-point format; Infinite
                 precision signed integer operations; Integer
                 arithmetic; MP routines; Multiple precision library;
                 Multiple-precision integers; Portability; UNIX; UNIX
                 SVR4; UNIX V7; Windows NT; Word size",
  thesaurus =    "C language; Software libraries; Software portability;
                 Subroutines; Unix",
}


bibtype: article
filename: fparith.bib
label: Rubenking:1995:UNI
author: Neil J. Rubenking
journal: j-PC-MAGAZINE
volume: 14
number: 20
pages: 293--??
year: 1995
CODEN: PCMGEP
ISSN: 0888-8507 (print), 1078-8085 (electronic) OR 08888507 (print), 10788085 (electronic)
ISSNL: 0888-8507 OR 08888507
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
fjournal: PC Magazine
acknowledgement: ack-nhfb
rawauthor: Neil J. Rubenking
title:
User-to-User --- The natural imperfection of floating-point calculations; customizing the Windows 95 boot process; providing a way for the user to exit

rawtitle:
User-to-User --- The natural imperfection of floating-point calculations; customizing the {Windows} 95 boot process; providing a way for the user to exit

entry:
@Article{Rubenking:1995:UNI,
  author =       "Neil J. Rubenking",
  title =        "User-to-User --- The natural imperfection of
                 floating-point calculations; customizing the {Windows}
                 95 boot process; providing a way for the user to exit",
  journal =      j-PC-MAGAZINE,
  volume =       "14",
  number =       "20",
  pages =        "293--??",
  year =         "1995",
  CODEN =        "PCMGEP",
  ISSN =         "0888-8507 (print), 1078-8085 (electronic)",
  ISSN-L =       "0888-8507",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "PC Magazine",
}


bibtype: article
filename: fparith.bib
label: Sammut:1995:AUD
author: K. M. Sammut and S. R. Jones
title: Arithmetic unit design for neural accelerators: cost performance issues
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 10
pages: 1256--1260
month: oct
monthnumber: 10
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.467702
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:30 MDT 2011
bibtimestamp: 2011.07.06 08:01:30 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=467702
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. M. Sammut and S. R. Jones
rawtitle: Arithmetic unit design for neural accelerators: cost performance issues
entry:
@Article{Sammut:1995:AUD,
  author =       "K. M. Sammut and S. R. Jones",
  title =        "Arithmetic unit design for neural accelerators: cost
                 performance issues",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "10",
  pages =        "1256--1260",
  month =        oct,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.467702",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=467702",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Sangwine:1995:CIT
author: S. J. Sangwine and D. A. Riach
title: Colour image thresholding at pixel rate using rational arithmetic hardware
publisher: pub-IEE
address: pub-IEE:adr
pages: 828--832
year: 1995
ISBN: 0-85296-642-3 OR 0852966423
ISBN13: 978-0-85296-642-6 OR 9780852966426
LCCN: A1632 .I553 1995
bibdate: Fri Nov 30 07:37:21 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.30 07:37:21 ???
acknowledgement: ack-nhfb
rawauthor: S. J. Sangwine and D. A. Riach
rawtitle: Colour image thresholding at pixel rate using rational arithmetic hardware
booktitle:
Fifth International Conference on Image Processing and its Applications: 4-6 July 1995: venue, Heriot-Watt University, Edinburgh, UK

abstract:
Thresholding of images is a common precursor to many object recognition or image analysis methods. Colours images contain more information than monochrome images of the same spatial resolution and in many applications of colour image processing there will be a need for thresholding. The paper presents a hardware implementation and development of a technique published by Pritchard et al. (1994). A brief review is given of the rational arithmetic representation; the authors then discuss the definition of colour purity, present a description of the thresholding algorithm as implemented in hardware and finally, give a block-level description of the hardware implementation and some results obtained

rawabstract:
Thresholding of images is a common precursor to many object recognition or image analysis methods. Colours images contain more information than monochrome images of the same spatial resolution and in many applications of colour image processing there will be a need for thresholding. The paper presents a hardware implementation and development of a technique published by Pritchard et al. (1994). A brief review is given of the rational arithmetic representation; the authors then discuss the definition of colour purity, present a description of the thresholding algorithm as implemented in hardware and finally, give a block-level description of the hardware implementation and some results obtained

rawbooktitle:
{Fifth International Conference on Image Processing and its Applications: 4-6 July 1995: venue, Heriot-Watt University, Edinburgh, UK}

entry:
@InProceedings{Sangwine:1995:CIT,
  author =       "S. J. Sangwine and D. A. Riach",
  booktitle =    "{Fifth International Conference on Image Processing
                 and its Applications: 4-6 July 1995: venue, Heriot-Watt
                 University, Edinburgh, UK}",
  title =        "Colour image thresholding at pixel rate using rational
                 arithmetic hardware",
  publisher =    pub-IEE,
  address =      pub-IEE:adr,
  pages =        "828--832",
  year =         "1995",
  ISBN =         "0-85296-642-3",
  ISBN-13 =      "978-0-85296-642-6",
  LCCN =         "A1632 .I553 1995",
  bibdate =      "Fri Nov 30 07:37:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Thresholding of images is a common precursor to many
                 object recognition or image analysis methods. Colours
                 images contain more information than monochrome images
                 of the same spatial resolution and in many applications
                 of colour image processing there will be a need for
                 thresholding. The paper presents a hardware
                 implementation and development of a technique published
                 by Pritchard et al. (1994). A brief review is given of
                 the rational arithmetic representation; the authors
                 then discuss the definition of colour purity, present a
                 description of the thresholding algorithm as
                 implemented in hardware and finally, give a block-level
                 description of the hardware implementation and some
                 results obtained",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sanyal:1995:CAS
author: S. Sanyal
title: Computer Arithmetic Systems
journal: j-COMP-J
volume: 38
number: 1
pages: 79--79
year: 1995
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/38.1.79
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:48:43 MST 2012
bibtimestamp: 2012.12.04 14:48:43 MST
URL: http://comjnl.oxfordjournals.org/content/38/1/79.full.pdf+html
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: S. Sanyal
rawtitle: Computer Arithmetic Systems
bibsource:
http://comjnl.oxfordjournals.org/content/38/1.toc; https://www.math.utah.edu/pub/tex/bib/compj1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Sanyal:1995:CAS,
  author =       "S. Sanyal",
  title =        "Computer Arithmetic Systems",
  journal =      j-COMP-J,
  volume =       "38",
  number =       "1",
  pages =        "79--79",
  month =        "????",
  year =         "1995",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/38.1.79",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:43 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/38/1.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/38/1/79.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: inproceedings
filename: fparith.bib
label: Sarma:1995:FBR
author: Debjit Das Sarma and David W. Matula
title: Faithful Bipartite ROM Reciprocal Tables
crossref: Knowles:1995:PSC
pages: 17--29
month: jul
monthnumber: 7
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Sarma.pdf
keywords: ARITH-12
acknowledgement: ack-sfo
rawauthor: Debjit Das Sarma and David W. Matula
rawtitle: Faithful Bipartite {ROM} Reciprocal Tables
entry:
@InProceedings{Sarma:1995:FBR,
  author =       "Debjit Das Sarma and David W. Matula",
  title =        "Faithful Bipartite {ROM} Reciprocal Tables",
  crossref =     "Knowles:1995:PSC",
  pages =        "17--29",
  month =        jul,
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Sarma.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
  xxnote =       "Check: page 29 is missing from PDF file; is it
                 blank?",
  xxpages =      "17--28??",
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1995:DAV
author: M. J. Schulte and E. E. Swartzlander, Jr.
title: Design and applications for variable-precision, interval arithmetic coprocessors
crossref: Kearfott:1996:AICa
pages: 166--172
year: 1995
bibdate: Tue Apr 07 16:25:50 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.07 16:25:50 ???
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and E. E. {Swartzlander, Jr.}
rawtitle: Design and applications for variable-precision, interval arithmetic coprocessors
entry:
@InProceedings{Schulte:1995:DAV,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Design and applications for variable-precision,
                 interval arithmetic coprocessors",
  crossref =     "Kearfott:1996:AICa",
  pages =        "166--172",
  year =         "1995",
  bibdate =      "Tue Apr 07 16:25:50 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-jf,
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1995:HDA
author: Michael J. Schulte and Eearl E. Swartzlander, Jr.
title: Hardware Design and Arithmetic Algorithms for a Variable-Precision, Interval Arithmetic Coprocessor
crossref: Knowles:1995:PSC
pages: 222--229
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Michael J. Schulte and Eearl E. {Swartzlander, Jr.}
rawtitle: Hardware Design and Arithmetic Algorithms for a Variable-Precision, Interval Arithmetic Coprocessor
URL:
http://mesa.ece.wisc.edu/publications/cp_1995-03.pdf; http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Schulte.pdf

entry:
@InProceedings{Schulte:1995:HDA,
  author =       "Michael J. Schulte and Eearl E. {Swartzlander, Jr.}",
  title =        "Hardware Design and Arithmetic Algorithms for a
                 Variable-Precision, Interval Arithmetic Coprocessor",
  crossref =     "Knowles:1995:PSC",
  pages =        "222--229",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-03.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Schulte.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: inproceedings
filename: fparith.bib
label: Schulte:1995:PSI
author: Michael J. Schulte and Eearl E. Swartzlander, Jr.
title: A Processor for Staggered Interval Arithmetic
crossref: Cappello:1995:ICA
pages: 104--112
year: 1995
bibdate: Mon Oct 20 07:16:07 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.10.20 07:16:07 MDT
URL: http://mesa.ece.wisc.edu/publications/cp_1995-02.pdf
acknowledgement: ack-nhfb
rawauthor: Michael J. Schulte and Eearl E. {Swartzlander, Jr.}
rawtitle: A Processor for Staggered Interval Arithmetic
entry:
@InProceedings{Schulte:1995:PSI,
  author =       "Michael J. Schulte and Eearl E. {Swartzlander, Jr.}",
  title =        "A Processor for Staggered Interval Arithmetic",
  crossref =     "Cappello:1995:ICA",
  pages =        "104--112",
  year =         "1995",
  bibdate =      "Mon Oct 20 07:16:07 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-02.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Schwarz:1995:RQC
author: E. M. Schwarz
title: Rounding for quadratically converging algorithms for division and square root
crossref: Singh:1995:CRT
volume: 1
pages: 600--603
month: oct
monthnumber: 10
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-sfo
rawauthor: E. M. Schwarz
rawtitle: Rounding for quadratically converging algorithms for division and square root
entry:
@InProceedings{Schwarz:1995:RQC,
  author =       "E. M. Schwarz",
  title =        "Rounding for quadratically converging algorithms for
                 division and square root",
  crossref =     "Singh:1995:CRT",
  volume =       "1",
  pages =        "600--603",
  month =        oct,
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Exactly rounded results are necessary for many
                 architectures such as IEEE 754 standard. For division
                 and square root, rounding is easy to perform if a
                 remainder is available. But for quadratically
                 converging algorithms, the remainder is not \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Shirazi:1995:QAF
author: N. Shirazi and A. Walters and P. Athanas
title: Quantitative analysis of floating point arithmetic on FPGA based custom computing machines
crossref: Athanas:1995:PIS
pages: 155--162
year: 1995
DOI: https://doi.org/10.1109/FPGA.1995.477421
bibdate: Sat Oct 9 13:02:18 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.09 13:02:18 ???
acknowledgement: ack-nhfb
rawauthor: N. Shirazi and A. Walters and P. Athanas
rawtitle: Quantitative analysis of floating point arithmetic on {FPGA} based custom computing machines
abstract:
Many algorithms rely on floating point arithmetic for the dynamic range of representations and require millions of calculations per second. Such computationally intensive algorithms are candidates for acceleration using custom computing machines (CCMs) being tailored for the application. Unfortunately, floating point operators require excessive area (or time) for conventional implementations. Instead, custom formats, derived for individual applications, are feasible on CCMs, and can be implemented on a fraction of a single FPGA. Using higher-level languages, like VHDL, facilitates the development of custom operators without significantly impacting operator performance or area. Properties, including area consumption and speed of working arithmetic operator units used in real-time applications, are discussed

rawabstract:
Many algorithms rely on floating point arithmetic for the dynamic range of representations and require millions of calculations per second. Such computationally intensive algorithms are candidates for acceleration using custom computing machines (CCMs) being tailored for the application. Unfortunately, floating point operators require excessive area (or time) for conventional implementations. Instead, custom formats, derived for individual applications, are feasible on CCMs, and can be implemented on a fraction of a single FPGA. Using higher-level languages, like VHDL, facilitates the development of custom operators without significantly impacting operator performance or area. Properties, including area consumption and speed of working arithmetic operator units used in real-time applications, are discussed

entry:
@InProceedings{Shirazi:1995:QAF,
  author =       "N. Shirazi and A. Walters and P. Athanas",
  title =        "Quantitative analysis of floating point arithmetic on
                 {FPGA} based custom computing machines",
  crossref =     "Athanas:1995:PIS",
  pages =        "155--162",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/FPGA.1995.477421",
  bibdate =      "Sat Oct 9 13:02:18 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many algorithms rely on floating point arithmetic for
                 the dynamic range of representations and require
                 millions of calculations per second. Such
                 computationally intensive algorithms are candidates for
                 acceleration using custom computing machines (CCMs)
                 being tailored for the application. Unfortunately,
                 floating point operators require excessive area (or
                 time) for conventional implementations. Instead, custom
                 formats, derived for individual applications, are
                 feasible on CCMs, and can be implemented on a fraction
                 of a single FPGA. Using higher-level languages, like
                 VHDL, facilitates the development of custom operators
                 without significantly impacting operator performance or
                 area. Properties, including area consumption and speed
                 of working arithmetic operator units used in real-time
                 applications, are discussed",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Sigvartsen:1995:TBF
author: Roy L. Sigvartsen and Roar Skogstrom
title: A test bench for floating point arithmetic
type: FFI rapport
number: 95/04099
institution: Forsvarets forskningsinstitut
address: Kjeller, Norway
pages: 54
year: 1995
bibdate: Thu May 09 08:08:19 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:08:19 ???
keywords: floating-point testing
acknowledgement: ack-nhfb
rawauthor: Roy L. Sigvartsen and Roar Skogstr{\o}m
rawtitle: A test bench for floating point arithmetic
entry:
@TechReport{Sigvartsen:1995:TBF,
  author =       "Roy L. Sigvartsen and Roar Skogstr{\o}m",
  title =        "A test bench for floating point arithmetic",
  type =         "{FFI} rapport",
  number =       "95/04099",
  institution =  "Forsvarets forskningsinstitut",
  address =      "Kjeller, Norway",
  pages =        "54",
  year =         "1995",
  bibdate =      "Thu May 09 08:08:19 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}


bibtype: book
filename: fparith.bib
label: Sites:1995:AAA
author: Richard L. Sites and Richard L. Witek
title: Alpha AXP Architecture Reference Manual
publisher: pub-DP
address: pub-DP:adr
edition: Second
pages: various
year: 1995
ISBN: 1-55558-145-5 OR 1555581455
ISBN13: 978-1-55558-145-9 OR 9781555581459
LCCN: QA76.9.A73A46 1995
bibdate: Thu Aug 07 13:41:17 1997
bibtimestamp: 1997.08.07 13:41:17 ???
acknowledgement: ack-nhfb
rawauthor: Richard L. Sites and Richard L. Witek
rawtitle: {Alpha AXP} Architecture Reference Manual
TOC:
Foreword Preface to the First Edition Preface to the Second Edition Part 1: Common Architecture (I) 1. Introduction (I) 1.1 The Alpha AXP Approach to RISC Architecture 1.2 Data Format Overview 1.3 Instruction Format Overview 1.4 Instruction Overview 1.5 Instruction Set Characteristics 1.6 Terminology and Conventions 2. Basic Architecture (I) 2.1 Addressing 2.2 Data Types 2.3 Big-endian Addressing Support 3. Instruction Formats (I) 3.1 Alpha AXP Registers 3.2 Notation 3.3 Instruction Formats 4. Instruction Descriptions (I) 4.1 Instruction Set Overview 4.2 Memory Integer Load/Store Instructions 4.3 Control Instructions 4.4 Integer Arithmetic Instructions 4.5 Logical and Shift Instructions 4.6 Byte-Manipulation Instructions 4.7 Floating-Point Instructions 4.8 Memory Format Floating-Point Instructions 4.9 Branch Format Floating-Point Instructions 4.10 Floating-Point Operate Format Instructions 4.11 Miscellaneous Instructions 4.12 VAX Compatibility Instructions 5. System Architecture and Programming Implications 5.1 Introduction 5.2 Physical Address Space Characteristics 5.3 Translation Buffers and Virtual Caches 5.4 Caches and Write Buffers 5.5 Data Sharing 5.6 Read/Write Ordering 5.7 Arithmetic Traps 6. Common PALcode Architecture (I) 6.1 PALcode 6.2 PALcode Instructions and Functions 6.3 PALcode Environment 6.4 Special Functions Required for PALcode 6.5 PALcode Effects on System Code 6.6 PALcode Replacement 6.7 Required PALcode Instructions 7. Console Subsystem Overview (I) 8. Input/Output Overview (I) Specific Operating System PALcode Architecture (II) Part 2: OpenVMS AXP Software (II-A) 1. Introduction to OpenVMS AXP (II-A) 1.1 Register Usage 2. OpenVMS AXP PALcode Instruction Descriptions (II-A) 2.1 Unprivileged General OpenVMS AXP PALcode Instructions 2.2 OpenVMS AXP Queue Data Types 2.3 Unprivileged OpenVMS AXP Queue PALcode Instructions 2.4 Unprivileged VAX Compatibility PALcode Instructions 2.5 Unprivileged PALcode Thread Instructions 2.6 Privileged PALcode Instructions 3. OpenVMS AXP Memory Management (II-A) 3.1 Introduction 3.2 Virtual Address Space 3.3 Physical Address Space 3.4 Memory Management Control 3.5 Page Table Entries 3.6 Memory Protection 3.7 Address Translation 3.8 Translation Buffer 3.9 Address Space Numbers 3.10 Memory Management Faults 4. OpenVMS AXP Process Structure (II-A) 4.1 Process Definition 4.2 Hardware Privileged Process Context 4.3 Asynchronous System Traps (AST) 4.4 Process Context Switching 5. OpenVMS AXP Internal Processor Registers (II-A) 5.1 Internal Processor Registers 5.2 Stack Pointer Internal Processor Registers 5.3 IPR Summary

rawTOC:
Foreword \\ Preface to the First Edition \\ Preface to the Second Edition \\ Part 1: Common Architecture (I) \\ 1. Introduction (I) \\ 1.1 The Alpha AXP Approach to RISC Architecture \\ 1.2 Data Format Overview \\ 1.3 Instruction Format Overview \\ 1.4 Instruction Overview \\ 1.5 Instruction Set Characteristics \\ 1.6 Terminology and Conventions \\ 2. Basic Architecture (I) \\ 2.1 Addressing \\ 2.2 Data Types \\ 2.3 Big-endian Addressing Support \\ 3. Instruction Formats (I) \\ 3.1 Alpha AXP Registers \\ 3.2 Notation \\ 3.3 Instruction Formats \\ 4. Instruction Descriptions (I) \\ 4.1 Instruction Set Overview \\ 4.2 Memory Integer Load/Store Instructions \\ 4.3 Control Instructions \\ 4.4 Integer Arithmetic Instructions \\ 4.5 Logical and Shift Instructions \\ 4.6 Byte-Manipulation Instructions \\ 4.7 Floating-Point Instructions \\ 4.8 Memory Format Floating-Point Instructions \\ 4.9 Branch Format Floating-Point Instructions \\ 4.10 Floating-Point Operate Format Instructions \\ 4.11 Miscellaneous Instructions \\ 4.12 VAX Compatibility Instructions \\ 5. System Architecture and Programming Implications \\ 5.1 Introduction \\ 5.2 Physical Address Space Characteristics \\ 5.3 Translation Buffers and Virtual Caches \\ 5.4 Caches and Write Buffers \\ 5.5 Data Sharing \\ 5.6 Read/Write Ordering \\ 5.7 Arithmetic Traps \\ 6. Common PALcode Architecture (I) \\ 6.1 PALcode \\ 6.2 PALcode Instructions and Functions \\ 6.3 PALcode Environment \\ 6.4 Special Functions Required for PALcode \\ 6.5 PALcode Effects on System Code \\ 6.6 PALcode Replacement \\ 6.7 Required PALcode Instructions \\ 7. Console Subsystem Overview (I) \\ 8. Input/Output Overview (I) \\ Specific Operating System PALcode Architecture (II) \\ Part 2: OpenVMS AXP Software (II-A) \\ 1. Introduction to OpenVMS AXP (II-A) \\ 1.1 Register Usage \\ 2. OpenVMS AXP PALcode Instruction Descriptions (II-A) \\ 2.1 Unprivileged General OpenVMS AXP PALcode Instructions \\ 2.2 OpenVMS AXP Queue Data Types \\ 2.3 Unprivileged OpenVMS AXP Queue PALcode Instructions \\ 2.4 Unprivileged VAX Compatibility PALcode Instructions \\ 2.5 Unprivileged PALcode Thread Instructions \\ 2.6 Privileged PALcode Instructions \\ 3. OpenVMS AXP Memory Management (II-A) \\ 3.1 Introduction \\ 3.2 Virtual Address Space \\ 3.3 Physical Address Space \\ 3.4 Memory Management Control \\ 3.5 Page Table Entries \\ 3.6 Memory Protection \\ 3.7 Address Translation \\ 3.8 Translation Buffer \\ 3.9 Address Space Numbers \\ 3.10 Memory Management Faults \\ 4. OpenVMS AXP Process Structure (II-A) \\ 4.1 Process Definition \\ 4.2 Hardware Privileged Process Context \\ 4.3 Asynchronous System Traps (AST) \\ 4.4 Process Context Switching \\ 5. OpenVMS AXP Internal Processor Registers (II-A) \\ 5.1 Internal Processor Registers \\ 5.2 Stack Pointer Internal Processor Registers \\ 5.3 IPR Summary

entry:
@Book{Sites:1995:AAA,
  author =       "Richard L. Sites and Richard L. Witek",
  title =        "{Alpha AXP} Architecture Reference Manual",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  edition =      "Second",
  pages =        "various",
  year =         "1995",
  ISBN =         "1-55558-145-5",
  ISBN-13 =      "978-1-55558-145-9",
  LCCN =         "QA76.9.A73A46 1995",
  bibdate =      "Thu Aug 07 13:41:17 1997",
  bibsource =    "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/microchip.bib",
  price =        "US\$52.95",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword \\
                 Preface to the First Edition \\
                 Preface to the Second Edition \\
                 Part 1: Common Architecture (I) \\
                 1. Introduction (I) \\
                 1.1 The Alpha AXP Approach to RISC Architecture \\
                 1.2 Data Format Overview \\
                 1.3 Instruction Format Overview \\
                 1.4 Instruction Overview \\
                 1.5 Instruction Set Characteristics \\
                 1.6 Terminology and Conventions \\
                 2. Basic Architecture (I) \\
                 2.1 Addressing \\
                 2.2 Data Types \\
                 2.3 Big-endian Addressing Support \\
                 3. Instruction Formats (I) \\
                 3.1 Alpha AXP Registers \\
                 3.2 Notation \\
                 3.3 Instruction Formats \\
                 4. Instruction Descriptions (I) \\
                 4.1 Instruction Set Overview \\
                 4.2 Memory Integer Load/Store Instructions \\
                 4.3 Control Instructions \\
                 4.4 Integer Arithmetic Instructions \\
                 4.5 Logical and Shift Instructions \\
                 4.6 Byte-Manipulation Instructions \\
                 4.7 Floating-Point Instructions \\
                 4.8 Memory Format Floating-Point Instructions \\
                 4.9 Branch Format Floating-Point Instructions \\
                 4.10 Floating-Point Operate Format Instructions \\
                 4.11 Miscellaneous Instructions \\
                 4.12 VAX Compatibility Instructions \\
                 5. System Architecture and Programming Implications \\
                 5.1 Introduction \\
                 5.2 Physical Address Space Characteristics \\
                 5.3 Translation Buffers and Virtual Caches \\
                 5.4 Caches and Write Buffers \\
                 5.5 Data Sharing \\
                 5.6 Read/Write Ordering \\
                 5.7 Arithmetic Traps \\
                 6. Common PALcode Architecture (I) \\
                 6.1 PALcode \\
                 6.2 PALcode Instructions and Functions \\
                 6.3 PALcode Environment \\
                 6.4 Special Functions Required for PALcode \\
                 6.5 PALcode Effects on System Code \\
                 6.6 PALcode Replacement \\
                 6.7 Required PALcode Instructions \\
                 7. Console Subsystem Overview (I) \\
                 8. Input/Output Overview (I) \\
                 Specific Operating System PALcode Architecture (II) \\
                 Part 2: OpenVMS AXP Software (II-A) \\
                 1. Introduction to OpenVMS AXP (II-A) \\
                 1.1 Register Usage \\
                 2. OpenVMS AXP PALcode Instruction Descriptions (II-A)
                 \\
                 2.1 Unprivileged General OpenVMS AXP PALcode
                 Instructions \\
                 2.2 OpenVMS AXP Queue Data Types \\
                 2.3 Unprivileged OpenVMS AXP Queue PALcode Instructions
                 \\
                 2.4 Unprivileged VAX Compatibility PALcode Instructions
                 \\
                 2.5 Unprivileged PALcode Thread Instructions \\
                 2.6 Privileged PALcode Instructions \\
                 3. OpenVMS AXP Memory Management (II-A) \\
                 3.1 Introduction \\
                 3.2 Virtual Address Space \\
                 3.3 Physical Address Space \\
                 3.4 Memory Management Control \\
                 3.5 Page Table Entries \\
                 3.6 Memory Protection \\
                 3.7 Address Translation \\
                 3.8 Translation Buffer \\
                 3.9 Address Space Numbers \\
                 3.10 Memory Management Faults \\
                 4. OpenVMS AXP Process Structure (II-A) \\
                 4.1 Process Definition \\
                 4.2 Hardware Privileged Process Context \\
                 4.3 Asynchronous System Traps (AST) \\
                 4.4 Process Context Switching \\
                 5. OpenVMS AXP Internal Processor Registers (II-A) \\
                 5.1 Internal Processor Registers \\
                 5.2 Stack Pointer Internal Processor Registers \\
                 5.3 IPR Summary",
}


bibtype: article
filename: fparith.bib
label: Siu:1995:TMP
author: Kai-Yeung Y. Siu and V. Roychowdhury and T. Kailath
title: Toward Massively Parallel Design of Multipliers
journal: j-J-PAR-DIST-COMP
volume: 24
number: 1
pages: 86--93
month: jan
monthnumber: 1
year: 1995
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1995.1008
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:18:56 MST 2000
bibtimestamp: 2000.03.09 09:18:56 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Department of Electr. and Comput. Eng., California University, Irvine, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: T Theoretical or Mathematical
rawauthor: Kai-Yeung Y. Siu and V. Roychowdhury and T. Kailath
rawtitle: Toward Massively Parallel Design of Multipliers
URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production/pdf

keywords:
AND-OR circuits; arithmetic computation; asymptotic time complexity; circuits; computation delays; computational complexity; digital arithmetic; fan-in threshold circuits; gates; hardware; logic; massively parallel design; massively parallel high-speed multipliers; multiplication; multipliers; multiplying; parallel processing; parity; polynomial; speed; symmetric functions; threshold; threshold elements; unbounded fan-in/fan-out; VLSI technology

entry:
@Article{Siu:1995:TMP,
  author =       "Kai-Yeung Y. Siu and V. Roychowdhury and T. Kailath",
  title =        "Toward Massively Parallel Design of Multipliers",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "24",
  number =       "1",
  pages =        "86--93",
  month =        jan,
  year =         "1995",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1995.1008",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:56 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C4210 (Formal logic); C4240C (Computational
                 complexity); C5110 (Logic elements); C5120 (Logic and
                 switching circuits); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Electr. and Comput. Eng., California
                 University, Irvine, CA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "AND-OR circuits; arithmetic computation; asymptotic
                 time complexity; circuits; computation delays;
                 computational complexity; digital arithmetic; fan-in
                 threshold circuits; gates; hardware; logic; massively
                 parallel design; massively parallel high-speed
                 multipliers; multiplication; multipliers; multiplying;
                 parallel processing; parity; polynomial; speed;
                 symmetric functions; threshold; threshold elements;
                 unbounded fan-in/fan-out; VLSI technology",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Sleijpen:1995:MCP
author: Gerard L. G. Sleijpen and Henk A. van der Vorst
title: Maintaining convergence properties of BiCGstab methods in finite precision arithmetic
journal: j-NUMER-ALGORITHMS
volume: 10
number: 3--4
pages: 203--223
month: oct
monthnumber: 10
year: 1995
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65F10 (65Y20)
MRnumber: MR1355732 (96g:65037)
bibdate: Sat Dec 31 06:28:14 2005
bibtimestamp: 2005.12.31 06:28:14 ???
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Math. Inst., Utrecht University, Netherlands
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: G{\`e}rard L. G. Sleijpen and Henk A. van der Vorst
rawtitle: Maintaining convergence properties of {BiCGstab} methods in finite precision arithmetic
bibsource:
http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib; MathSciNet database

keywords:
Bi-CG coefficient accuracy; Bi-CG iteration coefficients; Bi-CG process; BiCGstab methods; computational complexity; conjugate gradient methods; convergence of numerical methods; convergence property maintenance; convergence speed; finite precision arithmetic; hybrid methods; matrix algebra; rounding errors; roundoff errors

entry:
@Article{Sleijpen:1995:MCP,
  author =       "G{\`e}rard L. G. Sleijpen and Henk A. van der Vorst",
  title =        "Maintaining convergence properties of {BiCGstab}
                 methods in finite precision arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "3--4",
  pages =        "203--223",
  month =        oct,
  year =         "1995",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F10 (65Y20)",
  MRnumber =     "MR1355732 (96g:65037)",
  bibdate =      "Sat Dec 31 06:28:14 2005",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290H (Linear algebra); C4130 (Interpolation and
                 function approximation); C4140 (Linear algebra); C4240C
                 (Computational complexity)",
  corpsource =   "Math. Inst., Utrecht University, Netherlands",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Bi-CG coefficient accuracy; Bi-CG iteration
                 coefficients; Bi-CG process; BiCGstab methods;
                 computational complexity; conjugate gradient methods;
                 convergence of numerical methods; convergence property
                 maintenance; convergence speed; finite precision
                 arithmetic; hybrid methods; matrix algebra; rounding
                 errors; roundoff errors",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Smith:1995:CFA
author: Roger Alan Smith
title: A Continued-Fraction Analysis of Trigonometric Argument Reduction
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 11
pages: 1348--1351
month: nov
monthnumber: 11
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.475133
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Dec 08 10:21:28 2006
bibtimestamp: 2006.12.08 10:21:28 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Roger Alan Smith
rawtitle: A Continued-Fraction Analysis of Trigonometric Argument Reduction
abstract:
The calculation of a trigonometric function of a large argument x is effectively carried out by finding the integer $N$ and $ 0 leq alpha < 1 $ such that $ x = (N + alpha ) pi / 4 $. This reduction modulo $ pi / 4 $ makes it possible to calculate a trigonometric function of a reduced argument, either $ alpha pi / 4 $ or $ (1 - alpha ) pi / 4 $, which lies in the interval $ (0, pi / 4) $. Payne and Hanek [1] described an efficient algorithm for computing $ alpha $ to a predetermined level of accuracy. They noted that if $x$ differs only slightly from an integral multiple $ pi / 2 $, the reduction must be carried out quite accurately to avoid loss of significance in the reduced argument. We present a simple method using continued fractions for determining, for all numbers $x$ for which the greatest number of insignificant leading bits occur. Applications are made IEEE single-precision and double-precision formats and two extended- precision formats.

keywords:
argument reduction; computer arithmetic; continued fractions; nonlinear optimization; Payne/Hanek radian reduction; range reduction; trigonometric functions

rawabstract:
The calculation of a trigonometric function of a large argument x is effectively carried out by finding the integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x = (N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4 $ makes it possible to calculate a trigonometric function of a reduced argument, either $ \alpha \pi / 4 $ or $ (1 - \alpha) \pi / 4 $, which lies in the interval $ (0, \pi / 4) $. Payne and Hanek [1] described an efficient algorithm for computing $ \alpha $ to a predetermined level of accuracy. They noted that if $x$ differs only slightly from an integral multiple $ \pi / 2 $, the reduction must be carried out quite accurately to avoid loss of significance in the reduced argument. We present a simple method using continued fractions for determining, for all numbers $x$ for which the greatest number of insignificant leading bits occur. Applications are made IEEE single-precision and double-precision formats and two extended- precision formats.

entry:
@Article{Smith:1995:CFA,
  author =       "Roger Alan Smith",
  title =        "A Continued-Fraction Analysis of Trigonometric
                 Argument Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1348--1351",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475133",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Dec 08 10:21:28 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  abstract =     "The calculation of a trigonometric function of a large
                 argument x is effectively carried out by finding the
                 integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x =
                 (N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4
                 $ makes it possible to calculate a trigonometric
                 function of a reduced argument, either $ \alpha \pi / 4
                 $ or $ (1 - \alpha) \pi / 4 $, which lies in the
                 interval $ (0, \pi / 4) $. Payne and Hanek [1]
                 described an efficient algorithm for computing $ \alpha
                 $ to a predetermined level of accuracy. They noted that
                 if $x$ differs only slightly from an integral multiple
                 $ \pi / 2 $, the reduction must be carried out quite
                 accurately to avoid loss of significance in the reduced
                 argument. We present a simple method using continued
                 fractions for determining, for all numbers $x$ for
                 which the greatest number of insignificant leading bits
                 occur. Applications are made IEEE single-precision and
                 double-precision formats and two extended- precision
                 formats.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "argument reduction; computer arithmetic; continued
                 fractions; nonlinear optimization; Payne/Hanek radian
                 reduction; range reduction; trigonometric functions",
}


bibtype: article
filename: fparith.bib
label: Smith:1995:FTC
author: J. C. Smith and F. J. Taylor
title: A fault-tolerant CEQRNS processing element for linear systolic array DSP applications
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 9
pages: 1121--1130
month: sep
monthnumber: 9
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.464390
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:29 MDT 2011
bibtimestamp: 2011.07.06 08:01:29 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=464390
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. C. Smith and F. J. Taylor
rawtitle: A fault-tolerant {CEQRNS} processing element for linear systolic array {DSP} applications
entry:
@Article{Smith:1995:FTC,
  author =       "J. C. Smith and F. J. Taylor",
  title =        "A fault-tolerant {CEQRNS} processing element for
                 linear systolic array {DSP} applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "9",
  pages =        "1121--1130",
  month =        sep,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.464390",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=464390",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Soderquist:1995:APC
author: Peter Soderquist and Miriam Leeser
crossref: Knowles:1995:PSC
pages: 132--139
month: jul
monthnumber: 7
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf
keywords: ARITH-12
acknowledgement: ack-sfo
rawauthor: Peter Soderquist and Miriam Leeser
title:
An Area / Performance Comparison of Subtractive and Multiplicative Divide / Square Root Implementations

rawtitle:
An Area\slash Performance Comparison of Subtractive and Multiplicative Divide\slash Square Root Implementations

entry:
@InProceedings{Soderquist:1995:APC,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "An Area\slash Performance Comparison of Subtractive
                 and Multiplicative Divide\slash Square Root
                 Implementations",
  crossref =     "Knowles:1995:PSC",
  pages =        "132--139",
  month =        jul,
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: phdthesis
filename: fparith.bib
label: Song:1995:RCT
author: Gi-Yong Song
title: Robust checksum test in algorithm-based fault tolerance on 2-D processor arrays
type: Thesis (Ph.D.)
school: University of Southwestern Louisiana
address: Lafayette, LA, USA
pages: 95
year: 1995
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: Gi-Yong Song
rawtitle: Robust checksum test in algorithm-based fault tolerance on {2-D} processor arrays
keywords:
error-correcting codes (information theory); fault-tolerant computing; floating-point arithmetic; floating-point testing

entry:
@PhdThesis{Song:1995:RCT,
  author =       "Gi-Yong Song",
  title =        "Robust checksum test in algorithm-based fault
                 tolerance on {2-D} processor arrays",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Southwestern Louisiana",
  address =      "Lafayette, LA, USA",
  pages =        "95",
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "error-correcting codes (information theory);
                 fault-tolerant computing; floating-point arithmetic;
                 floating-point testing",
}


bibtype: article
filename: fparith.bib
label: Srinivas:1995:FRD
author: H. R. Srinivas and K. K. Parhi
title: A fast radix-4 division algorithm and its architecture
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 6
pages: 826--831
month: jun
monthnumber: 6
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.391179
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:28 MDT 2011
bibtimestamp: 2011.07.06 08:01:28 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=391179
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. R. Srinivas and K. K. Parhi
rawtitle: A fast radix-4 division algorithm and its architecture
entry:
@Article{Srinivas:1995:FRD,
  author =       "H. R. Srinivas and K. K. Parhi",
  title =        "A fast radix-4 division algorithm and its
                 architecture",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "6",
  pages =        "826--831",
  month =        jun,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.391179",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=391179",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: Suarez:1995:CAA
author: Elisardo Antelo Suarez
type: Tesis doctorales
school: Universidade de Santiago de Compostela
address: Santiago de Compostela, Spain
pages: ix + 210
year: 1995
ISBN: 84-8121-348-9 OR 8481213489
ISBN13: 978-84-8121-348-5 OR 9788481213485
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
keywords: 0544:Electrical engineering; Applied sciences; Electrical engineering
language: Spanish
acknowledgement: ack-nhfb
rawauthor: Elisardo Antelo Su{\'a}rez
title:
Algoritmos y arquitecturas CORDIC con aritmetica redundante para procesamiento de alta velocidad (Spanish) [CORDIC algorithms and architectures with redundant arithmetic for high-speed processing]

URL:
https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/cordic-algorithms-architectures-with-redundant/docview/304224973/se-2

rawtitle:
Algoritmos y arquitecturas {CORDIC} con aritm{\'e}tica redundante para procesamiento de alta velocidad ({Spanish}) [{CORDIC} algorithms and architectures with redundant arithmetic for high-speed processing]

entry:
@PhdThesis{Suarez:1995:CAA,
  author =       "Elisardo Antelo Su{\'a}rez",
  title =        "Algoritmos y arquitecturas {CORDIC} con aritm{\'e}tica
                 redundante para procesamiento de alta velocidad
                 ({Spanish}) [{CORDIC} algorithms and architectures with
                 redundant arithmetic for high-speed processing]",
  type =         "Tesis doctorales",
  school =       "Universidade de Santiago de Compostela",
  address =      "Santiago de Compostela, Spain",
  pages =        "ix + 210",
  year =         "1995",
  ISBN =         "84-8121-348-9",
  ISBN-13 =      "978-84-8121-348-5",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/cordic-algorithms-architectures-with-redundant/docview/304224973/se-2",
  acknowledgement = ack-nhfb,
  keywords =     "0544:Electrical engineering; Applied sciences;
                 Electrical engineering",
  language =     "Spanish",
  ris-m1 =       "C519384",
}


bibtype: article
filename: fparith.bib
label: Tatsaki:1995:ICB
author: A. Tatsaki and T. Stouraitis and C. Goutis
title: Image coder based on residue number system for progressive transmission
journal: j-ELECT-LETTERS
volume: 31
number: 6
pages: 442--443
month: mar
monthnumber: 3
year: 1995
CODEN: ELLEAK
DOI: https://doi.org/10.1109/12.403714
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8573
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: A. Tatsaki and T. Stouraitis and C. Goutis
rawtitle: Image coder based on residue number system for progressive transmission
entry:
@Article{Tatsaki:1995:ICB,
  author =       "A. Tatsaki and T. Stouraitis and C. Goutis",
  title =        "Image coder based on residue number system for
                 progressive transmission",
  journal =      j-ELECT-LETTERS,
  volume =       "31",
  number =       "6",
  pages =        "442--443",
  month =        mar,
  year =         "1995",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1109/12.403714",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8573",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A computationally efficient algorithm for image
                 compression and progressive transmission is presented.
                 A prime-factor discrete cosine transform (DCT) is
                 applied, where the coefficients are computed in three
                 groups and are residue represented by a \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Thimbleby:1995:NCW
author: Harold Thimbleby
title: A New Calculator and Why it is Necessary
journal: j-COMP-J
volume: 38
number: 6
pages: 418--433
year: 1995
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/38.6.418
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:48:45 MST 2012
bibtimestamp: 2012.12.04 14:48:45 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
classcodes: C5430 (Microcomputers); C6180 (User interfaces)
corpsource: Department of Computer Science, Middlesex University, London, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: Harold Thimbleby
rawtitle: A New Calculator and Why it is Necessary
bibsource:
http://comjnl.oxfordjournals.org/content/38/6.toc; http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.index.html; https://www.math.utah.edu/pub/tex/bib/compj1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/38/6/418.full.pdf+html; http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.body.html#AbstractThimbleby

keywords:
conventional calculators; declarative design; declarative system; design issues; electronic calculators; interactive system; user interfaces

entry:
@Article{Thimbleby:1995:NCW,
  author =       "Harold Thimbleby",
  title =        "A New Calculator and Why it is Necessary",
  journal =      j-COMP-J,
  volume =       "38",
  number =       "6",
  pages =        "418--433",
  month =        "????",
  year =         "1995",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/38.6.418",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:45 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/38/6.toc;
                 http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.index.html;
                 https://www.math.utah.edu/pub/tex/bib/compj1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/38/6/418.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.body.html#AbstractThimbleby",
  acknowledgement = ack-nhfb,
  classcodes =   "C5430 (Microcomputers); C6180 (User interfaces)",
  corpsource =   "Department of Computer Science, Middlesex University,
                 London, UK",
  email-1 =      "haro1d@mdx.ac.UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "conventional calculators; declarative design;
                 declarative system; design issues; electronic
                 calculators; interactive system; user interfaces",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Thomas:1995:IFC
author: Jim Thomas and Jerome T. Coonen
title: An Introduction to Floating-Point C Extensions
journal: j-CCCUJ
volume: 13
number: 1
pages: 49--??
month: jan
monthnumber: 1
year: 1995
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Fri Aug 30 16:52:23 MDT 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.30 16:52:23 MDT
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: Jim Thomas and Jerome T. Coonen
rawtitle: An Introduction to Floating-Point {C} Extensions
entry:
@Article{Thomas:1995:IFC,
  author =       "Jim Thomas and Jerome T. Coonen",
  title =        "An Introduction to Floating-Point {C} Extensions",
  journal =      j-CCCUJ,
  volume =       "13",
  number =       "1",
  pages =        "49--??",
  month =        jan,
  year =         "1995",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: inproceedings
filename: fparith.bib
label: Tsuji:1995:ASF
author: K. Tsuji
title: An Algorithm for Sum of Floating-Point Numbers without Round-Off Error
crossref: Bainov:1995:PTI
pages: 181--190
year: 1995
bibdate: Sat Jun 02 08:14:13 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 08:14:13 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: K. Tsuji
rawtitle: An Algorithm for Sum of Floating-Point Numbers without Round-Off Error
entry:
@InProceedings{Tsuji:1995:ASF,
  author =       "K. Tsuji",
  title =        "An Algorithm for Sum of Floating-Point Numbers without
                 Round-Off Error",
  crossref =     "Bainov:1995:PTI",
  pages =        "181--190",
  year =         "1995",
  bibdate =      "Sat Jun 02 08:14:13 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: techreport
filename: fparith.bib
label: Turner:1995:PSI
author: P. R. Turner Daniel W. Lozier
title: Parallel and Serial Implementations of SLI Arithmetic
type: Internal report
number: NISTIT-5660
institution: National Institute of Standards and Technology
address: Gaithersburg, MD, USA
pages: 181--190
day: 1
month: jun
monthnumber: 6
year: 1995
bibdate: Tue Nov 05 15:29:02 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.11.05 15:29:02 ???
acknowledgement: ack-nhfb
rawauthor: P. R. Turner Daniel W. Lozier
rawtitle: Parallel and Serial Implementations of {SLI} Arithmetic
entry:
@TechReport{Turner:1995:PSI,
  author =       "P. R. Turner Daniel W. Lozier",
  title =        "Parallel and Serial Implementations of {SLI}
                 Arithmetic",
  type =         "Internal report",
  number =       "NISTIT-5660",
  institution =  "National Institute of Standards and Technology",
  address =      "Gaithersburg, MD, USA",
  day =          "1",
  month =        jun,
  year =         "1995",
  bibdate =      "Tue Nov 05 15:29:02 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Ueda:1995:DMA
author: T. Ueda
title: Decimal Multiplying Assembly and Multiply Module
pages: 181--190
month: jan
monthnumber: 1
year: 1995
bibdate: Fri Jun 24 20:43:45 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:43:45 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
howpublished: U.S. Patent number 5,379,245.
rawauthor: T. Ueda
rawtitle: Decimal Multiplying Assembly and Multiply Module
entry:
@Misc{Ueda:1995:DMA,
  author =       "T. Ueda",
  title =        "Decimal Multiplying Assembly and Multiply Module",
  howpublished = "U.S. Patent number 5,379,245.",
  month =        jan,
  year =         "1995",
  bibdate =      "Fri Jun 24 20:43:45 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: VanDrunen:1995:ARA
author: R. VanDrunen and L. Spaanenburg and P. Lucassen and J. A. G. Nijhuis
title: Arithmetic for Relative Accuracy
crossref: Knowles:1995:PSC
pages: 208--209, 239--250
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_vanDrunen.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: R. VanDrunen and L. Spaanenburg and P. Lucassen and J. A. G. Nijhuis
rawtitle: Arithmetic for Relative Accuracy
entry:
@InProceedings{VanDrunen:1995:ARA,
  author =       "R. VanDrunen and L. Spaanenburg and P. Lucassen and J.
                 A. G. Nijhuis",
  title =        "Arithmetic for Relative Accuracy",
  crossref =     "Knowles:1995:PSC",
  pages =        "208--209, 239--250",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_vanDrunen.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Vinnakota:1995:IMS
author: B. Vinnakota
title: Implementing multiplication with split read-only memory
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 11
pages: 1352--1356
month: nov
monthnumber: 11
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.475134
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:30 MDT 2011
bibtimestamp: 2011.07.06 08:01:30 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475134
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. Vinnakota
rawtitle: Implementing multiplication with split read-only memory
entry:
@Article{Vinnakota:1995:IMS,
  author =       "B. Vinnakota",
  title =        "Implementing multiplication with split read-only
                 memory",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1352--1356",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475134",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475134",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Wang:1995:NDT
author: Zhongde Wang and G. A. Jullien and W. C. Miller
title: A new design technique for column compression multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 8
pages: 962--970
month: aug
monthnumber: 8
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.403712
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 08:01:29 MDT 2011
bibtimestamp: 2011.07.06 08:01:29 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403712
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Zhongde Wang and G. A. Jullien and W. C. Miller
rawtitle: A new design technique for column compression multipliers
entry:
@Article{Wang:1995:NDT,
  author =       "Zhongde Wang and G. A. Jullien and W. C. Miller",
  title =        "A new design technique for column compression
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "8",
  pages =        "962--970",
  month =        aug,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.403712",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403712",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Wei:1995:CNM
author: Belle W. Y. Wei and He Du and Honglu Chen
title: A Complex-Number Multiplier Using Radix-$4$ Digits
crossref: Knowles:1995:PSC
pages: 84--90
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Wei.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Belle W. Y. Wei and He Du and Honglu Chen
rawtitle: A Complex-Number Multiplier Using Radix-$4$ Digits
entry:
@InProceedings{Wei:1995:CNM,
  author =       "Belle W. Y. Wei and He Du and Honglu Chen",
  title =        "A Complex-Number Multiplier Using Radix-$4$ Digits",
  crossref =     "Knowles:1995:PSC",
  pages =        "84--90",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Wei.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: article
filename: fparith.bib
label: Williams:1995:SBA
author: T. Williams and N. Patkar and G. Shen
title: SPARC64: a 64-b 64-active-instruction out-of-order-execution MCM processor
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 30
number: 11
pages: 1215--1226
month: nov
monthnumber: 11
year: 1995
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
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 ???
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-sfo
rawauthor: T. Williams and N. Patkar and G. Shen
rawtitle: {SPARC64}: a 64-b 64-active-instruction out-of-order-execution {MCM} processor
entry:
@Article{Williams:1995:SBA,
  author =       "T. Williams and N. Patkar and G. Shen",
  title =        "{SPARC64}: a 64-b 64-active-instruction
                 out-of-order-execution {MCM} processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "11",
  pages =        "1215--1226",
  month =        nov,
  year =         "1995",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}


bibtype: article
filename: fparith.bib
label: Wong:1995:FEE
author: W. F. Wong and E. Goto
title: Fast evaluation of the elementary functions in single precision
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 3
pages: 453--457
month: mar
monthnumber: 3
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.372037
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Dec 14 11:25:18 MST 1995
bibtimestamp: 1995.12.14 11:25:18 MST
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Department of Inf. Syst. and Computer Science, Nat. University of Singapore, Singapore
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Error analysis; Floating point arithmetic
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast evaluation of the elementary functions in single precision
abstract:
In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies.

keywords:
Adders; Difference method; Elementary functions; Fast evaluation; Floating point multiplies; Inverse trigonometric functions; Logarithm functions; Reciprocal; Single precision; Square root; Truncated Taylor series

rawabstract:
In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies.

entry:
@Article{Wong:1995:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in single
                 precision",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "3",
  pages =        "453--457",
  month =        mar,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.372037",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  abstract =     "In this paper we introduce a new method for the fast
                 evaluation of the elementary functions in single
                 precision based on the evaluation of truncated Taylor
                 series using a difference method. We assume the
                 availability of large and fast (at least for read
                 purposes) memory. We call this method the ATA
                 (Add-Table lookup-Add) method. As the name implies, the
                 hardware required for the method are adders (both two/
                 and multi/operand adders) and fast tables. For IEEE
                 single precision numbers our initial estimates indicate
                 that we can calculate the basic elementary functions,
                 namely reciprocal, square root, logarithm, exponential,
                 trigonometric and inverse trigonometric functions,
                 within the latency of two to four floating point
                 multiplies.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Inf. Syst. and Computer Science, Nat.
                 University of Singapore, Singapore",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Difference method; Elementary functions; Fast
                 evaluation; Floating point multiplies; Inverse
                 trigonometric functions; Logarithm functions;
                 Reciprocal; Single precision; Square root; Truncated
                 Taylor series",
  thesaurus =    "Error analysis; Floating point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Wu:1995:SRM
author: Youfeng Wu
title: Strength Reduction of Multiplications by Integer Constants
journal: j-SIGPLAN
volume: 30
number: 2
pages: 42--48
month: feb
monthnumber: 2
year: 1995
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 09:17:00 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:17:00 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Youfeng Wu
rawtitle: Strength Reduction of Multiplications by Integer Constants
entry:
@Article{Wu:1995:SRM,
  author =       "Youfeng Wu",
  title =        "Strength Reduction of Multiplications by Integer
                 Constants",
  journal =      j-SIGPLAN,
  volume =       "30",
  number =       "2",
  pages =        "42--48",
  month =        feb,
  year =         "1995",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:00 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: article
filename: fparith.bib
label: Ypma:1995:HDN
author: Tjalling J. Ypma
title: Historical Development of the Newton--Raphson Method
journal: j-SIAM-REVIEW
volume: 37
number: 4
pages: 531--551
month: dec
monthnumber: 12
year: 1995
CODEN: SIREAD
DOI: https://doi.org/10.1137/1037125
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 01A05 (65-03)
MRnumber: 97b:01003
MRreviewer: M. Z. Nashed
bibdate: Sat Mar 29 09:55:35 MDT 2014
bibtimestamp: 2014.03.29 09:55:35 MDT
URL: http://epubs.siam.org/23425.htm; http://link.aip.org/link/?SIR/37/531/1
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliation: Western Washington Univ
affiliationaddress: Bellingham, WA, USA
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: December 1995
rawauthor: Tjalling J. Ypma
rawtitle: Historical Development of the {Newton--Raphson} Method
bibsource:
Compendex database; http://epubs.siam.org/toc/siread/37/4; http://www.siam.org/journals/sirev/sirev374.htm; 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/siamreview.bib

abstract:
This expository paper traces the development of the Newton--Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.

keywords:
Algebra; Algorithms; Approximation theory; Differentiation (calculus); Finite difference method; Fluxional calculus; Isaac Newton; Iterative methods; Joseph Raphson; Linearization; Newton--Raphson method; Nonlinear algebraic equations; Nonlinear equations; Nonpolynomial equation; Polynomials; Secant method; Thomas Simpson

rawabstract:
This expository paper traces the development of the Newton--Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.

entry:
@Article{Ypma:1995:HDN,
  author =       "Tjalling J. Ypma",
  title =        "Historical Development of the {Newton--Raphson}
                 Method",
  journal =      j-SIAM-REVIEW,
  volume =       "37",
  number =       "4",
  pages =        "531--551",
  month =        dec,
  year =         "1995",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1037125",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "01A05 (65-03)",
  MRnumber =     "97b:01003",
  MRreviewer =   "M. Z. Nashed",
  bibdate =      "Sat Mar 29 09:55:35 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/37/4;
                 http://www.siam.org/journals/sirev/sirev374.htm;
                 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/siamreview.bib",
  URL =          "http://epubs.siam.org/23425.htm;
                 http://link.aip.org/link/?SIR/37/531/1",
  abstract =     "This expository paper traces the development of the
                 Newton--Raphson method for solving nonlinear algebraic
                 equations through the extant notes, letters, and
                 publications of Isaac Newton, Joseph Raphson, and
                 Thomas Simpson. It is shown how Newton's formulation
                 differed from the iterative process of Raphson, and
                 that Simpson was the first to give a general
                 formulation, in terms of fluxional calculus, applicable
                 to nonpolynomial equations. Simpson's extension of the
                 method to systems of equations is exhibited.",
  acknowledgement = ack-nhfb,
  affiliation =  "Western Washington Univ",
  affiliationaddress = "Bellingham, WA, USA",
  classification = "921.1; 921.2; 921.6",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algebra; Algorithms; Approximation theory;
                 Differentiation (calculus); Finite difference method;
                 Fluxional calculus; Isaac Newton; Iterative methods;
                 Joseph Raphson; Linearization; Newton--Raphson method;
                 Nonlinear algebraic equations; Nonlinear equations;
                 Nonpolynomial equation; Polynomials; Secant method;
                 Thomas Simpson",
  onlinedate =   "December 1995",
}


bibtype: inproceedings
filename: fparith.bib
label: Yu:1995:MRF
author: Robert K. Yu and Gregory B. Zyner
title: 167 MHz Radix-$4$ Floating Point Multiplier
crossref: Knowles:1995:PSC
pages: 149--154
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Yu.pdf
keywords: ARITH-12; UltraSPARC
acknowledgement: ack-nhfb
rawauthor: Robert K. Yu and Gregory B. Zyner
rawtitle: {167 MHz} Radix-$4$ Floating Point Multiplier
entry:
@InProceedings{Yu:1995:MRF,
  author =       "Robert K. Yu and Gregory B. Zyner",
  title =        "{167 MHz} Radix-$4$ Floating Point Multiplier",
  crossref =     "Knowles:1995:PSC",
  pages =        "149--154",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Yu.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12; UltraSPARC",
}


bibtype: article
filename: fparith.bib
label: Zaytoun:1995:SFR
author: M. M. Zaytoun and T. J. Owens
title: State feedback robust to rounding errors
journal: j-ELECT-LETTERS
volume: 31
number: 13
pages: 1108--1109
day: 22
month: jun
monthnumber: 6
year: 1995
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
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: Electronics Letters
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: M. M. Zaytoun and T. J. Owens
rawtitle: State feedback robust to rounding errors
entry:
@Article{Zaytoun:1995:SFR,
  author =       "M. M. Zaytoun and T. J. Owens",
  title =        "State feedback robust to rounding errors",
  journal =      j-ELECT-LETTERS,
  volume =       "31",
  number =       "13",
  pages =        "1108--1109",
  day =          "22",
  month =        jun,
  year =         "1995",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "An algorithm for delivering a state feedback
                 controller that assigns desired distinct closed-loop
                 eigenvalues to the closed-loop system and is robust to
                 rounding errors in the elements of the controller is
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Zhou:1995:HSD
author: Feng Zhou and Peter Kornerup
title: High Speed DCT / IDCT Using a Pipelined CORDIC Algorithm
crossref: Knowles:1995:PSC
pages: 180--187
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Feng.pdf
keywords: ARITH-12
acknowledgement: ack-nhfb
rawauthor: Feng Zhou and Peter Kornerup
rawtitle: High Speed {DCT}\slash {IDCT} Using a Pipelined {CORDIC} Algorithm
bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database

entry:
@InProceedings{Zhou:1995:HSD,
  author =       "Feng Zhou and Peter Kornerup",
  title =        "High Speed {DCT}\slash {IDCT} Using a Pipelined
                 {CORDIC} Algorithm",
  crossref =     "Knowles:1995:PSC",
  pages =        "180--187",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Feng.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: inproceedings
filename: fparith.bib
label: Ahrendt:1996:FHC
author: Timm Ahrendt
title: Fast High-Precision Computations of Complex Square Roots
crossref: LakshmanYN:1996:IPI
pages: 142--149
year: 1996
bibdate: Thu Mar 12 08:43:16 MST 1998
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.03.12 08:43:16 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/
keywords: algebraic computation; algorithms; ISSAC; measurement; SIGNUM; SIGSAM; symbolic computation
acknowledgement: ack-nhfb
rawauthor: Timm Ahrendt
rawtitle: Fast High-Precision Computations of Complex Square Roots
subject:
bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf F.1.1 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Models of Computation, Bounded-action devices. bf G.1.5 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. bf G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.

entry:
@InProceedings{Ahrendt:1996:FHC,
  author =       "Timm Ahrendt",
  title =        "Fast High-Precision Computations of Complex Square
                 Roots",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "142--149",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Bounded-action devices.
                 {\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  xxtitle =      "Fast high-precision computation of complex square
                 roots",
}


bibtype: techreport
filename: fparith.bib
label: Al-Twaijry:1996:OPR
author: H. Al-Twaijry and M. J. Flynn
title: Optimum placement and routing of multiplier partial product trees
type: Technical report
number: CSL-TR-96-706
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 142--149
month: sep
monthnumber: 9
year: 1996
bibdate: Mon Dec 24 10:13:01 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.24 10:13:01 ???
acknowledgement: ack-nhfb
rawauthor: H. Al-Twaijry and M. J. Flynn
rawtitle: Optimum placement and routing of multiplier partial product trees
entry:
@TechReport{Al-Twaijry:1996:OPR,
  author =       "H. Al-Twaijry and M. J. Flynn",
  title =        "Optimum placement and routing of multiplier partial
                 product trees",
  type =         "Technical report",
  number =       "CSL-TR-96-706",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        sep,
  year =         "1996",
  bibdate =      "Mon Dec 24 10:13:01 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Alefeld:1996:EII
author: G. E. Alefeld and F. A. Potra and W. Voelker
title: Effective Improvements of the Internal-Newton-Method
crossref: Alefeld:1996:SCV
pages: 133--139
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. E. Alefeld and F. A. Potra and W. Voelker
rawtitle: Effective Improvements of the Internal-{Newton}-Method
entry:
@InProceedings{Alefeld:1996:EII,
  author =       "G. E. Alefeld and F. A. Potra and W. Voelker",
  title =        "Effective Improvements of the
                 Internal-{Newton}-Method",
  crossref =     "Alefeld:1996:SCV",
  pages =        "133--139",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Andraos:1996:FPU
author: S. Andraos
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
title: Fixed point unsigned fractional representation in residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 555--558
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594239
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. Andraos
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
rawtitle: Fixed point unsigned fractional representation in residue number system
entry:
@InProceedings{Andraos:1996:FPU,
  author =       "S. Andraos",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "Fixed point unsigned fractional representation in
                 residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "555--558",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594239",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Representing fractions is one of the fundamental
                 problems in the Residue Number System (RNS) which is
                 considered an integer number system with no fractional
                 representation. This is one of its main drawbacks and
                 one of the main obstacles in its \ldots{}",
}


bibtype: mastersthesis
filename: fparith.bib
label: Angarai:1996:NRS
author: Vijayanand Jaganaathan Angarai
title: Number representation schemes for energy efficient computer arithmetic
type: Thesis (M.S.)
school: University of Texas at Dallas
address: Dallas, TX, USA
pages: ix + 57
year: 1996
bibdate: Mon Mar 05 14:32:21 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.05 14:32:21 ???
acknowledgement: ack-nhfb
rawauthor: Vijayanand Jaganaathan Angarai
rawtitle: Number representation schemes for energy efficient computer arithmetic
entry:
@MastersThesis{Angarai:1996:NRS,
  author =       "Vijayanand Jaganaathan Angarai",
  title =        "Number representation schemes for energy efficient
                 computer arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Texas at Dallas",
  address =      "Dallas, TX, USA",
  pages =        "ix + 57",
  year =         "1996",
  bibdate =      "Mon Mar 05 14:32:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Anonymous:1996:DC
author: Anonymous
editor: Barry Cipra and Paul Zorn
booktitle: What's Happening in the Mathematical Sciences
title: Divide and Conquer
volume: 3
publisher: pub-AMS
address: pub-AMS:adr
pages: 39--47
year: 1996
ISBN: 0-8218-0355-7 (paperback) OR 0821803557 (paperback)
ISBN13: 978-0-8218-0355-4 (paperback) OR 9780821803554 (paperback)
LCCN: QA3 .C57 1996
bibdate: Thu Dec 08 16:31:52 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2016.12.08 16:31:52 ???
URL: http://www.ams.org/samplings/math-history/divide.pdf
keywords: Pentium divide flaw
acknowledgement: ack-nhfb
bookpages: vi + 111
rawauthor: Anonymous
rawbooktitle: What's Happening in the Mathematical Sciences
raweditor: Barry Cipra and Paul Zorn
rawtitle: Divide and Conquer
entry:
@InCollection{Anonymous:1996:DC,
  author =       "Anonymous",
  editor =       "Barry Cipra and Paul Zorn",
  booktitle =    "What's Happening in the Mathematical Sciences",
  title =        "Divide and Conquer",
  volume =       "3",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  bookpages =    "vi + 111",
  pages =        "39--47",
  year =         "1996",
  ISBN =         "0-8218-0355-7 (paperback)",
  ISBN-13 =      "978-0-8218-0355-4 (paperback)",
  LCCN =         "QA3 .C57 1996",
  bibdate =      "Thu Dec 08 16:31:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/samplings/math-history/divide.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Pentium divide flaw",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1996:FPF
author: Anonymous
title: Floating Point --- Finding Electronic / Mechanical Parts
journal: j-COMPUT-AIDED-ENG
volume: 15
number: 1
pages: 76--??
year: 1996
CODEN: CCAEDJ
ISSN: 0733-3536 (print), 2162-1365 (electronic) OR 07333536 (print), 21621365 (electronic)
ISSNL: 0733-3536 OR 07333536
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
fjournal: Computer-aided engineering: CAE
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Floating Point --- Finding Electronic\slash Mechanical Parts
entry:
@Article{Anonymous:1996:FPF,
  author =       "Anonymous",
  title =        "Floating Point --- Finding Electronic\slash Mechanical
                 Parts",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "15",
  number =       "1",
  pages =        "76--??",
  year =         "1996",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1996:IBT
author: Anonymous
title: Inquiry Board Traces Ariane 5 Failure to Overflow Error
journal: j-SIAM-NEWS
volume: 29
number: 8
pages: 1, 12, 13
month: oct
monthnumber: 10
year: 1996
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Sat Apr 28 18:48:53 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:48:53 ???
URL: http://www.siam.org/siamnews/general/ariane.htm
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: https://sinews.siam.org/
rawauthor: Anonymous
rawtitle: Inquiry Board Traces {Ariane 5} Failure to Overflow Error
entry:
@Article{Anonymous:1996:IBT,
  author =       "Anonymous",
  title =        "Inquiry Board Traces {Ariane 5} Failure to Overflow
                 Error",
  journal =      j-SIAM-NEWS,
  volume =       "29",
  number =       "8",
  pages =        "1, 12, 13",
  month =        oct,
  year =         "1996",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Apr 28 18:48:53 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.siam.org/siamnews/general/ariane.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROa
author: Anonymous
title: The Square Root of 3 to one million digits
volume: 628
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/3sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 3 to one million digits
entry:
@Book{Anonymous:1996:SROa,
  author =       "Anonymous",
  title =        "The Square Root of 3 to one million digits",
  volume =       "628",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/3sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROb
author: Anonymous
title: The Square Root of 5 to one million digits
volume: 629
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/5sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 5 to one million digits
entry:
@Book{Anonymous:1996:SROb,
  author =       "Anonymous",
  title =        "The Square Root of 5 to one million digits",
  volume =       "629",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/5sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROc
author: Anonymous
title: The Square Root of 6 to one million digits
volume: 630
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/6sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 6 to one million digits
entry:
@Book{Anonymous:1996:SROc,
  author =       "Anonymous",
  title =        "The Square Root of 6 to one million digits",
  volume =       "630",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/6sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROd
author: Anonymous
title: The Square Root of 7 to one million digits
volume: 631
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/7sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 7 to one million digits
entry:
@Book{Anonymous:1996:SROd,
  author =       "Anonymous",
  title =        "The Square Root of 7 to one million digits",
  volume =       "631",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/7sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROe
author: Anonymous
title: The Square Root of 8 to one million digits
volume: 632
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/8sqrt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 8 to one million digits
entry:
@Book{Anonymous:1996:SROe,
  author =       "Anonymous",
  title =        "The Square Root of 8 to one million digits",
  volume =       "632",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/8sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: book
filename: fparith.bib
label: Anonymous:1996:SROf
author: Anonymous
title: The Square Root of 10 to one million digits
volume: 635
publisher: pub-PROJECT-GUTENBERG
address: pub-PROJECT-GUTENBERG:adr
pages: 1, 12, 13
year: 1996
bibdate: Sun Jan 24 10:00:27 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1999.01.24 10:00:27 MST
series: ser-PROJECT-GUTENBERG
URL: ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/10srt10.zip
subject: Mathematical constants.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: The Square Root of 10 to one million digits
entry:
@Book{Anonymous:1996:SROf,
  author =       "Anonymous",
  title =        "The Square Root of 10 to one million digits",
  volume =       "635",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/10srt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}


bibtype: inbook
filename: fparith.bib
label: Antelo:1996:HRC
author: E. Antelo and J. D. Bruguera and T. Lang and J. Villalba and E. L. Zapata
booktitle: Euro-Par 96 Parallel Processing
title: High radix CORDIC rotation based on selection by rounding
publisher: pub-SV
address: pub-SV:adr
pages: 155--164
year: 1996
DOI: https://doi.org/10.1007/bfb0024698
ISBN: 3-540-70636-4 OR 3540706364
ISBN13: 978-3-540-70636-6 OR 9783540706366
ISSN: 1611-3349 OR 16113349
bibdate: Tue Oct 28 07:04:09 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.28 07:04:09 ???
acknowledgement: ack-nhfb
rawauthor: E. Antelo and J. D. Bruguera and T. Lang and J. Villalba and E. L. Zapata
rawbooktitle: Euro-Par 96 Parallel Processing
rawtitle: High radix {CORDIC} rotation based on selection by rounding
entry:
@InBook{Antelo:1996:HRC,
  author =       "E. Antelo and J. D. Bruguera and T. Lang and J.
                 Villalba and E. L. Zapata",
  booktitle =    "Euro-Par 96 Parallel Processing",
  title =        "High radix {CORDIC} rotation based on selection by
                 rounding",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "155--164",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/bfb0024698",
  ISBN =         "3-540-70636-4",
  ISBN-13 =      "978-3-540-70636-6",
  ISSN =         "1611-3349",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Anuta:1996:BLA
author: M. A. Anuta and Daniel W. Lozier and N. Schabanel and P. R. Turner
title: Basic Linear Algebra Operations in SLI Arithmetic
crossref: Bouge:1996:EPP
pages: 193--202
year: 1996
DOI: https://doi.org/10.1007/BFb0024702
bibdate: Fri Jul 09 07:17:24 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.07.09 07:17:24 ???
acknowledgement: ack-nhfb
rawauthor: M. A. Anuta and Daniel W. Lozier and N. Schabanel and P. R. Turner
rawtitle: Basic Linear Algebra Operations in {SLI} Arithmetic
URL:
http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5811.ps.Z; https://www.nist.gov/publications/basic-linear-algebra-operations-sli-arithmetic

entry:
@InProceedings{Anuta:1996:BLA,
  author =       "M. A. Anuta and Daniel W. Lozier and N. Schabanel and
                 P. R. Turner",
  title =        "Basic Linear Algebra Operations in {SLI} Arithmetic",
  crossref =     "Bouge:1996:EPP",
  pages =        "193--202",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/BFb0024702",
  bibdate =      "Fri Jul 09 07:17:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5811.ps.Z;
                 https://www.nist.gov/publications/basic-linear-algebra-operations-sli-arithmetic",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Anuta:1996:MMC
author: M. A. Anuta and Daniel W. Lozier and P. R. Turner
title: The MasPar MP-1 as a Computer Arithmetic Laboratory
journal: j-J-RES-NATL-BUR-STAND
volume: 101
number: 2
pages: 165--174
month: mar
monthnumber: 3
year: 1996
CODEN: JRNBAG
DOI: https://doi.org/10.6028/jres.101.018
ISSN: 0091-0635 (print), 2376-5305 (electronic) OR 00910635 (print), 23765305 (electronic)
ISSNL: 0091-0635 OR 00910635
bibdate: Fri Jul 09 07:18:42 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.07.09 07:18:42 ???
URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4907584/
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: M. A. Anuta and Daniel W. Lozier and P. R. Turner
rawtitle: The {MasPar MP-1} as a Computer Arithmetic Laboratory
abstract:
This paper is a blueprint for the use of a massively parallel SIMD computer architecture for the simulation of various forms of computer arithmetic. The particular system used is a DEC/MasPar MP-1 with 4096 processors in a square array. This architecture has many advantages for such simulations due largely to the simplicity of the individual processors. Arithmetic operations can be spread across the processor array to simulate a hardware chip. Alternatively they may be performed on individual processors to allow simulation of a massively parallel implementation of the arithmetic. Compromises between these extremes permit speed-area tradeoffs to be examined. The paper includes a description of the architecture and its features. It then summarizes some of the arithmetic systems which have been, or are to be, implemented. The implementation of the level-index and symmetric level-index, LI and SLI, systems is described in some detail. An extensive bibliography is included.

keywords:
computer arithmetic, fixed-point and floating-point arithmetic, logarithmic and level-index arithmetic, residue number system arithmetic, serial and parallel simulation of computer arithmetic

rawabstract:
This paper is a blueprint for the use of a massively parallel SIMD computer architecture for the simulation of various forms of computer arithmetic. The particular system used is a DEC/MasPar MP-1 with 4096 processors in a square array. This architecture has many advantages for such simulations due largely to the simplicity of the individual processors. Arithmetic operations can be spread across the processor array to simulate a hardware chip. Alternatively they may be performed on individual processors to allow simulation of a massively parallel implementation of the arithmetic. Compromises between these extremes permit speed-area tradeoffs to be examined. The paper includes a description of the architecture and its features. It then summarizes some of the arithmetic systems which have been, or are to be, implemented. The implementation of the level-index and symmetric level-index, LI and SLI, systems is described in some detail. An extensive bibliography is included.

entry:
@Article{Anuta:1996:MMC,
  author =       "M. A. Anuta and Daniel W. Lozier and P. R. Turner",
  title =        "The {MasPar MP-1} as a Computer Arithmetic
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  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "101",
  number =       "2",
  pages =        "165--174",
  month =        mar # "\slash " # apr,
  year =         "1996",
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  DOI =          "https://doi.org/10.6028/jres.101.018",
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  ISSN-L =       "0091-0635",
  bibdate =      "Fri Jul 09 07:18:42 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4907584/",
  abstract =     "This paper is a blueprint for the use of a massively
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                 advantages for such simulations due largely to the
                 simplicity of the individual processors. Arithmetic
                 operations can be spread across the processor array to
                 simulate a hardware chip. Alternatively they may be
                 performed on individual processors to allow simulation
                 of a massively parallel implementation of the
                 arithmetic. Compromises between these extremes permit
                 speed-area tradeoffs to be examined. The paper includes
                 a description of the architecture and its features. It
                 then summarizes some of the arithmetic systems which
                 have been, or are to be, implemented. The
                 implementation of the level-index and symmetric
                 level-index, LI and SLI, systems is described in some
                 detail. An extensive bibliography is included.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  keywords =     "computer arithmetic, fixed-point and floating-point
                 arithmetic, logarithmic and level-index arithmetic,
                 residue number system arithmetic, serial and parallel
                 simulation of computer arithmetic",
}


bibtype: article
filename: fparith.bib
label: Arioli:1996:REA
author: M. Arioli and C. Fassino
title: Roundoff error analysis of algorithms based on Krylov subspace methods
journal: j-BIT-NUM-MATH
volume: 36
number: 2
pages: 189--205
month: jun
monthnumber: 6
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01731978
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65F10 (15A23 65G05)
MRnumber: 98e:65018
MRreviewer: Jean-Marie Chesneaux
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: M. Arioli and C. Fassino
rawtitle: Roundoff error analysis of algorithms based on {Krylov} subspace methods
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=189

entry:
@Article{Arioli:1996:REA,
  author =       "M. Arioli and C. Fassino",
  title =        "Roundoff error analysis of algorithms based on
                 {Krylov} subspace methods",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "189--205",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731978",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F10 (15A23 65G05)",
  MRnumber =     "98e:65018",
  MRreviewer =   "Jean-Marie Chesneaux",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=189",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: inproceedings
filename: fparith.bib
label: Bajard:1996:NED
author: J.-C. Bajard and L.-S. Didier and Jean-Michel Muller
title: A new Euclidean division algorithm for residue number systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 45--54
year: 1996
DOI: https://doi.org/10.1109/ASAP.1996.542800
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: J.-C. Bajard and L.-S. Didier and Jean-Michel Muller
rawtitle: A new {Euclidean} division algorithm for residue number systems
booktitle:
Proceedings of International Conference on Application Specific Systems, Architectures and Processors, 1996. ASAP 96

rawbooktitle:
Proceedings of International Conference on Application Specific Systems, Architectures and Processors, 1996. {ASAP 96}

entry:
@InProceedings{Bajard:1996:NED,
  author =       "J.-C. Bajard and L.-S. Didier and Jean-Michel Muller",
  booktitle =    "Proceedings of International Conference on Application
                 Specific Systems, Architectures and Processors, 1996.
                 {ASAP 96}",
  title =        "A new {Euclidean} division algorithm for residue
                 number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "45--54",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.1996.542800",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "We propose in this paper a new algorithm and
                 architecture for performing divisions in residue number
                 systems. Our algorithm is suitable for residue number
                 systems with large moduli, with the aim of manipulating
                 very large integers on a parallel \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Barber:1996:QAC
author: C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa
title: The Quickhull Algorithm for Convex Hulls
journal: j-TOMS
volume: 22
number: 4
pages: 469--483
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/235815.235821
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:36 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:36 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, reliability
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa
rawtitle: The {Quickhull Algorithm} for Convex Hulls
abstract:
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimensional Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of ``thick'' facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

subject:
bf I.3.5: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages and systems.

rawabstract:
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimensional Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of ``thick'' facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

entry:
@Article{Barber:1996:QAC,
  author =       "C. Bradford Barber and David P. Dobkin and Hannu
                 Huhdanpaa",
  title =        "The {Quickhull Algorithm} for Convex Hulls",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "469--483",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235821",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/",
  abstract =     "The convex hull of a set of points is the smallest
                 convex set that contains the points. This article
                 presents a practical convex hull algorithm that
                 combines the two-dimensional Quickhull Algorithm with
                 the general-dimensional Beneath-Beyond Algorithm. It is
                 similar to the randomized, incremental algorithms for
                 convex hull and Delaunay triangulation. We provide
                 empirical evidence that the algorithm runs faster when
                 the input contains nonextreme points and that it uses
                 less memory. Computational geometry algorithms have
                 traditionally assumed that input sets are well behaved.
                 When an algorithm is implemented with floating-point
                 arithmetic, this assumption can lead to serious errors.
                 We briefly describe a solution to this problem when
                 computing the convex hull in two, three, or four
                 dimensions. The output is a set of ``thick'' facets
                 that contain all possible exact convex hulls of the
                 input. A variation is effective in five or more
                 dimensions.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, reliability",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages and systems.",
}


bibtype: inproceedings
filename: fparith.bib
label: Berlejung:1996:PSM
author: H. M. E. Berlejung
title: Processing Software Metrics in an Integrated Development Environment for Pascal-XSC
crossref: Alefeld:1996:SCV
pages: 79--83
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: H. M. E. Berlejung
rawtitle: Processing Software Metrics in an Integrated Development Environment for {Pascal-XSC}
entry:
@InProceedings{Berlejung:1996:PSM,
  author =       "H. M. E. Berlejung",
  title =        "Processing Software Metrics in an Integrated
                 Development Environment for {Pascal-XSC}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "79--83",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Berner:1996:PMV
author: S. Berner
title: A Parallel Method for Verified Global Optimization
crossref: Alefeld:1996:SCV
pages: 200--206
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: S. Berner
rawtitle: A Parallel Method for Verified Global Optimization
entry:
@InProceedings{Berner:1996:PMV,
  author =       "S. Berner",
  title =        "A Parallel Method for Verified Global Optimization",
  crossref =     "Alefeld:1996:SCV",
  pages =        "200--206",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Blum:1996:RPD
author: Manuel Blum and H. Wasserman
title: Reflections on the Pentium Division Bug
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 4
pages: 385--393
month: apr
monthnumber: 4
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.494097
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:10 MDT 2011
bibtimestamp: 2011.07.06 19:47:10 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Manuel Blum and H. Wasserman
rawtitle: Reflections on the {Pentium} Division Bug
URL:
http://http.cs.berkeley.edu/~blum/pentium.ps; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=494097

abstract:
We review the field of em result-checking and suggest that it be extended to a methodology for enforcing hardware / software reliability. We thereby formulate a vision for ``self-monitoring'' hardware / software whose reliability is augmented through embedded suites of run-time correctness checkers. In particular, we suggest that embedded checkers and correctors may be employed to safeguard against arithmetic errors such as that which has bedeviled the Intel Pentium Microprocessor. We specify checkers and correctors suitable for monitoring the multiplication and division functionalities of an arbitrary arithmetic processor and seamlessly correcting erroneous output which may occur for any reason during the lifetime of the chip.

keywords:
Built-in testing; concurrent error detection; fault tolerance; Pentium; reliability; result-checking; verification

rawabstract:
We review the field of {\em result-checking\/} and suggest that it be extended to a methodology for enforcing hardware\slash software reliability. We thereby formulate a vision for ``self-monitoring'' hardware\slash software whose reliability is augmented through embedded suites of run-time correctness checkers. In particular, we suggest that embedded checkers and correctors may be employed to safeguard against arithmetic errors such as that which has bedeviled the Intel Pentium Microprocessor. We specify checkers and correctors suitable for monitoring the multiplication and division functionalities of an arbitrary arithmetic processor and seamlessly correcting erroneous output which may occur for any reason during the lifetime of the chip.

entry:
@Article{Blum:1996:RPD,
  author =       "Manuel Blum and H. Wasserman",
  title =        "Reflections on the {Pentium} Division Bug",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "4",
  pages =        "385--393",
  month =        apr,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.494097",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://http.cs.berkeley.edu/~blum/pentium.ps;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=494097",
  abstract =     "We review the field of {\em result-checking\/} and
                 suggest that it be extended to a methodology for
                 enforcing hardware\slash software reliability. We
                 thereby formulate a vision for ``self-monitoring''
                 hardware\slash software whose reliability is augmented
                 through embedded suites of run-time correctness
                 checkers. In particular, we suggest that embedded
                 checkers and correctors may be employed to safeguard
                 against arithmetic errors such as that which has
                 bedeviled the Intel Pentium Microprocessor. We specify
                 checkers and correctors suitable for monitoring the
                 multiplication and division functionalities of an
                 arbitrary arithmetic processor and seamlessly
                 correcting erroneous output which may occur for any
                 reason during the lifetime of the chip.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Built-in testing; concurrent error detection; fault
                 tolerance; Pentium; reliability; result-checking;
                 verification",
}


bibtype: article
filename: fparith.bib
label: Bockenfeld:1996:TNT
author: Don Bockenfeld
title: TSQRT: a New Trick for an Old Dog
journal: j-CCCUJ
volume: 14
number: 3
pages: 39--41
month: mar
monthnumber: 3
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Sat Feb 10 08:57:37 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.10 08:57:37 ???
note: Implements a small table-driven square root function in C, using exclusively integer operations.
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: Don Bockenfeld
rawnote: Implements a small table-driven square root function in C, using exclusively integer operations.
rawtitle: {TSQRT}: a New Trick for an Old Dog
entry:
@Article{Bockenfeld:1996:TNT,
  author =       "Don Bockenfeld",
  title =        "{TSQRT}: a New Trick for an Old Dog",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "3",
  pages =        "39--41",
  month =        mar,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Sat Feb 10 08:57:37 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Implements a small table-driven square root function
                 in C, using exclusively integer operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: article
filename: fparith.bib
label: Burger:1996:PFP
author: Robert G. Burger and R. Kent Dybvig
title: Printing Floating-Point Numbers Quickly and Accurately
journal: j-SIGPLAN
volume: 31
number: 5
pages: 108--116
month: may
monthnumber: 5
year: 1996
CODEN: SINODQ
DOI: https://doi.org/10.1145/231379.231397
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Mon Feb 03 07:07:43 2003
bibtimestamp: 2003.02.03 07:07:43 ???
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/231379/p108-burger/
fjournal: ACM SIGPLAN Notices
keywords: algorithms; design; theory
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Indiana University, Bloomington, IN, USA
annote: Published as part of the Proceedings of PLDI'96.
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Robert G. Burger and R. Kent Dybvig
rawtitle: Printing Floating-Point Numbers Quickly and Accurately
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/231379/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

note:
This paper offers a significantly faster algorithm than that of cite Steele:1990:HPF, together with a correctness proof and an implementation in Scheme. See also cite Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR.

subject:
bf I.3.3 Computing Methodologies, COMPUTER GRAPHICS, Picture/Image Generation, Display algorithms. bf F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.

rawnote:
This paper offers a significantly faster algorithm than that of \cite{Steele:1990:HPF}, together with a correctness proof and an implementation in Scheme. See also \cite{Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR}.

entry:
@Article{Burger:1996:PFP,
  author =       "Robert G. Burger and R. Kent Dybvig",
  title =        "Printing Floating-Point Numbers Quickly and
                 Accurately",
  journal =      j-SIGPLAN,
  volume =       "31",
  number =       "5",
  pages =        "108--116",
  month =        may,
  year =         "1996",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/231379.231397",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Mon Feb 03 07:07:43 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/231379/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper offers a significantly faster algorithm
                 than that of \cite{Steele:1990:HPF}, together with a
                 correctness proof and an implementation in Scheme. See
                 also
                 \cite{Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR}.",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/231379/p108-burger/",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Indiana University,
                 Bloomington, IN, USA",
  annote =       "Published as part of the Proceedings of PLDI'96.",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; design; theory",
  subject =      "{\bf I.3.3} Computing Methodologies, COMPUTER
                 GRAPHICS, Picture/Image Generation, Display algorithms.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}


bibtype: techreport
filename: fparith.bib
label: Burnikel:1996:HPF
author: Christoph Burnikel and Jochen Konemann
title: High precision floating point numbers in LEDA
type: Report
number: MPI I 96 1 002
institution: Max-Planck-Institut fur Informatik
address: Saarbrucken, Germany
pages: 7
year: 1996
bibdate: Thu May 09 09:03:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:03:32 ???
acknowledgement: ack-nhfb
rawauthor: Christoph Burnikel and Jochen K{\"o}nemann
rawtitle: High precision floating point numbers in {LEDA}
entry:
@TechReport{Burnikel:1996:HPF,
  author =       "Christoph Burnikel and Jochen K{\"o}nemann",
  title =        "High precision floating point numbers in {LEDA}",
  type =         "Report",
  number =       "MPI I 96 1 002",
  institution =  "Max-Planck-Institut f{\"u}r Informatik",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "7",
  year =         "1996",
  bibdate =      "Thu May 09 09:03:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Candev:1996:AIA
author: M. Candev
title: On the Application of an Interval Algorithm for Set Inversion
crossref: Alefeld:1996:SCV
pages: 140--146
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: M. Candev
rawtitle: On the Application of an Interval Algorithm for Set Inversion
entry:
@InProceedings{Candev:1996:AIA,
  author =       "M. Candev",
  title =        "On the Application of an Interval Algorithm for Set
                 Inversion",
  crossref =     "Alefeld:1996:SCV",
  pages =        "140--146",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Cappuccino:1996:DDH
author: G. Cappuccino and P. Corsonello and G. Cocorullo
title: Design and demonstration of high throughput square rooting circuit
journal: j-ELECT-LETTERS
volume: 32
number: 5
pages: 434
year: 1996
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: G. Cappuccino and P. Corsonello and G. Cocorullo
rawtitle: Design and demonstration of high throughput square rooting circuit
entry:
@Article{Cappuccino:1996:DDH,
  author =       "G. Cappuccino and P. Corsonello and G. Cocorullo",
  title =        "Design and demonstration of high throughput square
                 rooting circuit",
  journal =      j-ELECT-LETTERS,
  volume =       "32",
  number =       "5",
  pages =        "434",
  month =        "????",
  year =         "1996",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Not \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chaitin-Chatelin:1996:FPA
author: F. Chaitin-Chatelin
title: Is Finite Precision Arithmetic Useful For Physics?
journal: j-J-UCS
volume: 2
number: 5
pages: 380--??
day: 28
month: may
monthnumber: 5
year: 1996
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
bibdate: Wed May 28 19:32:35 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.05.28 19:32:35 MDT
URL: http://www.jucs.org/is_finite_precision_arithmetic_useful_for_physics
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: F. Chaitin-Chatelin
rawtitle: Is Finite Precision Arithmetic Useful For Physics?
entry:
@Article{Chaitin-Chatelin:1996:FPA,
  author =       "F. Chaitin-Chatelin",
  title =        "Is Finite Precision Arithmetic Useful For Physics?",
  journal =      j-J-UCS,
  volume =       "2",
  number =       "5",
  pages =        "380--??",
  day =          "28",
  month =        may,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/is_finite_precision_arithmetic_useful_for_physics",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: book
filename: fparith.bib
label: Chaitin-Chatelin:1996:LFP
author: Francoise Chaitin-Chatelin and Valerie Fraysse
title: Lectures on Finite Precision Computations
publisher: pub-SIAM
address: pub-SIAM:adr
pages: xv + 235
year: 1996
ISBN: 0-89871-358-7 OR 0898713587
ISBN13: 978-0-89871-358-9 OR 9780898713589
LCCN: QA297 .C417 1996
bibdate: Wed Nov 16 14:38:30 MST 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2005.11.16 14:38:30 MST
series: Software, environments, tools
keywords: Matlab
subject: numerical calculations; data processing; error analysis (mathematics); toolbox PRECISE
acknowledgement: ack-nhfb
rawauthor: Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie Frayss{\'e}
rawtitle: Lectures on Finite Precision Computations
TOC:
1. General Presentation 2. Computability in Finite Precision 3. Measures of Stability for Regular Problems 4. Computation in the Neighbourhood of a Singularity 5. Arithmetic Quality of Reliable Algorithms 6. Numerical Stability in Finite Precision 7. Software Tools for Round-Off Error Analysis in Algorithms 8. The Toolbox PRECISE for Computer Experimentation 9. Experiments with PRECISE 10. Robustness to Nonnormality 11. Qualitative Computing 12. More Numerical Illustrations with PRECISE Annex: The Toolbox PRECISE for MATLAB.

rawTOC:
1. General Presentation \\ 2. Computability in Finite Precision \\ 3. Measures of Stability for Regular Problems \\ 4. Computation in the Neighbourhood of a Singularity \\ 5. Arithmetic Quality of Reliable Algorithms \\ 6. Numerical Stability in Finite Precision \\ 7. Software Tools for Round-Off Error Analysis in Algorithms \\ 8. The Toolbox PRECISE for Computer Experimentation \\ 9. Experiments with PRECISE \\ 10. Robustness to Nonnormality \\ 11. Qualitative Computing \\ 12. More Numerical Illustrations with PRECISE \\ Annex: The Toolbox PRECISE for MATLAB.

entry:
@Book{Chaitin-Chatelin:1996:LFP,
  author =       "Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie
                 Frayss{\'e}",
  title =        "Lectures on Finite Precision Computations",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xv + 235",
  year =         "1996",
  ISBN =         "0-89871-358-7",
  ISBN-13 =      "978-0-89871-358-9",
  LCCN =         "QA297 .C417 1996",
  bibdate =      "Wed Nov 16 14:38:30 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Software, environments, tools",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab",
  subject =      "numerical calculations; data processing; error
                 analysis (mathematics); toolbox PRECISE",
  tableofcontents = "1. General Presentation \\
                 2. Computability in Finite Precision \\
                 3. Measures of Stability for Regular Problems \\
                 4. Computation in the Neighbourhood of a Singularity
                 \\
                 5. Arithmetic Quality of Reliable Algorithms \\
                 6. Numerical Stability in Finite Precision \\
                 7. Software Tools for Round-Off Error Analysis in
                 Algorithms \\
                 8. The Toolbox PRECISE for Computer Experimentation \\
                 9. Experiments with PRECISE \\
                 10. Robustness to Nonnormality \\
                 11. Qualitative Computing \\
                 12. More Numerical Illustrations with PRECISE \\
                 Annex: The Toolbox PRECISE for MATLAB.",
}


bibtype: article
filename: fparith.bib
label: Chen:1996:VAC
title: Verification of All Circuits in a Floating-Point Unit Using Word-Level Model Checking
journal: j-LECT-NOTES-COMP-SCI
volume: 1166
pages: 19--33
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Jun 02 07:43:02 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 07:43:02 ???
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawtitle: Verification of All Circuits in a Floating-Point Unit Using Word-Level Model Checking
author:
Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote and T. Kam and M. Khaira and J. O. Leary and X. Zhao

rawauthor:
Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote and T. Kam and M. Khaira and J. O. Leary and X. Zhao

entry:
@Article{Chen:1996:VAC,
  author =       "Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote
                 and T. Kam and M. Khaira and J. O. Leary and X. Zhao",
  title =        "Verification of All Circuits in a Floating-Point Unit
                 Using Word-Level Model Checking",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1166",
  pages =        "19--33",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Jun 02 07:43:02 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Chesneaux:1996:CSS
author: J.-M. Chesneaux and B. Troff
title: Computational Stability Study Using the CADNA Software Applied to the Navier--Stokes Solver PEGASE
crossref: Alefeld:1996:SCV
pages: 84--90
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: J.-M. Chesneaux and B. Troff
rawtitle:
Computational Stability Study Using the {CADNA} Software Applied to the {Navier--Stokes} Solver {PEGASE}

entry:
@InProceedings{Chesneaux:1996:CSS,
  author =       "J.-M. Chesneaux and B. Troff",
  title =        "Computational Stability Study Using the {CADNA}
                 Software Applied to the {Navier--Stokes} Solver
                 {PEGASE}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "84--90",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Chren:1996:DPP
author: W. A. Chren, Jr. and C. H. Brogdon and D. Andrevska
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
title: Delay-power product simulation results for one-hot residue number system arithmetic circuits
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 544--547
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594237
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: W. A. {Chren, Jr.} and C. H. Brogdon and D. Andrevska
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
rawtitle: Delay-power product simulation results for one-hot residue number system arithmetic circuits
entry:
@InProceedings{Chren:1996:DPP,
  author =       "W. A. {Chren, Jr.} and C. H. Brogdon and D.
                 Andrevska",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "Delay-power product simulation results for one-hot
                 residue number system arithmetic circuits",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "544--547",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594237",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "We present Spice simulations which verify previous
                 analytical estimates of the delay-power product of
                 One-Hot Residue adders and multipliers. These
                 simulations show greater than a 50\% reduction in the
                 product below binary adders and an order of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Chren:1996:DSD
author: W. A. Chren, Jr.
title: Delta-sigma demodulator with large oversampling ratio using the one-hot residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 473--476
year: 1996
DOI: https://doi.org/10.1109/ISCAS.1996.541749
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: W. A. {Chren, Jr.}
rawtitle: Delta-sigma demodulator with large oversampling ratio using the one-hot residue number system
booktitle:
IEEE International Symposium on Circuits and Systems. ISCAS '96, Connecting the World, 12--15 May 1996

rawbooktitle:
{IEEE} International Symposium on Circuits and Systems. {ISCAS '96}, Connecting the World, 12--15 May 1996

entry:
@InProceedings{Chren:1996:DSD,
  author =       "W. A. {Chren, Jr.}",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems. {ISCAS '96}, Connecting the World, 12--15 May
                 1996",
  title =        "Delta-sigma demodulator with large oversampling ratio
                 using the one-hot residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "473--476",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1996.541749",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A residue number system-based delta-sigma demodulator
                 is presented which demonstrates a significant
                 improvement in oversampling ratio in comparison with
                 equivalent binary designs. The second order design
                 employs a two-stage cascade architecture with
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Chren:1996:RDU
author: W. A. Chren, Jr. and C. H. Brogdon
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
title: RSA decryption using the one-hot residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 551--554
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594238
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: W. A. {Chren, Jr.} and C. H. Brogdon
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
rawtitle: {RSA} decryption using the one-hot residue number system
entry:
@InProceedings{Chren:1996:RDU,
  author =       "W. A. {Chren, Jr.} and C. H. Brogdon",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "{RSA} decryption using the one-hot residue number
                 system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "551--554",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594238",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The design of an RSA decryption circuit which uses the
                 One-Hot Residue Number System is presented. Large
                 modulus adders and multipliers are described which
                 reduce the area of previous (barrel shifter-based)
                 designs while preserving their low power \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Ciminiera:1996:CSM
author: L. Ciminiera and P. Montuschi
title: Carry-save multiplication schemes without final addition
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 9
pages: 1050--1055
month: sep
monthnumber: 9
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.537128
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:13 MDT 2011
bibtimestamp: 2011.07.06 19:47:13 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537128
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. Ciminiera and P. Montuschi
rawtitle: Carry-save multiplication schemes without final addition
entry:
@Article{Ciminiera:1996:CSM,
  author =       "L. Ciminiera and P. Montuschi",
  title =        "Carry-save multiplication schemes without final
                 addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "9",
  pages =        "1050--1055",
  month =        sep,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.537128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537128",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Clarke:1996:VSD
author: E. M. Clarke and S. M. German and X. Zhao
title: Verifying the SRT division algorithm using theorem proving techniques
journal: j-LECT-NOTES-COMP-SCI
volume: 1102
pages: 111--??
year: 1996
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Fri Sep 6 19:46:15 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.06 19:46:15 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: E. M. Clarke and S. M. German and X. Zhao
rawtitle: Verifying the {SRT} division algorithm using theorem proving techniques
entry:
@Article{Clarke:1996:VSD,
  author =       "E. M. Clarke and S. M. German and X. Zhao",
  title =        "Verifying the {SRT} division algorithm using theorem
                 proving techniques",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1102",
  pages =        "111--??",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Sep 6 19:46:15 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Clarke:1996:WLS
author: E. M. Clarke and M. Khaira and X. Zhao
title: Word-level symbolic model checking: avoiding the Pentium FDIV error
crossref: IEEE:1996:DAC
pages: 645--648
year: 1996
bibdate: Sat Jun 02 07:44:08 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.06.02 07:44:08 ???
acknowledgement: ack-nhfb
rawauthor: E. M. Clarke and M. Khaira and X. Zhao
rawtitle: Word-level symbolic model checking: avoiding the {Pentium FDIV} error
URL:
http://www.acm.org/pubs/articles/proceedings/dac/240518/p645-clarke/p645-clarke.pdf; http://www.acm.org/pubs/citations/proceedings/dac/240518/p645-clarke/; http://www.acm.org/pubs/contents/proceedings/dac/240518/

entry:
@InProceedings{Clarke:1996:WLS,
  author =       "E. M. Clarke and M. Khaira and X. Zhao",
  title =        "Word-level symbolic model checking: avoiding the
                 {Pentium FDIV} error",
  crossref =     "IEEE:1996:DAC",
  pages =        "645--648",
  year =         "1996",
  bibdate =      "Sat Jun 02 07:44:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/dac/240518/p645-clarke/p645-clarke.pdf;
                 http://www.acm.org/pubs/citations/proceedings/dac/240518/p645-clarke/;
                 http://www.acm.org/pubs/contents/proceedings/dac/240518/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Corliss:1996:VPE
author: G. F. Corliss and R. Rihm
title: Validating an A Priori Enclosure Using High-Order Taylor Series
crossref: Alefeld:1996:SCV
pages: 228--238
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: G. F. Corliss and R. Rihm
rawtitle: Validating an {A} Priori Enclosure Using High-Order {Taylor} Series
entry:
@InProceedings{Corliss:1996:VPE,
  author =       "G. F. Corliss and R. Rihm",
  title =        "Validating an {A} Priori Enclosure Using High-Order
                 {Taylor} Series",
  crossref =     "Alefeld:1996:SCV",
  pages =        "228--238",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Crenshaw:1996:PTF
author: Jack W. Crenshaw
title: Programmer's Toolbox: Floating-Point Math, Part 3
journal: j-EMBED-SYS-PROG
volume: 9
number: 1
pages: 19--??
year: 1996
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
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
fjournal: Embedded Systems Programming
acknowledgement: ack-nhfb
rawauthor: Jack W. Crenshaw
rawtitle: Programmer's Toolbox: Floating-Point Math, Part 3
entry:
@Article{Crenshaw:1996:PTF,
  author =       "Jack W. Crenshaw",
  title =        "Programmer's Toolbox: Floating-Point Math, Part 3",
  journal =      j-EMBED-SYS-PROG,
  volume =       "9",
  number =       "1",
  pages =        "19--??",
  year =         "1996",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: techreport
filename: fparith.bib
label: Darcy:1996:FMF
author: Joseph D. Darcy and David Gay
title: FLECKmarks: Measuring Floating Point Performance using a FulL IEEE Compliant Arithmetic BenchmarK
type: Technical report
institution: Department of Computer Science, University of California, Berkeley
address: Berkeley, CA, USA
pages: 19--??
month: dec
monthnumber: 12
year: 1996
bibdate: Mon Feb 18 12:25:24 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.18 12:25:24 ???
URL: http://www.cs.berkeley.edu/~darcy/Research/fleckmrk.pdf
acknowledgement: ack-nhfb
rawauthor: Joseph D. Darcy and David Gay
remark:
From the first author's home Web page: ``Errata: The `subnormal' timings for x86 processors are incorrect; they do not perform operations on subnormals at full speed. However, what values are subnormals on the x86 are different than on other processors due to that architecture's unusual floating-point register design. On the x86, when a 64-bit double value is loaded into a register, it has the 15 bit exponent of the 80-bit double extended format instead of the 11 bit exponent of the double format. Confusingly, this occurs even if the processor's precision control is set to round to double precision. The test programs in this project used computations that would be subnormal in a pure double format, not in double with extended exponent range (non-zero subnormals in double with extended exponent range would round to zero in pure double). Operations on subnormals in double precision with extended exponent range should take about 100 cycles on the Pentium Pro and subsequent Intel x86 chips.par Thanks to David Scott of Intel for pointing out this error.

rawtitle:
{FLECKmarks}: Measuring Floating Point Performance using a {FulL IEEE Compliant Arithmetic BenchmarK}

entry:
@TechReport{Darcy:1996:FMF,
  author =       "Joseph D. Darcy and David Gay",
  title =        "{FLECKmarks}: Measuring Floating Point Performance
                 using a {FulL IEEE Compliant Arithmetic BenchmarK}",
  type =         "Technical report",
  institution =  "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1996",
  bibdate =      "Mon Feb 18 12:25:24 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~darcy/Research/fleckmrk.pdf",
  acknowledgement = ack-nhfb,
  remark =       "From the first author's home Web page: ``Errata: The
                 `subnormal' timings for x86 processors are incorrect;
                 they do not perform operations on subnormals at full
                 speed. However, what values are subnormals on the x86
                 are different than on other processors due to that
                 architecture's unusual floating-point register design.
                 On the x86, when a 64-bit double value is loaded into a
                 register, it has the 15 bit exponent of the 80-bit
                 double extended format instead of the 11 bit exponent
                 of the double format. Confusingly, this occurs even if
                 the processor's precision control is set to round to
                 double precision. The test programs in this project
                 used computations that would be subnormal in a pure
                 double format, not in double with extended exponent
                 range (non-zero subnormals in double with extended
                 exponent range would round to zero in pure double).
                 Operations on subnormals in double precision with
                 extended exponent range should take about 100 cycles on
                 the Pentium Pro and subsequent Intel x86
                 chips.\par

                 Thanks to David Scott of Intel for pointing out this
                 error.",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1996:NCD
author: V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A. Jullien and W. C. Miller
title: Near Canonic Double-Based Number System (DBNS) with Applications in Digital Signal Processing
crossref: Luk:1996:PSC
pages: 14--25
year: 1996
DOI: https://doi.org/10.1117/12.255433
bibdate: Sat May 14 17:15:05 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.05.14 17:15:05 ???
URL: http://spie.org/x648.html?product_id=235316; http://www.gbv.de/dms/bowker/toc/9780819422347
keywords: Double-Based Number System (DBNS)
acknowledgement: ack-nhfb
rawauthor: V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A. Jullien and W. C. Miller
rawtitle: Near Canonic Double-Based Number System ({DBNS}) with Applications in Digital Signal Processing
entry:
@InProceedings{Dimitrov:1996:NCD,
  author =       "V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A.
                 Jullien and W. C. Miller",
  title =        "Near Canonic Double-Based Number System ({DBNS}) with
                 Applications in Digital Signal Processing",
  crossref =     "Luk:1996:PSC",
  pages =        "14--25",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255433",
  bibdate =      "Sat May 14 17:15:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://spie.org/x648.html?product_id=235316;
                 http://www.gbv.de/dms/bowker/toc/9780819422347",
  acknowledgement = ack-nhfb,
  keywords =     "Double-Based Number System (DBNS)",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrov:1996:RNS
author: V. S. Dimitrov and G. A. Jullien and W. C. Miller
booktitle: IEEE 39th Midwest symposium on Circuits and Systems, 1996
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 533--536
year: 1996
DOI: https://doi.org/10.1109/MWSCAS.1996.594227
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: V. S. Dimitrov and G. A. Jullien and W. C. Miller
rawbooktitle: {IEEE 39th} Midwest symposium on Circuits and Systems, 1996
title:
A residue number system implementation of real orthogonal transforms via approximation over a direct product of quadratic number rings

rawtitle:
A residue number system implementation of real orthogonal transforms via approximation over a direct product of quadratic number rings

entry:
@InProceedings{Dimitrov:1996:RNS,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "A residue number system implementation of real
                 orthogonal transforms via approximation over a direct
                 product of quadratic number rings",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--536",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594227",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recent work has focused on doing residue computations
                 that are quantization within a dense ring of integers
                 in the real domain. The aims of the paper are to
                 provide and efficient algorithm for approximation of
                 the real input signal with arbitrarily \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrova:1996:NAS
author: N. S. Dimitrova
title: On a Numerical Approach for Solving a Class of Nonlinear Systems
crossref: Alefeld:1996:SCV
pages: 147--153
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: N. S. Dimitrova
rawtitle: On a Numerical Approach for Solving a Class of Nonlinear Systems
entry:
@InProceedings{Dimitrova:1996:NAS,
  author =       "N. S. Dimitrova",
  title =        "On a Numerical Approach for Solving a Class of
                 Nonlinear Systems",
  crossref =     "Alefeld:1996:SCV",
  pages =        "147--153",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Djebbari:1996:GAS
author: A. Djebbari and S. A. Elahmar and M. F. Belbachir and J. M. Rouvaen
booktitle: 3rd International Conference on Signal Processing, 1996
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 154--157
year: 1996
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: A. Djebbari and S. A. Elahmar and M. F. Belbachir and J. M. Rouvaen
rawbooktitle: 3rd International Conference on Signal Processing, 1996
title:
Global asymptotic stability of normal digital filters with rounding and two's complement truncation quantization

rawtitle:
Global asymptotic stability of normal digital filters with rounding and two's complement truncation quantization

entry:
@InProceedings{Djebbari:1996:GAS,
  author =       "A. Djebbari and S. A. Elahmar and M. F. Belbachir and
                 J. M. Rouvaen",
  booktitle =    "3rd International Conference on Signal Processing,
                 1996",
  title =        "Global asymptotic stability of normal digital filters
                 with rounding and two's complement truncation
                 quantization",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "154--157",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Normal form digital filters are investigated for limit
                 cycles due to both two's complement truncation and
                 rounding quantization. Conditions for existence are
                 derived. A method, based on an exhaustive search and
                 applicable to above types of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Dobner:1996:AAD
author: H.-J. Dobner and W. Klein
title: Application of Automatic Differentiation Techniques to Circuit Simulation
crossref: Alefeld:1996:SCV
pages: 329--333
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: H.-J. Dobner and W. Klein
rawtitle: Application of Automatic Differentiation Techniques to Circuit Simulation
entry:
@InProceedings{Dobner:1996:AAD,
  author =       "H.-J. Dobner and W. Klein",
  title =        "Application of Automatic Differentiation Techniques to
                 Circuit Simulation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "329--333",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Dobronets:1996:PEE
author: B. S. Dobronets
title: A Posteriori Error Estimation for Partial Differential Equations
crossref: Alefeld:1996:SCV
pages: 239--244
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: B. S. Dobronets
rawtitle: A Posteriori Error Estimation for Partial Differential Equations
entry:
@InProceedings{Dobronets:1996:PEE,
  author =       "B. S. Dobronets",
  title =        "A Posteriori Error Estimation for Partial Differential
                 Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "239--244",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: El-Guibaly:1996:HSC
author: Fayez El-Guibaly and A. Sabaa
title: High-speed CORDIC algorithm
crossref: Luk:1996:PSC
pages: 512--512
year: 1996
DOI: https://doi.org/10.1117/12.255460
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: Fayez El-Guibaly and A. Sabaa
rawtitle: High-speed {CORDIC} algorithm
entry:
@InProceedings{El-Guibaly:1996:HSC,
  author =       "Fayez El-Guibaly and A. Sabaa",
  title =        "High-speed {CORDIC} algorithm",
  crossref =     "Luk:1996:PSC",
  pages =        "512--512",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255460",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Farag:1996:LPR
author: Emad N. Farag and M. Anwarul Hasan and Mohamed I. Elmasry
title: Low-power radix 2 division algorithm with minimum add / sub operations
crossref: Luk:1996:PSC
pages: 39--511
year: 1996
DOI: https://doi.org/10.1117/12.255450
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: Emad N. Farag and M. Anwarul Hasan and Mohamed I. Elmasry
rawtitle: Low-power radix 2 division algorithm with minimum add\slash sub operations
entry:
@InProceedings{Farag:1996:LPR,
  author =       "Emad N. Farag and M. Anwarul Hasan and Mohamed I.
                 Elmasry",
  title =        "Low-power radix 2 division algorithm with minimum
                 add\slash sub operations",
  crossref =     "Luk:1996:PSC",
  pages =        "39--511",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255450",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Feldstein:1996:OUM
author: Alan Feldstein and Peter R. Turner
title: Overflow and underflow in multiplication and division
journal: j-APPL-NUM-MATH
volume: 21
number: 3
pages: 221--239
day: 20
month: aug
monthnumber: 8
year: 1996
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65Y99
MRnumber: 97f:65086; 1 416 857
bibdate: Wed Jul 28 14:36:31 MDT 1999
bibtimestamp: 1999.07.28 14:36:31 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
affiliation: Arizona State Univ
affiliationaddress: AZ, USA
journalURL: http://www.sciencedirect.com/science/journal/01689274
journalabr: Appl Numer Math
rawauthor: Alan Feldstein and Peter R. Turner
rawtitle: Overflow and underflow in multiplication and division
bibsource:
Compendex database; http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1996&volume=21&issue=3; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1996&volume=21&issue=3&aid=692

keywords:
Differential equations; Digital arithmetic; Division; Floating point exponents; Floating point fractions; Logarithmic distribution; Mathematical models; Multiplication; Natural sciences computing; Overflow; Underflow

entry:
@Article{Feldstein:1996:OUM,
  author =       "Alan Feldstein and Peter R. Turner",
  title =        "Overflow and underflow in multiplication and
                 division",
  journal =      j-APPL-NUM-MATH,
  volume =       "21",
  number =       "3",
  pages =        "221--239",
  day =          "20",
  month =        aug,
  year =         "1996",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65Y99",
  MRnumber =     "97f:65086; 1 416 857",
  bibdate =      "Wed Jul 28 14:36:31 MDT 1999",
  bibsource =    "Compendex database;
                 http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1996&volume=21&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1996&volume=21&issue=3&aid=692",
  acknowledgement = ack-nhfb,
  affiliation =  "Arizona State Univ",
  affiliationaddress = "AZ, USA",
  classification = "721.1; 723.2; 921; 921.2; 921.6",
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
  journalabr =   "Appl Numer Math",
  keywords =     "Differential equations; Digital arithmetic; Division;
                 Floating point exponents; Floating point fractions;
                 Logarithmic distribution; Mathematical models;
                 Multiplication; Natural sciences computing; Overflow;
                 Underflow",
}


bibtype: article
filename: fparith.bib
label: Fenn:1996:MDD
author: S. T. J. Fenn and M. Benaissa and D. Taylor
title: $ mathrm GF(2^m) $ multiplication and division over the dual basis
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 319--327
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485570
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485570
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. T. J. Fenn and M. Benaissa and D. Taylor
rawtitle: {$ \mathrm {GF}(2^m) $} multiplication and division over the dual basis
entry:
@Article{Fenn:1996:MDD,
  author =       "S. T. J. Fenn and M. Benaissa and D. Taylor",
  title =        "{$ \mathrm {GF}(2^m) $} multiplication and division
                 over the dual basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "319--327",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485570",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485570",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Flynn:1996:SPT
booktitle: NSF / MIPS Conference on Experimental Research on Computer Systems, June 1996
title: The SNAP Project: Towards Sub-Nanosecond Arithmetic
pages: ??--??
year: 1996
bibdate: Mon Jul 18 17:18:49 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.18 17:18:49 ???
URL: ftp://arith.stanford.edu/tr/snap_nsf.ps.Z
acknowledgement: ack-nhfb
rawbooktitle: {NSF\slash MIPS} Conference on Experimental Research on Computer Systems, June 1996
rawtitle: The {SNAP} Project: Towards Sub-Nanosecond Arithmetic
author:
Michael J. Flynn and Stuart Oberman and Steve Fu and Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and Eric Schwarz and Nhon Quach

rawauthor:
Michael J. Flynn and Stuart Oberman and Steve Fu and Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and Eric Schwarz and Nhon Quach

entry:
@InProceedings{Flynn:1996:SPT,
  author =       "Michael J. Flynn and Stuart Oberman and Steve Fu and
                 Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and
                 Eric Schwarz and Nhon Quach",
  booktitle =    "{NSF\slash MIPS} Conference on Experimental Research
                 on Computer Systems, June 1996",
  title =        "The {SNAP} Project: Towards Sub-Nanosecond
                 Arithmetic",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1996",
  bibdate =      "Mon Jul 18 17:18:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/snap_nsf.ps.Z",
  acknowledgement = ack-nhfb,
  pagecount =    "12",
}


bibtype: article
filename: fparith.bib
label: Fortune:1996:SAY
author: Steven Fortune and Christopher J. Van Wyk
title: Static analysis yields efficient exact integer arithmetic for computational geometry
journal: j-TOG
volume: 15
number: 3
pages: 223--248
month: jul
monthnumber: 7
year: 1996
CODEN: ATGRDF
ISSN: 0730-0301 (print), 1557-7368 (electronic) OR 07300301 (print), 15577368 (electronic)
ISSNL: 0730-0301 OR 07300301
bibdate: Sat Aug 31 16:39:46 MDT 1996
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.31 16:39:46 MDT
URL: http://www.acm.org/pubs/toc/Abstracts/0730-0301/230533.html
fjournal: ACM Transactions on Graphics
keywords: algorithms; experimentation
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J778
rawauthor: Steven Fortune and Christopher J. {Van Wyk}
rawtitle: Static analysis yields efficient exact integer arithmetic for computational geometry
abstract:
Geometric algorithms as usually described assuming that arithmetic operations are performed exactly on real numbers. A program implemented using a naive substitution of floating-point arithmetic for real arithmetic can fail, since geometric primitives depend upon sign-evaluation and may not be reliable if evaluated approximately. Geometric primitives are reliable if evaluated exactly with integer arithmetic, but this degrades performance since software extended-precision arithmetic is required.par We describe static-analysis techniques that reduce the performance cost of exact integer arithmetic used to implement geometric algorithms. We have used the techniques for a number of examples, including line-segment intersection in two dimensions, Delaunay triangulations, and a tree-dimensional boundary-based polyhedral modeler. In general, the techniques are appropriate for algorithms that use primitives of relatively low algebraic total degree, e.g., those involving flat objects (points, lines, planes) in two or three dimensions. The techniques have been package in a preprocessor for reasonably convenient use.

subject:
bf I.3.5: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages, and systems. bf D.3.4: Software, PROGRAMMING LANGUAGES, Processors, Preprocessors. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.

rawabstract:
Geometric algorithms as usually described assuming that arithmetic operations are performed exactly on real numbers. A program implemented using a naive substitution of floating-point arithmetic for real arithmetic can fail, since geometric primitives depend upon sign-evaluation and may not be reliable if evaluated approximately. Geometric primitives are reliable if evaluated exactly with integer arithmetic, but this degrades performance since software extended-precision arithmetic is required.\par We describe static-analysis techniques that reduce the performance cost of exact integer arithmetic used to implement geometric algorithms. We have used the techniques for a number of examples, including line-segment intersection in two dimensions, Delaunay triangulations, and a tree-dimensional boundary-based polyhedral modeler. In general, the techniques are appropriate for algorithms that use primitives of relatively low algebraic total degree, e.g., those involving flat objects (points, lines, planes) in two or three dimensions. The techniques have been package in a preprocessor for reasonably convenient use.

entry:
@Article{Fortune:1996:SAY,
  author =       "Steven Fortune and Christopher J. {Van Wyk}",
  title =        "Static analysis yields efficient exact integer
                 arithmetic for computational geometry",
  journal =      j-TOG,
  volume =       "15",
  number =       "3",
  pages =        "223--248",
  month =        jul,
  year =         "1996",
  CODEN =        "ATGRDF",
  ISSN =         "0730-0301 (print), 1557-7368 (electronic)",
  ISSN-L =       "0730-0301",
  bibdate =      "Sat Aug 31 16:39:46 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0730-0301/230533.html",
  abstract =     "Geometric algorithms as usually described assuming
                 that arithmetic operations are performed exactly on
                 real numbers. A program implemented using a naive
                 substitution of floating-point arithmetic for real
                 arithmetic can fail, since geometric primitives depend
                 upon sign-evaluation and may not be reliable if
                 evaluated approximately. Geometric primitives are
                 reliable if evaluated exactly with integer arithmetic,
                 but this degrades performance since software
                 extended-precision arithmetic is required.\par

                 We describe static-analysis techniques that reduce the
                 performance cost of exact integer arithmetic used to
                 implement geometric algorithms. We have used the
                 techniques for a number of examples, including
                 line-segment intersection in two dimensions, Delaunay
                 triangulations, and a tree-dimensional boundary-based
                 polyhedral modeler. In general, the techniques are
                 appropriate for algorithms that use primitives of
                 relatively low algebraic total degree, e.g., those
                 involving flat objects (points, lines, planes) in two
                 or three dimensions. The techniques have been package
                 in a preprocessor for reasonably convenient use.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Graphics",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J778",
  keywords =     "algorithms; experimentation",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages, and systems. {\bf
                 D.3.4}: Software, PROGRAMMING LANGUAGES, Processors,
                 Preprocessors. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}


bibtype: article
filename: fparith.bib
label: Ganesan:1996:CSM
author: Ravikanth Ganesan and Kannan Govindarajan and Min-You Wu
title: Comparing SIMD and MIMD Programming Modes
journal: j-J-PAR-DIST-COMP
volume: 35
number: 1
pages: 91--96
day: 25
month: may
monthnumber: 5
year: 1996
CODEN: JPDCER
DOI: https://doi.org/10.1006/jpdc.1996.0071
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Thu Mar 9 09:19:00 MST 2000
bibtimestamp: 2000.03.09 09:19:00 MST
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Department of Computer Science, State University of New York, Buffalo, NY, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: P Practical
rawauthor: Ravikanth Ganesan and Kannan Govindarajan and Min-You Wu
rawtitle: Comparing {SIMD} and {MIMD} Programming Modes
URL:
http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production; http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production/pdf

keywords:
application benchmarks; arithmetic operations; CM; CM-5; communication; Connection Machine; Fortran; message-passing Fortran; MIMD; parallel architectures; parallel programming; performance evaluation; programming modes; SIMD; software; synthetic benchmarks; time

entry:
@Article{Ganesan:1996:CSM,
  author =       "Ravikanth Ganesan and Kannan Govindarajan and Min-You
                 Wu",
  title =        "Comparing {SIMD} and {MIMD} Programming Modes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "35",
  number =       "1",
  pages =        "91--96",
  day =          "25",
  month =        may,
  year =         "1996",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1996.0071",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:19:00 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C5220P (Parallel architecture); C6110P (Parallel
                 programming)",
  corpsource =   "Department of Computer Science, State University of
                 New York, Buffalo, NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "application benchmarks; arithmetic operations; CM;
                 CM-5; communication; Connection Machine; Fortran;
                 message-passing Fortran; MIMD; parallel architectures;
                 parallel programming; performance evaluation;
                 programming modes; SIMD; software; synthetic
                 benchmarks; time",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Garg:1996:FTP
author: H. K. Garg and F. V. C. Mendis
booktitle: Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, 1996
title: On fault-tolerant polynomial residue number systems
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 206--209
year: 1996
DOI: https://doi.org/10.1109/ACSSC.1996.600858
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: H. K. Garg and F. V. C. Mendis
rawbooktitle: Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, 1996
rawtitle: On fault-tolerant polynomial residue number systems
entry:
@InProceedings{Garg:1996:FTP,
  author =       "H. K. Garg and F. V. C. Mendis",
  booktitle =    "Conference Record of the Thirtieth Asilomar Conference
                 on Signals, Systems and Computers, 1996",
  title =        "On fault-tolerant polynomial residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "206--209",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1996.600858",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Fault-tolerant convolution techniques have been
                 described for polynomials defined over the fields of
                 complex and real numbers. Fault-tolerant convolution
                 schemes are derived for polynomials defined over finite
                 integer rings. A new algorithm for \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Gibb:1996:FFI
author: S. Gibb and P. J. W. Graumann and Laurence E. Turner
title: FIR filter implementation using bit-serial arithmetic and partial summation trees
crossref: Luk:1996:PSC
pages: 63--74
year: 1996
DOI: https://doi.org/10.1117/12.255462
bibdate: Tue Jun 14 18:26:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.06.14 18:26:06 ???
acknowledgement: ack-nhfb
rawauthor: S. Gibb and P. J. W. Graumann and Laurence E. Turner
rawtitle: {FIR} filter implementation using bit-serial arithmetic and partial summation trees
entry:
@InProceedings{Gibb:1996:FFI,
  author =       "S. Gibb and P. J. W. Graumann and Laurence E. Turner",
  title =        "{FIR} filter implementation using bit-serial
                 arithmetic and partial summation trees",
  crossref =     "Luk:1996:PSC",
  pages =        "63--74",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255462",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: fparith.bib
label: Goldberg:1996:CA
author: David Goldberg
title: Computer Arithmetic
crossref: Hennessy:1996:CAQ
chapter: A
pages: A-1--A-77
year: 1996
bibdate: Mon May 20 10:05:22 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.20 10:05:22 ???
acknowledgement: ack-nhfb
rawauthor: David Goldberg
rawtitle: Computer Arithmetic
entry:
@InCollection{Goldberg:1996:CA,
  author =       "David Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:1996:CAQ",
  chapter =      "A",
  pages =        "A-1--A-77",
  year =         "1996",
  bibdate =      "Mon May 20 10:05:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Goldstine:1996:ENI
author: H. H. Goldstine and A. Goldstine
title: The Electronic Numerical Integrator and Computer (ENIAC)
journal: j-IEEE-ANN-HIST-COMPUT
volume: 18
number: 1
pages: 10--16
month: Spring
year: 1996
CODEN: IAHCEX
DOI: https://doi.org/10.1109/85.476557
ISSN: 1058-6180 (print), 1934-1547 (electronic) OR 10586180 (print), 19341547 (electronic)
ISSNL: 1058-6180 OR 10586180
bibdate: Fri Nov 28 16:50:50 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:50:50 ???
note: Reprint of 1946 technical report and cite Goldstine:1946:ENI.
URL: https://ieeexplore.ieee.org/iel4/85/10202/00476557.pdf
fjournal: IEEE Annals of the History of Computing
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85
rawauthor: H. H. Goldstine and A. Goldstine
rawnote: Reprint of 1946 technical report and \cite{Goldstine:1946:ENI}.
rawtitle: The {Electronic Numerical Integrator and Computer} ({ENIAC})
abstract:
It is our purpose in the succeeding pages to give a brief description of the ENIAC and an indication of the kinds of problems for which it can be used. This general purpose electronic computing machine was recently made public by the Army Ordnance Department for which it was developed by the Moore School of Electrical Engineering. The machine was developed primarily for the purpose of calculating firing tables for the armed forces. Its design is, however, sufficiently general to permit the solution of a large class of numerical problems which could hardly be attempted by more conventional computing tools.par In order easily to obtain sufficient accuracy for scientific computations, the ENIAC was designed as a digital device. The equipment normally handles signed 10-digit numbers expressed in the decimal system. It is, however, so constructed that operations with as many as 20 digits are possible.par The machine is automatically sequenced in the sense that all instructions needed to carry out a computation are given to it before the computation commences. It will be seen below how these instructions are given to the machine.

rawabstract:
It is our purpose in the succeeding pages to give a brief description of the ENIAC and an indication of the kinds of problems for which it can be used. This general purpose electronic computing machine was recently made public by the Army Ordnance Department for which it was developed by the Moore School of Electrical Engineering. The machine was developed primarily for the purpose of calculating firing tables for the armed forces. Its design is, however, sufficiently general to permit the solution of a large class of numerical problems which could hardly be attempted by more conventional computing tools.\par In order easily to obtain sufficient accuracy for scientific computations, the ENIAC was designed as a digital device. The equipment normally handles signed 10-digit numbers expressed in the decimal system. It is, however, so constructed that operations with as many as 20 digits are possible.\par The machine is automatically sequenced in the sense that all instructions needed to carry out a computation are given to it before the computation commences. It will be seen below how these instructions are given to the machine.

entry:
@Article{Goldstine:1996:ENI,
  author =       "H. H. Goldstine and A. Goldstine",
  title =        "The {Electronic Numerical Integrator and Computer}
                 ({ENIAC})",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "18",
  number =       "1",
  pages =        "10--16",
  month =        "Spring",
  year =         "1996",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.476557",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Fri Nov 28 16:50:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprint of 1946 technical report and
                 \cite{Goldstine:1946:ENI}.",
  URL =          "https://ieeexplore.ieee.org/iel4/85/10202/00476557.pdf",
  abstract =     "It is our purpose in the succeeding pages to give a
                 brief description of the ENIAC and an indication of the
                 kinds of problems for which it can be used. This
                 general purpose electronic computing machine was
                 recently made public by the Army Ordnance Department
                 for which it was developed by the Moore School of
                 Electrical Engineering. The machine was developed
                 primarily for the purpose of calculating firing tables
                 for the armed forces. Its design is, however,
                 sufficiently general to permit the solution of a large
                 class of numerical problems which could hardly be
                 attempted by more conventional computing tools.\par

                 In order easily to obtain sufficient accuracy for
                 scientific computations, the ENIAC was designed as a
                 digital device. The equipment normally handles signed
                 10-digit numbers expressed in the decimal system. It
                 is, however, so constructed that operations with as
                 many as 20 digits are possible.\par

                 The machine is automatically sequenced in the sense
                 that all instructions needed to carry out a computation
                 are given to it before the computation commences. It
                 will be seen below how these instructions are given to
                 the machine.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Gudenberg:1996:HSI
author: J. W. Von Gudenberg
title: Hardware Support for Interval Arithmetic
crossref: Alefeld:1996:SCV
pages: 32--37
year: 1996
bibdate: Mon May 20 06:32:10 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:32:10 MDT
acknowledgement: ack-nhfb
rawauthor: J. W. Von Gudenberg
rawtitle: Hardware Support for Interval Arithmetic
entry:
@InProceedings{Gudenberg:1996:HSI,
  author =       "J. W. Von Gudenberg",
  title =        "Hardware Support for Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "32--37",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Guedj:1996:EN
author: Denis Guedj
title: L'empire des nombres
publisher: Gallimard
address: Paris, France
pages: 176
year: 1996
ISBN: 2-07-053373-5 OR 2070533735
ISBN13: 978-2-07-053373-2 OR 9782070533732
bibdate: Sat Nov 29 06:57:01 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.29 06:57:01 ???
acknowledgement: ack-nhfb
rawauthor: Denis Guedj
rawtitle: {L}'empire des nombres
entry:
@Book{Guedj:1996:EN,
  author =       "Denis Guedj",
  title =        "{L}'empire des nombres",
  publisher =    "Gallimard",
  address =      "Paris, France",
  pages =        "176",
  year =         "1996",
  ISBN =         "2-07-053373-5",
  ISBN-13 =      "978-2-07-053373-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 06:57:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Gupta:1996:AAG
author: S. Gupta and J. Rajski and J. Tyszer
title: Arithmetic additive generators of pseudo-exhaustive test patterns
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 8
pages: 939--949
month: aug
monthnumber: 8
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.536236
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:13 MDT 2011
bibtimestamp: 2011.07.06 19:47:13 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=536236
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Gupta and J. Rajski and J. Tyszer
rawtitle: Arithmetic additive generators of pseudo-exhaustive test patterns
entry:
@Article{Gupta:1996:AAG,
  author =       "S. Gupta and J. Rajski and J. Tyszer",
  title =        "Arithmetic additive generators of pseudo-exhaustive
                 test patterns",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "8",
  pages =        "939--949",
  month =        aug,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.536236",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=536236",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Guyot:1996:STD
author: A. Guyot and M. Renaudin and B. El Hassan and V. Levering
booktitle: Proceedings of the Ninth International Conference on VLSI Design, 1996
title: Self timed division and square-root extraction
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 376--381
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: A. Guyot and M. Renaudin and B. El Hassan and V. Levering
rawbooktitle: Proceedings of the Ninth International Conference on {VLSI} Design, 1996
rawtitle: Self timed division and square-root extraction
entry:
@InProceedings{Guyot:1996:STD,
  author =       "A. Guyot and M. Renaudin and B. El Hassan and V.
                 Levering",
  booktitle =    "Proceedings of the Ninth International Conference on
                 {VLSI} Design, 1996",
  title =        "Self timed division and square-root extraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "376--381",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes a self-timed integrated circuit
                 for division and square-root extraction. First it
                 concentrates on the development and the proof of a new
                 mathematical algorithm. Then the design methodology and
                 the architecture of a self-timed \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Haller:1996:AFP
author: G. M. Haller and D. R. Freytag
journal: j-IEEE-TRANS-NUCL-SCI
volume: 43
number: 3
pages: 1610--1614
month: jun
monthnumber: 6
year: 1996
CODEN: IRNSAM
ISSN: 0018-9499 (print), 1558-1578 (electronic) OR 00189499 (print), 15581578 (electronic)
ISSNL: 0018-9499 OR 00189499
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Nuclear Science
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23
rawauthor: G. M. Haller and D. R. Freytag
title:
Analog floating-point BiCMOS sampling chip and architecture of the BaBar CsI calorimeter front-end electronics system at the SLAC B-factory

rawtitle:
Analog floating-point {BiCMOS} sampling chip and architecture of the {BaBar CsI} calorimeter front-end electronics system at the {SLAC} {B}-factory

entry:
@Article{Haller:1996:AFP,
  author =       "G. M. Haller and D. R. Freytag",
  title =        "Analog floating-point {BiCMOS} sampling chip and
                 architecture of the {BaBar CsI} calorimeter front-end
                 electronics system at the {SLAC} {B}-factory",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "43",
  number =       "3",
  pages =        "1610--1614",
  month =        jun,
  year =         "1996",
  CODEN =        "IRNSAM",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  summary =      "The design and implementation of an analog
                 floating-point sampling integrated circuit for the
                 BaBar detector at the SLAC B-Factory is described. The
                 CARE (Custom Auto-Range Encoding) circuit is part of an
                 18-bit dynamic range sampling system with a \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Hamacher:1996: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
edition: Fourth
pages: xix + 555
year: 1996
ISBN: 0-07-025883-X OR 007025883X
ISBN13: 978-0-07-025883-9 OR 9780070258839
LCCN: QA76.9.C643 H36 1996
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:1996: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,
  edition =      "Fourth",
  pages =        "xix + 555",
  year =         "1996",
  ISBN =         "0-07-025883-X",
  ISBN-13 =      "978-0-07-025883-9",
  LCCN =         "QA76.9.C643 H36 1996",
  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: Hartwig:1996:RNA
author: F. Hartwig and A. Lacroix
title: Roundoff noise analysis on the basis of an improved floating point error model
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 133--136
year: 1996
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: F. Hartwig and A. Lacroix
rawtitle: Roundoff noise analysis on the basis of an improved floating point error model
booktitle:
IEEE International Symposium on Circuits and Systems: ISCAS '96, `Connecting the World', 12--15 May 1996

rawbooktitle:
{IEEE} International Symposium on Circuits and Systems: {ISCAS '96}, `Connecting the World', 12--15 May 1996

entry:
@InProceedings{Hartwig:1996:RNA,
  author =       "F. Hartwig and A. Lacroix",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS '96}, `Connecting the World', 12--15
                 May 1996",
  title =        "Roundoff noise analysis on the basis of an improved
                 floating point error model",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "133--136",
  year =         "1996",
  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 =      "Until now floating point roundoff analysis utilized
                 the assumption of statistical decorrelation between
                 roundoff error and internal signals subject to a signal
                 flow graph. A quantization within a signal flow graph
                 has been treated like a single \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Hauser:1996:HFE
author: John R. Hauser
title: Handling floating-point exceptions in numeric programs
journal: j-TOPLAS
volume: 18
number: 2
pages: 139--174
month: mar
monthnumber: 3
year: 1996
CODEN: ATPSDT
DOI: https://doi.org/10.1145/227699.227701
ISSN: 0164-0925 (print), 1558-4593 (electronic) OR 01640925 (print), 15584593 (electronic)
ISSNL: 0164-0925 OR 01640925
bibdate: Tue Aug 13 11:46:35 MDT 1996
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.13 11:46:35 MDT
URL: http://www.acm.org/pubs/toc/Abstracts/0164-0925/227701.html
fjournal: ACM Transactions on Programming Languages and Systems
keywords: accurate floating-point summation; algorithms; design; languages; performance; standardization
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J783
rawauthor: John R. Hauser
rawtitle: Handling floating-point exceptions in numeric programs
abstract:
There are a number of schemes for handling arithmetic exceptions that can be used to improve the speed (or alternatively the reliability) of numeric code. Overflow and underflow are the most troublesome exceptions, and depending on the context in which the exception can occur, they may be addressed either: (1) through a ``brute force'' reevaluation with extended range, (2) by reevaluating using a technique known as em scaling, (3) by substituting an infinity or zero, or (4) in the case of underflow, with gradual underflow. In the first two of these cases, the offending computation is simply reevaluated using a safer but slower method. The latter two cases are cheaper, more automated schemes that ideally are built in as options within the computer system. Other arithmetic exceptions can be handled with similar methods. These and some other techniques are examined with an eye toward determining the support programming languages and computer systems ought to provide for floating-point exception handling. It is argued that the cheapest short-term solution would be to give full support to most of the em required (as opposed to recommended) special features of the IEC/IEEE Standard for Binary Floating-Point Arithmetic. An essential part of this support would include standardized access from high-level languages to the exception flags defined by the standard. Some possibilities outside the IEEE Standard are also considered, and a few thought on possible better-structured support within programming languages are discussed.

subject:
bf D.3.3: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Control structures. bf D.3.0: Software, PROGRAMMING LANGUAGES, General, Standards. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
There are a number of schemes for handling arithmetic exceptions that can be used to improve the speed (or alternatively the reliability) of numeric code. Overflow and underflow are the most troublesome exceptions, and depending on the context in which the exception can occur, they may be addressed either: (1) through a ``brute force'' reevaluation with extended range, (2) by reevaluating using a technique known as {\em scaling}, (3) by substituting an infinity or zero, or (4) in the case of underflow, with gradual underflow. In the first two of these cases, the offending computation is simply reevaluated using a safer but slower method. The latter two cases are cheaper, more automated schemes that ideally are built in as options within the computer system. Other arithmetic exceptions can be handled with similar methods. These and some other techniques are examined with an eye toward determining the support programming languages and computer systems ought to provide for floating-point exception handling. It is argued that the cheapest short-term solution would be to give full support to most of the {\em required\/} (as opposed to recommended) special features of the IEC/IEEE Standard for Binary Floating-Point Arithmetic. An essential part of this support would include standardized access from high-level languages to the exception flags defined by the standard. Some possibilities outside the IEEE Standard are also considered, and a few thought on possible better-structured support within programming languages are discussed.

entry:
@Article{Hauser:1996:HFE,
  author =       "John R. Hauser",
  title =        "Handling floating-point exceptions in numeric
                 programs",
  journal =      j-TOPLAS,
  volume =       "18",
  number =       "2",
  pages =        "139--174",
  month =        mar,
  year =         "1996",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/227699.227701",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Tue Aug 13 11:46:35 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0164-0925/227701.html",
  abstract =     "There are a number of schemes for handling arithmetic
                 exceptions that can be used to improve the speed (or
                 alternatively the reliability) of numeric code.
                 Overflow and underflow are the most troublesome
                 exceptions, and depending on the context in which the
                 exception can occur, they may be addressed either: (1)
                 through a ``brute force'' reevaluation with extended
                 range, (2) by reevaluating using a technique known as
                 {\em scaling}, (3) by substituting an infinity or zero,
                 or (4) in the case of underflow, with gradual
                 underflow. In the first two of these cases, the
                 offending computation is simply reevaluated using a
                 safer but slower method. The latter two cases are
                 cheaper, more automated schemes that ideally are built
                 in as options within the computer system. Other
                 arithmetic exceptions can be handled with similar
                 methods. These and some other techniques are examined
                 with an eye toward determining the support programming
                 languages and computer systems ought to provide for
                 floating-point exception handling. It is argued that
                 the cheapest short-term solution would be to give full
                 support to most of the {\em required\/} (as opposed to
                 recommended) special features of the IEC/IEEE Standard
                 for Binary Floating-Point Arithmetic. An essential part
                 of this support would include standardized access from
                 high-level languages to the exception flags defined by
                 the standard. Some possibilities outside the IEEE
                 Standard are also considered, and a few thought on
                 possible better-structured support within programming
                 languages are discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "accurate floating-point summation; algorithms; design;
                 languages; performance; standardization",
  subject =      "{\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language
                 Constructs and Features, Control structures. {\bf
                 D.3.0}: Software, PROGRAMMING LANGUAGES, General,
                 Standards. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms.",
}


