# bibtab

bibtype: article
filename: fparith.bib
label: Lee:2001:DLS
author: Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo
journal: j-COMPUT-MATH-APPL
volume: 42
number: 1--2
pages: 231--240
month: jul
monthnumber: 7
year: 2001
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:16 MST 2017
bibtimestamp: 2017.03.01 21:49:16 MST
URL: http://www.sciencedirect.com/science/article/pii/S089812210100147X
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo
title:
Design of a linear systolic array for computing modular multiplication and squaring in $ bf GF(2^m) $

bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Design of a linear systolic array for computing modular multiplication and squaring in {$ {\bf GF}(2^m) $}

entry:
@Article{Lee:2001:DLS,
  author =       "Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo",
  title =        "Design of a linear systolic array for computing
                 modular multiplication and squaring in {$ {\bf GF}(2^m)
                 $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "42",
  number =       "1--2",
  pages =        "231--240",
  month =        jul,
  year =         "2001",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S089812210100147X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: inproceedings
filename: fparith.bib
label: Lefevre:2001:WCC
author: Vincent Lefevre and Jean-Michel Muller
title: Worst Cases for Correct Rounding of the Elementary Functions in Double Precision
crossref: Burgess:2001:ISC
pages: 111--118
year: 2001
DOI: https://doi.org/10.1109/ARITH.2001.930110
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lefevre.pdf
keywords: ARITH-15; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Vincent Lef{\`e}vre and Jean-Michel Muller
rawtitle: Worst Cases for Correct Rounding of the Elementary Functions in Double Precision
entry:
@InProceedings{Lefevre:2001:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding of the Elementary
                 Functions in Double Precision",
  crossref =     "Burgess:2001:ISC",
  pages =        "111--118",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930110",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lefevre.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; correct rounding; floating-point
                 arithmetic",
  summary =      "We give the results of a four-year search for the
                 worst cases for correct rounding of the major
                 elementary functions in double precision. These results
                 allow the design of reasonably fast routines that will
                 compute these functions with correct \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lemieux:2001:FPM
author: Joe Lemieux
title: Fixed-Point Math in C
journal: j-EMBED-SYS-PROG
volume: 14
number: 1
pages: ??--??
month: apr
monthnumber: 4
year: 2001
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Fri Nov 28 18:24:03 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:24:03 ???
URL: http://www.embedded.com/story/OEG20010311S0022
fjournal: Embedded Systems Programming
acknowledgement: ack-mfc
rawauthor: Joe Lemieux
rawtitle: Fixed-Point Math in {C}
abstract:
Floating-point arithmetic can be expensive if you're using an integer-only processor. But floating-point values can be manipulated as integers, as a less expensive alternative.

rawabstract:
Floating-point arithmetic can be expensive if you're using an integer-only processor. But floating-point values can be manipulated as integers, as a less expensive alternative.

entry:
@Article{Lemieux:2001:FPM,
  author =       "Joe Lemieux",
  title =        "Fixed-Point Math in {C}",
  journal =      j-EMBED-SYS-PROG,
  volume =       "14",
  number =       "1",
  pages =        "??--??",
  month =        apr,
  year =         "2001",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 18:24:03 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/story/OEG20010311S0022",
  abstract =     "Floating-point arithmetic can be expensive if you're
                 using an integer-only processor. But floating-point
                 values can be manipulated as integers, as a less
                 expensive alternative.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: article
filename: fparith.bib
label: Leone:2001:NLC
author: M. Leone
title: A New Low Complexity Parallel Multiplier for a Class of Finite Fields
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 160--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: M. Leone
rawtitle: A New Low Complexity Parallel Multiplier for a Class of Finite Fields
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620160.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620160.pdf

entry:
@Article{Leone:2001:NLC,
  author =       "M. Leone",
  title =        "A New Low Complexity Parallel Multiplier for a Class
                 of Finite Fields",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "160--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620160.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620160.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Lester:2001:ECF
author: David Lester
title: Effective Continued Fractions
crossref: Burgess:2001:ISC
pages: 163--172
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lester.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: David Lester
rawtitle: Effective Continued Fractions
entry:
@InProceedings{Lester:2001:ECF,
  author =       "David Lester",
  title =        "Effective Continued Fractions",
  crossref =     "Burgess:2001:ISC",
  pages =        "163--172",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lester.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: techreport
filename: fparith.bib
label: Li:2001:LLF
author: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
title: The tt libm library and floating-point arithmetic for HP-UX on Itanium
type: Technical report
institution: Hewlett--Packard Company
address: Palo Alto, CA, USA
month: apr
monthnumber: 4
year: 2001
bibdate: Fri Jun 24 20:12:09 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:12:09 ???
acknowledgement: ack-nhfb
rawauthor: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
rawtitle: The {\tt libm} library and floating-point arithmetic for {HP-UX} on {Itanium}
URL:
http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf; http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html

entry:
@TechReport{Li:2001:LLF,
  author =       "Ren-Cang Li and Peter Markstein and Jon P. Okada and
                 James W. Thomas",
  title =        "The {\tt libm} library and floating-point arithmetic
                 for {HP-UX} on {Itanium}",
  type =         "Technical report",
  institution =  "Hewlett--Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "??",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri Jun 24 20:12:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
                 http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Li:2001:PMM
author: Keqin Li and V. Y. Pan
title: Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 5
pages: 519--525
month: may
monthnumber: 5
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.926164
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:03:10 MDT 2011
bibtimestamp: 2011.07.05 10:03:10 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=926164
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Keqin Li and V. Y. Pan
rawtitle: Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system
entry:
@Article{Li:2001:PMM,
  author =       "Keqin Li and V. Y. Pan",
  title =        "Parallel matrix multiplication on a linear array with
                 a reconfigurable pipelined bus system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "5",
  pages =        "519--525",
  month =        may,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.926164",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=926164",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Lippert:2001:HSM
author: Th. Lippert and N. Petkov and P. Palazzari and K. Schilling
title: Hyper-systolic matrix multiplication
journal: j-PARALLEL-COMPUTING
volume: 27
number: 6
pages: 737--759
month: may
monthnumber: 5
year: 2001
CODEN: PACOEJ
ISSN: 0167-8191 (print), 1872-7336 (electronic) OR 01678191 (print), 18727336 (electronic)
ISSNL: 0167-8191 OR 01678191
bibdate: Wed Jul 18 06:31:15 MDT 2001
bibsource: http://www.elsevier.com/locate/issn/01678191; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.07.18 06:31:15 MDT
fjournal: Parallel Computing
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01678191
rawauthor: Th. Lippert and N. Petkov and P. Palazzari and K. Schilling
rawtitle: Hyper-systolic matrix multiplication
URL:
http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/abstract.html; http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/article.pdf

entry:
@Article{Lippert:2001:HSM,
  author =       "Th. Lippert and N. Petkov and P. Palazzari and K.
                 Schilling",
  title =        "Hyper-systolic matrix multiplication",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "27",
  number =       "6",
  pages =        "737--759",
  month =        may,
  year =         "2001",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Wed Jul 18 06:31:15 MDT 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/01678191;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}


bibtype: inproceedings
filename: fparith.bib
label: Madhukumar:2001:EMH
author: A. S. Madhukumar and F. Chin
booktitle: 12th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, 2001
title: An efficient method for high-rate data transmission using residue number system based DS--CDMA
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: C-1--C-5
year: 2001
DOI: https://doi.org/10.1109/PIMRC.2001.965450
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. S. Madhukumar and F. Chin
rawbooktitle: 12th {IEEE} International Symposium on Personal, Indoor and Mobile Radio Communications, 2001
rawtitle: An efficient method for high-rate data transmission using residue number system based {DS--CDMA}
entry:
@InProceedings{Madhukumar:2001:EMH,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "12th {IEEE} International Symposium on Personal,
                 Indoor and Mobile Radio Communications, 2001",
  title =        "An efficient method for high-rate data transmission
                 using residue number system based {DS--CDMA}",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "C-1--C-5",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/PIMRC.2001.965450",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents an advanced architecture for a
                 residue number system (RNS) based CDMA system for
                 high-rate data transmission by combining RNS
                 representation, PSK/QAM modulation and orthogonal
                 modulation. The proposed system uses a lesser
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Madhukumar:2001:IBE
author: A. S. Madhukumar and F. Chin
booktitle: VTC 2001 Fall. IEEE VTS 54th Vehicular Technology Conference
title: Improving bandwidth efficiency for a residue number system based DS--CDMA system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 247--251
year: 2001
DOI: https://doi.org/10.1109/VTC.2001.956595
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. S. Madhukumar and F. Chin
rawbooktitle: {VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular Technology Conference
rawtitle: Improving bandwidth efficiency for a residue number system based {DS--CDMA} system
entry:
@InProceedings{Madhukumar:2001:IBE,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Improving bandwidth efficiency for a residue number
                 system based {DS--CDMA} system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "247--251",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.956595",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents a new method to improve bandwidth
                 efficiency of RNS based CDMA system by combining RNS
                 representation, PSK/QAM modulation and orthogonal
                 modulation. Using the proposed method significantly
                 reduces the computational complexity of \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Madhukumar:2001:IIR
author: A. S. Madhukumar and F. Chin
booktitle: VTC 2001 Fall. IEEE VTS 54th Vehicular Technology Conference
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2272--2276
year: 2001
DOI: https://doi.org/10.1109/VTC.2001.957150
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. S. Madhukumar and F. Chin
rawbooktitle: {VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular Technology Conference
title:
Incorporating incremental redundancy and link adaptation in communication systems using residue number systems

rawtitle:
Incorporating incremental redundancy and link adaptation in communication systems using residue number systems

entry:
@InProceedings{Madhukumar:2001:IIR,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Incorporating incremental redundancy and link
                 adaptation in communication systems using residue
                 number systems",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2272--2276",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.957150",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper explores the use of redundant residue
                 number systems to incorporate incremental redundancy in
                 a communication system. By exploiting this property
                 further, one can design an appropriate coding scheme
                 for transmission at the currently \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:2001:ITL
author: David W. Matula
title: Improved Table Lookup Algorithms for Postscaled Division
crossref: Burgess:2001:ISC
pages: 101--110
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Matula.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: David W. Matula
rawtitle: Improved Table Lookup Algorithms for Postscaled Division
entry:
@InProceedings{Matula:2001:ITL,
  author =       "David W. Matula",
  title =        "Improved Table Lookup Algorithms for Postscaled
                 Division",
  crossref =     "Burgess:2001:ISC",
  pages =        "101--110",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Matula.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: McFearin:2001:GAH
author: Lee D. McFearin and David W. Matula
title: Generation and Analysis of Hard to Round Cases for Binary Floating Point Division
crossref: Burgess:2001:ISC
pages: 119--127
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_McFearin.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Lee D. McFearin and David W. Matula
rawtitle: Generation and Analysis of Hard to Round Cases for Binary Floating Point Division
entry:
@InProceedings{McFearin:2001:GAH,
  author =       "Lee D. McFearin and David W. Matula",
  title =        "Generation and Analysis of Hard to Round Cases for
                 Binary Floating Point Division",
  crossref =     "Burgess:2001:ISC",
  pages =        "119--127",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_McFearin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  summary =      "We investigate two sets of hard to round p$\times$p
                 bit fractions arising from division of a normalized p
                 bit floating point dividend by a normalized p bit
                 floating point divisor. These sets are characterized by
                 the p$\times$p bit fraction's quotient \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Michel:2001:SCF
author: Claude Michel and Michel Rueher and Yahia Lebbah
title: Solving Constraints over Floating-Point Numbers
journal: j-LECT-NOTES-COMP-SCI
volume: 2239
pages: 524--538
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
MRclass: 90C08 (65G30 68T20)
MRnumber: MR1904621
bibdate: Sat Feb 2 13:07:24 MST 2002
bibtimestamp: 2002.02.02 13:07:24 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Claude Michel and Michel Rueher and Yahia Lebbah
rawtitle: Solving Constraints over Floating-Point Numbers
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2239.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2239/22390524.htm; http://link.springer-ny.com/link/service/series/0558/papers/2239/22390524.pdf

entry:
@Article{Michel:2001:SCF,
  author =       "Claude Michel and Michel Rueher and Yahia Lebbah",
  title =        "Solving Constraints over Floating-Point Numbers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2239",
  pages =        "524--538",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "90C08 (65G30 68T20)",
  MRnumber =     "MR1904621",
  bibdate =      "Sat Feb 2 13:07:24 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2239.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2239/22390524.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2239/22390524.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: phdthesis
filename: fparith.bib
label: Mobley:2001:ICW
author: Byron Paul Mobley
title: The ingenuity of common workmen: and the invention of the computer
type: Ph.D. thesis
school: Department of History, Iowa State University
address: Ames, IA, USA
pages: 301
year: 2001
ISBN: 0-493-46949-4 OR 0493469494
ISBN13: 978-0-493-46949-2 OR 9780493469492
bibdate: Thu Nov 18 11:31:13 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 11:31:13 ???
keywords: ABC (Atanasoff-Berry Computer); ENIAC (Electronic Numerical Integrator and Computer)
acknowledgement: ack-nhfb
rawauthor: Byron Paul Mobley
rawtitle: The ingenuity of common workmen: and the invention of the computer
abstract:
Since World War II, state support for scientific research has been assumed crucial to technological and economic progress. Governments accordingly spent tremendous sums to that end. Nothing epitomizes the alleged fruits of that involvement better than the electronic digital computer. The first such computer has been widely reputed to be the ENIAC, financed by the U.S. Army for the war but finished afterwards. Vastly improved computers followed, initially paid for in good share by the Federal Government of the United States, but with the private sector then dominating, both in development and use, and computers are of major significance. Despite the supposed success of public-supported science, evidence is that computers would have evolved much the same without it but at less expense. Indeed, the foundations of modern computer theory and technology were articulated before World War II, both as a tool of applied mathematics and for information processing, and the computer was itself on the cusp of reality. Contrary to popular understanding, the ENIAC actually represented a movement backwards and a dead end.par Rather, modern computation derived more directly, for example, from the prewar work of John Vincent Atanasoff and Clifford Berry, a physics professor and graduate student, respectively, at Iowa State College (now University) in Ames, Iowa. They built the Atanasoff Berry Computer (ABC), which, although special purpose and inexpensive, heralded the efficient and elegant design of modern computers. Moreover, while no one foresaw commercialization of computers based on the ungainly and costly ENIAC, the commercial possibilities of the ABC were immediately evident, although unrealized due to war. Evidence indicates, furthermore, that the private sector was willing and able to develop computers beyond the ABC and could have done so more effectively than government, to the most sophisticated machines. A full and inclusive history of computers suggests that Adam Smith, the eighteenth century Scottish philosopher, had it right. He believed that minimal and aloof government best served society, and that the inherent genius of citizens was itself enough to ensure the general prosperity.

rawabstract:
Since World War II, state support for scientific research has been assumed crucial to technological and economic progress. Governments accordingly spent tremendous sums to that end. Nothing epitomizes the alleged fruits of that involvement better than the electronic digital computer. The first such computer has been widely reputed to be the ENIAC, financed by the U.S. Army for the war but finished afterwards. Vastly improved computers followed, initially paid for in good share by the Federal Government of the United States, but with the private sector then dominating, both in development and use, and computers are of major significance. Despite the supposed success of public-supported science, evidence is that computers would have evolved much the same without it but at less expense. Indeed, the foundations of modern computer theory and technology were articulated before World War II, both as a tool of applied mathematics and for information processing, and the computer was itself on the cusp of reality. Contrary to popular understanding, the ENIAC actually represented a movement backwards and a dead end.\par Rather, modern computation derived more directly, for example, from the prewar work of John Vincent Atanasoff and Clifford Berry, a physics professor and graduate student, respectively, at Iowa State College (now University) in Ames, Iowa. They built the Atanasoff Berry Computer (ABC), which, although special purpose and inexpensive, heralded the efficient and elegant design of modern computers. Moreover, while no one foresaw commercialization of computers based on the ungainly and costly ENIAC, the commercial possibilities of the ABC were immediately evident, although unrealized due to war. Evidence indicates, furthermore, that the private sector was willing and able to develop computers beyond the ABC and could have done so more effectively than government, to the most sophisticated machines. A full and inclusive history of computers suggests that Adam Smith, the eighteenth century Scottish philosopher, had it right. He believed that minimal and aloof government best served society, and that the inherent genius of citizens was itself enough to ensure the general prosperity.

entry:
@PhdThesis{Mobley:2001:ICW,
  author =       "Byron Paul Mobley",
  title =        "The ingenuity of common workmen: and the invention of
                 the computer",
  type =         "{Ph.D.} thesis",
  school =       "Department of History, Iowa State University",
  address =      "Ames, IA, USA",
  pages =        "301",
  year =         "2001",
  ISBN =         "0-493-46949-4",
  ISBN-13 =      "978-0-493-46949-2",
  bibdate =      "Thu Nov 18 11:31:13 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Since World War II, state support for scientific
                 research has been assumed crucial to technological and
                 economic progress. Governments accordingly spent
                 tremendous sums to that end. Nothing epitomizes the
                 alleged fruits of that involvement better than the
                 electronic digital computer. The first such computer
                 has been widely reputed to be the ENIAC, financed by
                 the U.S. Army for the war but finished afterwards.
                 Vastly improved computers followed, initially paid for
                 in good share by the Federal Government of the United
                 States, but with the private sector then dominating,
                 both in development and use, and computers are of major
                 significance. Despite the supposed success of
                 public-supported science, evidence is that computers
                 would have evolved much the same without it but at less
                 expense. Indeed, the foundations of modern computer
                 theory and technology were articulated before World War
                 II, both as a tool of applied mathematics and for
                 information processing, and the computer was itself on
                 the cusp of reality. Contrary to popular understanding,
                 the ENIAC actually represented a movement backwards and
                 a dead end.\par

                 Rather, modern computation derived more directly, for
                 example, from the prewar work of John Vincent Atanasoff
                 and Clifford Berry, a physics professor and graduate
                 student, respectively, at Iowa State College (now
                 University) in Ames, Iowa. They built the Atanasoff
                 Berry Computer (ABC), which, although special purpose
                 and inexpensive, heralded the efficient and elegant
                 design of modern computers. Moreover, while no one
                 foresaw commercialization of computers based on the
                 ungainly and costly ENIAC, the commercial possibilities
                 of the ABC were immediately evident, although
                 unrealized due to war. Evidence indicates, furthermore,
                 that the private sector was willing and able to develop
                 computers beyond the ABC and could have done so more
                 effectively than government, to the most sophisticated
                 machines. A full and inclusive history of computers
                 suggests that Adam Smith, the eighteenth century
                 Scottish philosopher, had it right. He believed that
                 minimal and aloof government best served society, and
                 that the inherent genius of citizens was itself enough
                 to ensure the general prosperity.",
  acknowledgement = ack-nhfb,
  keywords =     "ABC (Atanasoff-Berry Computer); ENIAC (Electronic
                 Numerical Integrator and Computer)",
}


bibtype: article
filename: fparith.bib
label: Moller:2001:SEC
author: Bodo Moller
title: Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
journal: j-LECT-NOTES-COMP-SCI
volume: 2200
pages: 324--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:44 MST 2002
bibtimestamp: 2002.02.02 13:06:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Bodo M{\"o}ller
rawtitle: Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000324.htm; http://link.springer-ny.com/link/service/series/0558/papers/2200/22000324.pdf

entry:
@Article{Moller:2001:SEC,
  author =       "Bodo M{\"o}ller",
  title =        "Securing Elliptic Curve Point Multiplication against
                 Side-Channel Attacks",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2200",
  pages =        "324--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000324.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2200/22000324.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Montuschi:2001:BVH
author: P. Montuschi and T. Lang
title: Boosting very-high radix division with prescaling and selection by rounding
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 1
pages: 13--27
month: jan
monthnumber: 1
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.902750
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:03:08 MDT 2011
bibtimestamp: 2011.07.05 10:03:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902750
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and T. Lang
rawtitle: Boosting very-high radix division with prescaling and selection by rounding
entry:
@Article{Montuschi:2001:BVH,
  author =       "P. Montuschi and T. Lang",
  title =        "Boosting very-high radix division with prescaling and
                 selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "1",
  pages =        "13--27",
  month =        jan,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.902750",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902750",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An extension of the very-high radix division with
                 prescaling and selection by rounding is presented. This
                 extension consists of increasing the effective radix of
                 the implementation by obtaining a few additional bits
                 of the quotient per iteration, \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Morioka:2001:TEV
author: Sumio Morioka and Yasunao Katayama and Toshiyuki Yamane
title: Towards Efficient Verification of Arithmetic Algorithms over Galois Fields $ G F(2^m) $
journal: j-LECT-NOTES-COMP-SCI
volume: 2102
pages: 465--477
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:02 MST 2002
bibtimestamp: 2002.02.02 13:05:02 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Sumio Morioka and Yasunao Katayama and Toshiyuki Yamane
rawtitle: Towards Efficient Verification of Arithmetic Algorithms over {Galois} Fields {$ G F(2^m) $}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2102.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2102/21020465.htm; http://link.springer-ny.com/link/service/series/0558/papers/2102/21020465.pdf

entry:
@Article{Morioka:2001:TEV,
  author =       "Sumio Morioka and Yasunao Katayama and Toshiyuki
                 Yamane",
  title =        "Towards Efficient Verification of Arithmetic
                 Algorithms over {Galois} Fields {$ G F(2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2102",
  pages =        "465--477",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:02 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2102.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2102/21020465.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2102/21020465.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: MRaihi:2001:ACR
author: David M'Raihi and David Naccache and Michael Tunstall
title: Asymmetric Currency Rounding
journal: j-LECT-NOTES-COMP-SCI
volume: 1962
pages: 192--201
year: 2001
CODEN: LNCSD9
DOI: https://doi.org/10.1007/3-540-45472-1
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:02:55 MST 2002
bibtimestamp: 2002.02.02 13:02:55 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: David M'Ra{\"\i}hi and David Naccache and Michael Tunstall
rawtitle: Asymmetric Currency Rounding
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1962.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1962/19620192.htm; http://link.springer-ny.com/link/service/series/0558/papers/1962/19620192.pdf

abstract:
The euro was introduced on the first of January 1999 as a common currency in fourteen European nations. EC regulations are fundamentally different from usual banking practices for they forbid fees when converting national currencies to euros (fees would otherwise deter users from adopting the euro); this creates a unique fraud context where money can be made by taking advantage of the EC's official rounding rules. This paper proposes a public-key-based protection against such attacks. In our scheme, the parties conducting a transaction can not predict whether the rounding will cause loss or gain while the expected statistical difference between an amount and its euro-equivalent decreases exponentially as the number of transactions increases.

rawabstract:
The euro was introduced on the first of January 1999 as a common currency in fourteen European nations. EC regulations are fundamentally different from usual banking practices for they forbid fees when converting national currencies to euros (fees would otherwise deter users from adopting the euro); this creates a unique fraud context where money can be made by taking advantage of the EC's official rounding rules. This paper proposes a public-key-based protection against such attacks. In our scheme, the parties conducting a transaction can not predict whether the rounding will cause loss or gain while the expected statistical difference between an amount and its euro-equivalent decreases exponentially as the number of transactions increases.

entry:
@Article{MRaihi:2001:ACR,
  author =       "David M'Ra{\"\i}hi and David Naccache and Michael
                 Tunstall",
  title =        "Asymmetric Currency Rounding",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1962",
  pages =        "192--201",
  year =         "2001",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-45472-1",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:55 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1962.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1962/19620192.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1962/19620192.pdf",
  abstract =     "The euro was introduced on the first of January 1999
                 as a common currency in fourteen European nations. EC
                 regulations are fundamentally different from usual
                 banking practices for they forbid fees when converting
                 national currencies to euros (fees would otherwise
                 deter users from adopting the euro); this creates a
                 unique fraud context where money can be made by taking
                 advantage of the EC's official rounding rules. This
                 paper proposes a public-key-based protection against
                 such attacks. In our scheme, the parties conducting a
                 transaction can not predict whether the rounding will
                 cause loss or gain while the expected statistical
                 difference between an amount and its euro-equivalent
                 decreases exponentially as the number of transactions
                 increases.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Muller:2001:IEA
author: Norbert Th. Muller
title: The iRRAM: Exact Arithmetic in C++
journal: j-LECT-NOTES-COMP-SCI
volume: 2064
pages: 222--252
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:04:19 MST 2002
bibtimestamp: 2002.02.02 13:04:19 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Norbert Th. M{\"u}ller
rawtitle: The {iRRAM}: Exact Arithmetic in {C++}
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640222.htm; http://link.springer-ny.com/link/service/series/0558/papers/2064/20640222.pdf

entry:
@Article{Muller:2001:IEA,
  author =       "Norbert Th. M{\"u}ller",
  title =        "The {iRRAM}: Exact Arithmetic in {C++}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "222--252",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640222.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640222.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Naini:2001:GHS
author: Ajay Naini and Atul Dhablania and Warren James and Debjit Das Sarma
title: 1-GHz HAL SPARC64reg Dual Floating Point Unit with RAS Features
crossref: Burgess:2001:ISC
pages: 173--183
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Naini.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Ajay Naini and Atul Dhablania and Warren James and Debjit Das Sarma
rawtitle: {1-GHz HAL SPARC64\reg{}} Dual Floating Point Unit with {RAS} Features
entry:
@InProceedings{Naini:2001:GHS,
  author =       "Ajay Naini and Atul Dhablania and Warren James and
                 Debjit Das Sarma",
  title =        "{1-GHz HAL SPARC64\reg{}} Dual Floating Point Unit
                 with {RAS} Features",
  crossref =     "Burgess:2001:ISC",
  pages =        "173--183",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Naini.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Nakamura:2001:AAA
author: Yoshimasa Nakamura
title: Algorithms associated with arithmetic, geometric and harmonic means and integrable systems
journal: j-J-COMPUT-APPL-MATH
volume: 131
number: 1--2
pages: 161--174
day: 1
month: jun
monthnumber: 6
year: 2001
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00316-2
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65P40 (37N30 39A10)
MRnumber: 1835710
bibdate: Sat Feb 25 12:45:18 MST 2017
bibtimestamp: 2017.02.25 12:45:18 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700003162
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yoshimasa Nakamura
rawtitle: Algorithms associated with arithmetic, geometric and harmonic means and integrable systems
bibsource:
https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

entry:
@Article{Nakamura:2001:AAA,
  author =       "Yoshimasa Nakamura",
  title =        "Algorithms associated with arithmetic, geometric and
                 harmonic means and integrable systems",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "131",
  number =       "1--2",
  pages =        "161--174",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00316-2",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65P40 (37N30 39A10)",
  MRnumber =     "1835710",
  bibdate =      "Sat Feb 25 12:45:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003162",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: fparith.bib
label: Nannarelli:2001:TBR
author: A. Nannarelli and M. Re and G. C. Cardarilli
booktitle: ISCAS 2001, The 2001 IEEE International Symposium on Circuits and Systems, 6--9 May 2001
title: Tradeoffs between residue number system and traditional FIR filters
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 305--308
year: 2001
DOI: https://doi.org/10.1109/ISCAS.2001.921068
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: A. Nannarelli and M. Re and G. C. Cardarilli
rawbooktitle: {ISCAS 2001}, The 2001 {IEEE} International Symposium on Circuits and Systems, 6--9 May 2001
rawtitle: Tradeoffs between residue number system and traditional {FIR} filters
entry:
@InProceedings{Nannarelli:2001:TBR,
  author =       "A. Nannarelli and M. Re and G. C. Cardarilli",
  booktitle =    "{ISCAS 2001}, The 2001 {IEEE} International Symposium
                 on Circuits and Systems, 6--9 May 2001",
  title =        "Tradeoffs between residue number system and
                 traditional {FIR} filters",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "305--308",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2001.921068",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this work, a study on the implementation of FIR
                 filters in the Residue Number System (RNS) is carried
                 out. For different configurations, RNS filters are
                 compared with filters realized in the traditional two's
                 complement system (TCS) in terms of \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Ning:2001:ESI
author: Peng Ning and Yiqun Lisa Yin
title: Efficient Software Implementation for Finite Field Multiplication in Normal Basis
journal: j-LECT-NOTES-COMP-SCI
volume: 2229
pages: 177--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:15 MST 2002
bibtimestamp: 2002.02.02 13:07:15 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Peng Ning and Yiqun Lisa Yin
rawtitle: Efficient Software Implementation for Finite Field Multiplication in Normal Basis
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290177.htm; http://link.springer-ny.com/link/service/series/0558/papers/2229/22290177.pdf

entry:
@Article{Ning:2001:ESI,
  author =       "Peng Ning and Yiqun Lisa Yin",
  title =        "Efficient Software Implementation for Finite Field
                 Multiplication in Normal Basis",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2229",
  pages =        "177--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:15 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290177.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2229/22290177.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Nozaki:2001:IRA
author: H. Nozaki and M. Motoyama and A. Shimbo and S. Kawamura
title: Implementation of RSA Algorithm Based on RNS Montgomery Multiplication
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 364--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: H. Nozaki and M. Motoyama and A. Shimbo and S. Kawamura
rawtitle: Implementation of {RSA} Algorithm Based on {RNS Montgomery} Multiplication
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620364.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620364.pdf

entry:
@Article{Nozaki:2001:IRA,
  author =       "H. Nozaki and M. Motoyama and A. Shimbo and S.
                 Kawamura",
  title =        "Implementation of {RSA} Algorithm Based on {RNS
                 Montgomery} Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "364--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620364.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620364.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Oishi:2001:FEM
author: Shin'ichi Oishi
title: Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
journal: j-LINEAR-ALGEBRA-APPL
volume: 324
number: 1--3
pages: 133--146
day: 15
month: feb
monthnumber: 2
year: 2001
CODEN: LAAPAW
ISSN: 0024-3795 (print), 1873-1856 (electronic) OR 00243795 (print), 18731856 (electronic)
ISSNL: 0024-3795 OR 00243795
bibdate: Mon Mar 19 19:03:24 MST 2001
bibsource: http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.03.19 19:03:24 MST
fjournal: Linear Algebra and its Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00243795
rawauthor: Shin'ichi Oishi
rawtitle: Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
URL:
http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/article.pdf

entry:
@Article{Oishi:2001:FEM,
  author =       "Shin'ichi Oishi",
  title =        "Fast enclosure of matrix eigenvalues and singular
                 values via rounding mode controlled computation",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "324",
  number =       "1--3",
  pages =        "133--146",
  day =          "15",
  month =        feb,
  year =         "2001",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Mar 19 19:03:24 MST 2001",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}


bibtype: article
filename: fparith.bib
label: Okeya:2001:EEC
author: K. Okeya and K. Sakurai
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 126--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: K. Okeya and K. Sakurai
title:
Efficient Elliptic Curve Cryptosystems from a Scalar Multiplication Algorithm with Recovery of the $y$-Coordinate on a Montgomery-Form Elliptic Curve

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620126.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620126.pdf

rawtitle:
Efficient Elliptic Curve Cryptosystems from a Scalar Multiplication Algorithm with Recovery of the $y$-Coordinate on a {Montgomery}-Form Elliptic Curve

entry:
@Article{Okeya:2001:EEC,
  author =       "K. Okeya and K. Sakurai",
  title =        "Efficient Elliptic Curve Cryptosystems from a Scalar
                 Multiplication Algorithm with Recovery of the
                 $y$-Coordinate on a {Montgomery}-Form Elliptic Curve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "126--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620126.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620126.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: book
filename: fparith.bib
label: Overton:2001:NCI
author: Michael L. Overton
publisher: pub-SIAM
address: pub-SIAM:adr
pages: xiv + 104
year: 2001
LCCN: QA76.9.M35 O94 2001
MRclass: 65-02 (65G30 68M07 68N99)
MRnumber: MR1828597 (2003b:65002)
MRreviewer: Jesse L. Barlow
bibdate: Fri Apr 27 16:50:46 2001
bibtimestamp: 2001.04.27 16:50:46 ???
URL: http://www.cs.nyu.edu/cs/faculty/overton/book/; http://www.siam.org/catalog/mcc07/ot76.htm
acknowledgement: ack-nhfb
rawauthor: Michael L. Overton
title:
Numerical Computing with IEEE Floating Point Arithmetic, Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises

ISBN:
0-89871-482-6 (hardcover), 0-89871-571-7 (paperback), 0-89871-807-4 (ebook) OR 0898714826 (hardcover), 0898715717 (paperback), 0898718074 (ebook)

ISBN13:
978-0-89871-482-1 (hardcover), 978-0-89871-571-2 (print), 978-0-89871-807-2 (e-book) OR 9780898714821 (hardcover), 9780898715712 (print), 9780898718072 (ebook)

bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/numana2000.bib

abstract:
Are you familiar with the IEEE floating point arithmetic standard? Would you like to understand it better? This book gives a broad overview of numerical computing, in a historical context, with a special focus on the IEEE standard for binary floating point arithmetic. Key ideas are developed step by step, taking the reader from floating point representation, correctly rounded arithmetic, and the IEEE philosophy on exceptions, to an understanding of the crucial concepts of conditioning and stability, explained in a simple yet rigorous context. It gives technical details that are not readily available elsewhere and includes challenging exercises that go beyond the topics covered in the text. Numerical Computing with IEEE Floating Point Arithmetic provides an easily accessible yet detailed discussion of IEEE Std 754-1985, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and the cutting edge of industry, it is supported by virtually every modern computer. Other topics include the floating point architecture of the Intel microprocessors and a discussion of programming language support for the standard.

TOC:
1: Introduction 2: The real numbers 3: Computer representation of numbers 4: IEEE floating point representation 5: Rounding 6: Correctly rounded floating point operations 7: Exceptions 8: The Intel microprocessors 9: Programming languages 10: Floating point in C 11: Cancellation 12: Conditioning of problems 13: Stability of algorithms 14: Conclusion

rawabstract:
Are you familiar with the IEEE floating point arithmetic standard? Would you like to understand it better? This book gives a broad overview of numerical computing, in a historical context, with a special focus on the IEEE standard for binary floating point arithmetic. Key ideas are developed step by step, taking the reader from floating point representation, correctly rounded arithmetic, and the IEEE philosophy on exceptions, to an understanding of the crucial concepts of conditioning and stability, explained in a simple yet rigorous context. It gives technical details that are not readily available elsewhere and includes challenging exercises that go beyond the topics covered in the text. Numerical Computing with IEEE Floating Point Arithmetic provides an easily accessible yet detailed discussion of IEEE Std 754-1985, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and the cutting edge of industry, it is supported by virtually every modern computer. Other topics include the floating point architecture of the Intel microprocessors and a discussion of programming language support for the standard.

rawtitle:
Numerical Computing with {IEEE} Floating Point Arithmetic, Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises

rawTOC:
1: Introduction \\ 2: The real numbers \\ 3: Computer representation of numbers \\ 4: IEEE floating point representation \\ 5: Rounding \\ 6: Correctly rounded floating point operations \\ 7: Exceptions \\ 8: The Intel microprocessors \\ 9: Programming languages \\ 10: Floating point in C \\ 11: Cancellation \\ 12: Conditioning of problems \\ 13: Stability of algorithms \\ 14: Conclusion

entry:
@Book{Overton:2001:NCI,
  author =       "Michael L. Overton",
  title =        "Numerical Computing with {IEEE} Floating Point
                 Arithmetic, Including One Theorem, One Rule of Thumb,
                 and One Hundred and One Exercises",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiv + 104",
  year =         "2001",
  ISBN =         "0-89871-482-6 (hardcover), 0-89871-571-7 (paperback),
                 0-89871-807-4 (ebook)",
  ISBN-13 =      "978-0-89871-482-1 (hardcover), 978-0-89871-571-2
                 (print), 978-0-89871-807-2 (e-book)",
  LCCN =         "QA76.9.M35 O94 2001",
  MRclass =      "65-02 (65G30 68M07 68N99)",
  MRnumber =     "MR1828597 (2003b:65002)",
  MRreviewer =   "Jesse L. Barlow",
  bibdate =      "Fri Apr 27 16:50:46 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
  price =        "US\$40.00",
  URL =          "http://www.cs.nyu.edu/cs/faculty/overton/book/;
                 http://www.siam.org/catalog/mcc07/ot76.htm",
  abstract =     "Are you familiar with the IEEE floating point
                 arithmetic standard? Would you like to understand it
                 better? This book gives a broad overview of numerical
                 computing, in a historical context, with a special
                 focus on the IEEE standard for binary floating point
                 arithmetic. Key ideas are developed step by step,
                 taking the reader from floating point representation,
                 correctly rounded arithmetic, and the IEEE philosophy
                 on exceptions, to an understanding of the crucial
                 concepts of conditioning and stability, explained in a
                 simple yet rigorous context. It gives technical details
                 that are not readily available elsewhere and includes
                 challenging exercises that go beyond the topics covered
                 in the text. Numerical Computing with IEEE Floating
                 Point Arithmetic provides an easily accessible yet
                 detailed discussion of IEEE Std 754-1985, arguably the
                 most important standard in the computer industry. The
                 result of an unprecedented cooperation between academic
                 computer scientists and the cutting edge of industry,
                 it is supported by virtually every modern computer.
                 Other topics include the floating point architecture of
                 the Intel microprocessors and a discussion of
                 programming language support for the standard.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Introduction \\
                 2: The real numbers \\
                 3: Computer representation of numbers \\
                 4: IEEE floating point representation \\
                 5: Rounding \\
                 6: Correctly rounded floating point operations \\
                 7: Exceptions \\
                 8: The Intel microprocessors \\
                 9: Programming languages \\
                 10: Floating point in C \\
                 11: Cancellation \\
                 12: Conditioning of problems \\
                 13: Stability of algorithms \\
                 14: Conclusion",
}


bibtype: inproceedings
filename: fparith.bib
label: Paliouras:2001:LPP
author: V. Paliouras and T. Stouraitis
title: Low-Power Properties of the Logarithmic Number System
crossref: Burgess:2001:ISC
pages: 229--236
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Paliouras.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: V. Paliouras and T. Stouraitis
rawtitle: Low-Power Properties of the Logarithmic Number System
entry:
@InProceedings{Paliouras:2001:LPP,
  author =       "V. Paliouras and T. Stouraitis",
  title =        "Low-Power Properties of the Logarithmic Number
                 System",
  crossref =     "Burgess:2001:ISC",
  pages =        "229--236",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Paliouras.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Park:2001:ADI
author: Young-Ho Park and Sangtae Jeong and Chang Han Kim and Jongin Lim
title: An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
journal: j-LECT-NOTES-COMP-SCI
volume: 2274
pages: 323--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:07 MDT 2002
bibtimestamp: 2002.09.10 19:09:07 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Young-Ho Park and Sangtae Jeong and Chang Han Kim and Jongin Lim
rawtitle: An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740323.htm; http://link.springer-ny.com/link/service/series/0558/papers/2274/22740323.pdf

entry:
@Article{Park:2001:ADI,
  author =       "Young-Ho Park and Sangtae Jeong and Chang Han Kim and
                 Jongin Lim",
  title =        "An Alternate Decomposition of an Integer for Faster
                 Point Multiplication on Certain Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2274",
  pages =        "323--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:07 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740323.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2274/22740323.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Park:2001:IMM
author: Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin Lim and Maenghee Sung
title: An Improved Method of Multiplication on Certain Elliptic Curves
journal: j-LECT-NOTES-COMP-SCI
volume: 2274
pages: 310--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:07 MDT 2002
bibtimestamp: 2002.09.10 19:09:07 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin Lim and Maenghee Sung
rawtitle: An Improved Method of Multiplication on Certain Elliptic Curves
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740310.htm; http://link.springer-ny.com/link/service/series/0558/papers/2274/22740310.pdf

entry:
@Article{Park:2001:IMM,
  author =       "Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin
                 Lim and Maenghee Sung",
  title =        "An Improved Method of Multiplication on Certain
                 Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2274",
  pages =        "310--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:07 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740310.htm;
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  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Phillips:2001:MMM
author: B. Phillips
booktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
title: Modular multiplication in the Montgomery residue number system
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1637--1640
year: 2001
DOI: https://doi.org/10.1109/ACSSC.2001.987762
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: B. Phillips
rawbooktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
rawtitle: Modular multiplication in the {Montgomery} residue number system
entry:
@InProceedings{Phillips:2001:MMM,
  author =       "B. Phillips",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Modular multiplication in the {Montgomery} residue
                 number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1637--1640",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2001.987762",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper considers the evaluation of long wordlength
                 modular products. An algorithm is described in which
                 long wordlength (e.g. 1024-bit) integers are
                 represented by short-wordlength (e.g. 32-bit)
                 Montgomery (1985) residues. Long integer modular
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Phillips:2001:MRN
author: B. J. Phillips
title: Montgomery residue number systems
journal: j-ELECT-LETTERS
volume: 37
number: 21
pages: 1286--1287
day: 11
month: oct
monthnumber: 10
year: 2001
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:20010852
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=20889
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: B. J. Phillips
rawtitle: {Montgomery} residue number systems
entry:
@Article{Phillips:2001:MRN,
  author =       "B. J. Phillips",
  title =        "{Montgomery} residue number systems",
  journal =      j-ELECT-LETTERS,
  volume =       "37",
  number =       "21",
  pages =        "1286--1287",
  day =          "11",
  month =        oct,
  year =         "2001",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20010852",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=20889",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The Montgomery residue number system (MRNS) for long
                 word-length arithmetic is introduced. MRNS, a
                 modification of the residue number system (RNS),
                 represents a long integer as a set of smaller
                 Montgomery residues. Long integer addition, subtraction
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Phillips:2001:OSL
author: Braden Phillips
title: Optimised Squaring of Long Integers Using Precomputed Partial Products
crossref: Burgess:2001:ISC
pages: 73--82
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Phillips.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Braden Phillips
rawtitle: Optimised Squaring of Long Integers Using Precomputed Partial Products
entry:
@InProceedings{Phillips:2001:OSL,
  author =       "Braden Phillips",
  title =        "Optimised Squaring of Long Integers Using Precomputed
                 Partial Products",
  crossref =     "Burgess:2001:ISC",
  pages =        "73--82",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Phillips.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Pietronero:2001:EUD
author: L. Pietronero and E. Tosatti and V. Tosatti and A. Vespignani
title: Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf
journal: j-PHYSICA-A
volume: 293
pages: 297--304
year: 2001
CODEN: PHYADX
DOI: https://doi.org/10.1016/S0378-4371(00)00633-6
ISSN: 0378-4371 (print), 1873-2119 (electronic) OR 03784371 (print), 18732119 (electronic)
ISSNL: 0378-4371 OR 03784371
bibdate: Thu Feb 15 16:36:18 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 16:36:18 ???
fjournal: Physica A. Statistical Mechanics and its Applications
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784371
rawauthor: L. Pietronero and E. Tosatti and V. Tosatti and A. Vespignani
rawtitle: Explaining the uneven distribution of numbers in nature: the laws of {Benford} and {Zipf}
abstract:
The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the Benford's law in terms of multiplicative processes. We show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity. Finally, we derive a relation between the generalized Benford's law and the popular Zipf's law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics.

rawabstract:
The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the Benford's law in terms of multiplicative processes. We show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity. Finally, we derive a relation between the generalized Benford's law and the popular Zipf's law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics.

entry:
@Article{Pietronero:2001:EUD,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "Explaining the uneven distribution of numbers in
                 nature: the laws of {Benford} and {Zipf}",
  journal =      j-PHYSICA-A,
  volume =       "293",
  number =       "??",
  pages =        "297--304",
  month =        "????",
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00633-6",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 15 16:36:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The distribution of first digits in numbers series
                 obtained from very different origins shows a marked
                 asymmetry in favor of small digits that goes under the
                 name of Benford's law. We analyze in detail this
                 property for different data sets and give a general
                 explanation for the origin of the Benford's law in
                 terms of multiplicative processes. We show that this
                 law can be also generalized to series of numbers
                 generated from more complex systems like the catalogs
                 of seismic activity. Finally, we derive a relation
                 between the generalized Benford's law and the popular
                 Zipf's law which characterize the rank order statistics
                 and has been extensively applied to many problems
                 ranging from city population to linguistics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Pillai:2001:LPA
author: R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili and S. Y. A. Shah
title: A Low Power Approach to Floating Point Adder Design for DSP Applications
journal: j-J-VLSI-SIGNAL-PROC
volume: 27
number: 3
pages: 195--213
month: mar
monthnumber: 3
year: 2001
CODEN: JVSPED
DOI: https://doi.org/10.1023/A:1008140025773
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
bibdate: Thu May 09 09:49:01 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:49:01 ???
fjournal: Journal of VLSI Signal Processing
acknowledgement: ack-nhfb
rawauthor: R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili and S. Y. A. Shah
rawtitle: A Low Power Approach to Floating Point Adder Design for {DSP} Applications
abstract:
The demand for high performance, low power floating point adder cores has been on the rise during the recent years particularly for DSP applications. In this paper, we present a new architecture for a low power, IEEE compatible, floating point adder, that is fast and has low latency. The functional partitioning of the adder into three distinct, clock gated data paths allows activity reduction. The switching activity function of the proposed adder is represented as a three state FSM. During any given operation cycle, only one of the data paths is active, during which time, the logic assertion status of the circuit nodes of the other data paths are held at their previous states. Critical path delay and latency are reduced by incorporating speculative rounding and pseudo leading zero anticipatory logic as well as data path simplifications. In contrast to conventional high speed floating point adders that use leading zero anticipatory logic, the proposed scheme offers a worst case power reduction of 50%.

rawabstract:
The demand for high performance, low power floating point adder cores has been on the rise during the recent years particularly for DSP applications. In this paper, we present a new architecture for a low power, IEEE compatible, floating point adder, that is fast and has low latency. The functional partitioning of the adder into three distinct, clock gated data paths allows activity reduction. The switching activity function of the proposed adder is represented as a three state FSM. During any given operation cycle, only one of the data paths is active, during which time, the logic assertion status of the circuit nodes of the other data paths are held at their previous states. Critical path delay and latency are reduced by incorporating speculative rounding and pseudo leading zero anticipatory logic as well as data path simplifications. In contrast to conventional high speed floating point adders that use leading zero anticipatory logic, the proposed scheme offers a worst case power reduction of 50\%.

entry:
@Article{Pillai:2001:LPA,
  author =       "R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili
                 and S. Y. A. Shah",
  title =        "A Low Power Approach to Floating Point Adder Design
                 for {DSP} Applications",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "27",
  number =       "3",
  pages =        "195--213",
  month =        mar,
  year =         "2001",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008140025773",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Thu May 09 09:49:01 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The demand for high performance, low power floating
                 point adder cores has been on the rise during the
                 recent years particularly for DSP applications. In this
                 paper, we present a new architecture for a low power,
                 IEEE compatible, floating point adder, that is fast and
                 has low latency. The functional partitioning of the
                 adder into three distinct, clock gated data paths
                 allows activity reduction. The switching activity
                 function of the proposed adder is represented as a
                 three state FSM. During any given operation cycle, only
                 one of the data paths is active, during which time, the
                 logic assertion status of the circuit nodes of the
                 other data paths are held at their previous states.
                 Critical path delay and latency are reduced by
                 incorporating speculative rounding and pseudo leading
                 zero anticipatory logic as well as data path
                 simplifications. In contrast to conventional high speed
                 floating point adders that use leading zero
                 anticipatory logic, the proposed scheme offers a worst
                 case power reduction of 50\%.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}


bibtype: inproceedings
filename: fparith.bib
label: Pineiro:2001:FPC
author: J. A. Pineiro and J. D. Bruguera and J.-M. Muller
title: Faithful Powering Computation Using Table Look-Up and a Fused Accumulation Tree
crossref: Burgess:2001:ISC
pages: 40--50
year: 2001
bibdate: Fri May 3 13:52:01 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:52:01 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Pineiro.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: J. A. Pi{\~n}eiro and J. D. Bruguera and J.-M. Muller
rawtitle: Faithful Powering Computation Using Table Look-Up and a Fused Accumulation Tree
entry:
@InProceedings{Pineiro:2001:FPC,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera and J.-M.
                 Muller",
  title =        "Faithful Powering Computation Using Table Look-Up and
                 a Fused Accumulation Tree",
  crossref =     "Burgess:2001:ISC",
  pages =        "40--50",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Pineiro.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  xxnote =       "Check pages: one reference has 40--47??",
}


bibtype: inproceedings
filename: fparith.bib
label: Rajagopal:2001:LAD
author: Sridhar Rajagopal and Joseph R. Cavallaro
title: On-Line Arithmetic for Detection in Digital Communication Receivers
crossref: Burgess:2001:ISC
pages: 257--265
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Rajagopal.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Sridhar Rajagopal and Joseph R. Cavallaro
rawtitle: On-Line Arithmetic for Detection in Digital Communication Receivers
entry:
@InProceedings{Rajagopal:2001:LAD,
  author =       "Sridhar Rajagopal and Joseph R. Cavallaro",
  title =        "On-Line Arithmetic for Detection in Digital
                 Communication Receivers",
  crossref =     "Burgess:2001:ISC",
  pages =        "257--265",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Rajagopal.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: book
filename: fparith.bib
label: Ralston:2001:FCN
author: Anthony Ralston and Philip Rabinowitz
title: A first course in numerical analysis
publisher: pub-DOVER
address: pub-DOVER:adr
edition: Second
pages: xviii + 556 + 50
year: 2001
ISBN: 0-486-41454-X (paperback) OR 048641454X (paperback)
ISBN13: 978-0-486-41454-6 (paperback) OR 9780486414546 (paperback)
LCCN: QA297 .R3 2001
bibdate: Fri Aug 20 10:13:32 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 10:13:32 MDT
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Anthony Ralston and Philip Rabinowitz
rawtitle: A first course in numerical analysis
URL:
http://www.loc.gov/catdir/description/dover032/00064343.html; http://www.loc.gov/catdir/toc/dover031/00064343.html

remark:
This Dover edition, first published in 2001, is an unabridged, slightly corrected republication of the second edition of the work originally published in cite Ralston:1965:FC and issued in a revised second edition in cite Ralston:1978:FCN.

entry:
@Book{Ralston:2001:FCN,
  author =       "Anthony Ralston and Philip Rabinowitz",
  title =        "A first course in numerical analysis",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "xviii + 556 + 50",
  year =         "2001",
  ISBN =         "0-486-41454-X (paperback)",
  ISBN-13 =      "978-0-486-41454-6 (paperback)",
  LCCN =         "QA297 .R3 2001",
  bibdate =      "Fri Aug 20 10:13:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/00064343.html;
                 http://www.loc.gov/catdir/toc/dover031/00064343.html",
  acknowledgement = ack-nhfb,
  remark =       "This Dover edition, first published in 2001, is an
                 unabridged, slightly corrected republication of the
                 second edition of the work originally published in
                 \cite{Ralston:1965:FC} and issued in a revised second
                 edition in \cite{Ralston:1978:FCN}.",
  subject =      "Numerical analysis",
}


bibtype: inproceedings
filename: fparith.bib
label: Rejeb:2001:IDR
author: B. Rejeb and H. Henkelmann and W. Anheier
booktitle: The 8th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2001
title: Integer division in residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 259--262
year: 2001
DOI: https://doi.org/10.1109/ICECS.2001.957729
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: B. Rejeb and H. Henkelmann and W. Anheier
rawbooktitle: The 8th {IEEE} International Conference on Electronics, Circuits and Systems, {ICECS 2001}
rawtitle: Integer division in residue number system
entry:
@InProceedings{Rejeb:2001:IDR,
  author =       "B. Rejeb and H. Henkelmann and W. Anheier",
  booktitle =    "The 8th {IEEE} International Conference on
                 Electronics, Circuits and Systems, {ICECS 2001}",
  title =        "Integer division in residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "259--262",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.2001.957729",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Division, sign detection and number comparison are the
                 more difficult operations in residue number systems
                 (RNS). These shortcomings limited most RNS
                 implementations to additions, subtractions and
                 multiplications. In this paper, a high level \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Reyhani-Masoleh:2001:FNB
author: Arash Reyhani-Masoleh and M. Anwar Hasan
title: Fast Normal Basis Multiplication Using General Purpose Processors
journal: j-LECT-NOTES-COMP-SCI
volume: 2259
pages: 230--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:44 MST 2002
bibtimestamp: 2002.02.02 13:07:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Arash Reyhani-Masoleh and M. Anwar Hasan
rawtitle: Fast Normal Basis Multiplication Using General Purpose Processors
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590230.htm; http://link.springer-ny.com/link/service/series/0558/papers/2259/22590230.pdf

entry:
@Article{Reyhani-Masoleh:2001:FNB,
  author =       "Arash Reyhani-Masoleh and M. Anwar Hasan",
  title =        "Fast Normal Basis Multiplication Using General Purpose
                 Processors",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "230--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590230.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590230.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Rinfret:2001:BSI
author: Denis Rinfret and Patrick O'Neil and Elizabeth O'Neil
title: Bit-sliced index arithmetic
journal: j-SIGMOD
volume: 30
number: 2
pages: 47--57
month: jun
monthnumber: 6
year: 2001
CODEN: SRECD8
ISSN: 0163-5808 (print), 1943-5835 (electronic) OR 01635808 (print), 19435835 (electronic)
ISSNL: 0163-5808 OR 01635808
bibdate: Mon Jan 12 08:46:06 MST 2004
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.01.12 08:46:06 MST
fjournal: ACM SIGMOD Record
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J689
rawauthor: Denis Rinfret and Patrick O'Neil and Elizabeth O'Neil
rawtitle: Bit-sliced index arithmetic
entry:
@Article{Rinfret:2001:BSI,
  author =       "Denis Rinfret and Patrick O'Neil and Elizabeth
                 O'Neil",
  title =        "Bit-sliced index arithmetic",
  journal =      j-SIGMOD,
  volume =       "30",
  number =       "2",
  pages =        "47--57",
  month =        jun,
  year =         "2001",
  CODEN =        "SRECD8",
  ISSN =         "0163-5808 (print), 1943-5835 (electronic)",
  ISSN-L =       "0163-5808",
  bibdate =      "Mon Jan 12 08:46:06 MST 2004",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMOD Record",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J689",
}


bibtype: article
filename: fparith.bib
label: Ring:2001:MPA
author: Michael C. Ring
title: MAPM, A Portable Arbitrary Precision Math Library in C
journal: j-CCCUJ
volume: 19
number: 11
pages: ??--??
month: nov
monthnumber: 11
year: 2001
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Tue May 14 18:09:34 MDT 2002
bibtimestamp: 2002.05.14 18:09:34 MDT
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: Michael C. Ring
rawtitle: {MAPM}, {A} Portable Arbitrary Precision Math Library in {C}
bibsource:
http://www.cuj.com/articles/2001/0111/0111toc.htm?topic=articles; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Frustrated by the finiteness of fixed-size arithmetic? This math library gives you the precision you need.

rawabstract:
Frustrated by the finiteness of fixed-size arithmetic? This math library gives you the precision you need.

entry:
@Article{Ring:2001:MPA,
  author =       "Michael C. Ring",
  title =        "{MAPM}, {A} Portable Arbitrary Precision Math Library
                 in {C}",
  journal =      j-CCCUJ,
  volume =       "19",
  number =       "11",
  pages =        "??--??",
  month =        nov,
  year =         "2001",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:34 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/2001/0111/0111toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Frustrated by the finiteness of fixed-size arithmetic?
                 This math library gives you the precision you need.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: article
filename: fparith.bib
label: Rudra:2001:ERE
author: A. Rudra and P. K. Dubey and C. S. Jutla and V. Kumar and J. R. Rao and P. Rohatgi
title: Efficient Rijndael Encryption Implementation with Composite Field Arithmetic
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 171--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: A. Rudra and P. K. Dubey and C. S. Jutla and V. Kumar and J. R. Rao and P. Rohatgi
rawtitle: Efficient {Rijndael} Encryption Implementation with Composite Field Arithmetic
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620171.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620171.pdf

entry:
@Article{Rudra:2001:ERE,
  author =       "A. Rudra and P. K. Dubey and C. S. Jutla and V. Kumar
                 and J. R. Rao and P. Rohatgi",
  title =        "Efficient {Rijndael} Encryption Implementation with
                 Composite Field Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "171--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620171.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620171.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Rugina:2001:RUD
author: Radu Rugina and Martin Rinard
title: Recursion Unrolling for Divide and Conquer Programs
journal: j-LECT-NOTES-COMP-SCI
volume: 2017
pages: 34--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:03:35 MST 2002
bibtimestamp: 2002.02.02 13:03:35 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Radu Rugina and Martin Rinard
rawtitle: Recursion Unrolling for Divide and Conquer Programs
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2017.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2017/20170034.htm; http://link.springer-ny.com/link/service/series/0558/papers/2017/20170034.pdf

entry:
@Article{Rugina:2001:RUD,
  author =       "Radu Rugina and Martin Rinard",
  title =        "Recursion Unrolling for Divide and Conquer Programs",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2017",
  pages =        "34--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:35 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2017.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2017/20170034.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2017/20170034.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Rump:2001:RPS
author: Siegfried M. Rump
title: Rigorous and Portable Standard Functions
journal: j-BIT-NUM-MATH
volume: 41
number: 3
pages: 540--562
month: jun
monthnumber: 6
year: 2001
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1023/A:1021971313412
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 15:06:04 MST 2006
bibtimestamp: 2006.01.04 15:06:04 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540
keywords: elementary functions; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Siegfried M. Rump
rawtitle: Rigorous and Portable Standard Functions
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3; http://www.mai.liu.se/BIT/contents/bit41.html; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

rawabstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

entry:
@Article{Rump:2001:RPS,
  author =       "Siegfried M. Rump",
  title =        "Rigorous and Portable Standard Functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "540--562",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021971313412",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
  abstract =     "Today's floating point implementations of elementary
                 transcendental functions are usually very accurate.
                 However, with few exceptions, the actual accuracy is
                 not known. In the present paper we describe a rigorous,
                 accurate, fast and portable implementation of the
                 elementary standard functions based on some existing
                 approximate standard functions. The scheme is outlined
                 for IEEE 754, but not difficult to adapt to other
                 floating point formats. A Matlab implementation is
                 available on the net. Accuracy of the proposed
                 algorithms can be rigorously estimated. As an example
                 we prove that the relative accuracy of the exponential
                 function is better than 2.07 eps in a slightly reduced
                 argument range (eps denoting the relative rounding
                 error unit). Otherwise, extensive computational tests
                 suggest for all elementary functions and all suitable
                 arguments an accuracy better than about 3 eps.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions; floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Sakai:2001:PMS
author: Yasuyuki Sakai and Kouichi Sakurai
title: On the Power of Multidoubling in Speeding Up Elliptic Scalar Multiplication
journal: j-LECT-NOTES-COMP-SCI
volume: 2259
pages: 268--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:44 MST 2002
bibtimestamp: 2002.02.02 13:07:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Yasuyuki Sakai and Kouichi Sakurai
rawtitle: On the Power of Multidoubling in Speeding Up Elliptic Scalar Multiplication
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590268.htm; http://link.springer-ny.com/link/service/series/0558/papers/2259/22590268.pdf

entry:
@Article{Sakai:2001:PMS,
  author =       "Yasuyuki Sakai and Kouichi Sakurai",
  title =        "On the Power of Multidoubling in Speeding Up Elliptic
                 Scalar Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "268--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590268.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590268.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Savas:2001:SUM
author: Erkay Savas and Alexandre F. Tenca and Cetin K. Koc
title: A Scalable and Unified Multiplier Architecture for Finite Fields GF$ (p) $ and GF$ (2 m) $
journal: j-LECT-NOTES-COMP-SCI
volume: 1965
pages: 277--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:02:57 MST 2002
bibtimestamp: 2002.02.02 13:02:57 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Erkay Savas and Alexandre F. Tenca and {\c{C}}etin K. Ko{\c{c}}
rawtitle: A Scalable and Unified Multiplier Architecture for Finite Fields {GF}$ (p) $ and {GF}$ (2 m) $
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650277.htm; http://link.springer-ny.com/link/service/series/0558/papers/1965/19650277.pdf

entry:
@Article{Savas:2001:SUM,
  author =       "Erkay Savas and Alexandre F. Tenca and {\c{C}}etin K.
                 Ko{\c{c}}",
  title =        "A Scalable and Unified Multiplier Architecture for
                 Finite Fields {GF}$ (p) $ and {GF}$ (2 m) $",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1965",
  pages =        "277--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650277.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1965/19650277.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Schmookler:2001:LZA
author: Martin S. Schmookler and Kevin J. Nowka
title: Leading Zero Anticipation and Detection --- a Comparison of Methods
crossref: Burgess:2001:ISC
pages: 7--12
year: 2001
DOI: https://doi.org/10.1109/ARITH.2001.930098
bibdate: Fri May 3 13:52:01 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:52:01 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Schmookler.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Martin S. Schmookler and Kevin J. Nowka
rawtitle: Leading Zero Anticipation and Detection --- a Comparison of Methods
abstract:
Design of the leading zero anticipator (LZA) or detector (LZD) is pivotal to the normalization of results for addition and fused multiplication-addition in high-performance floating point processors. This paper formalizes the analysis and describes some alternative organizations and implementations from the known art. It shows how choices made in the design are often dependent on the overall design of the addition unit, on how subtraction is handled when the exponents are the same, and on how it detects and corrects for the possible one-bit error of the LZA.

rawabstract:
Design of the leading zero anticipator (LZA) or detector (LZD) is pivotal to the normalization of results for addition and fused multiplication-addition in high-performance floating point processors. This paper formalizes the analysis and describes some alternative organizations and implementations from the known art. It shows how choices made in the design are often dependent on the overall design of the addition unit, on how subtraction is handled when the exponents are the same, and on how it detects and corrects for the possible one-bit error of the LZA.

entry:
@InProceedings{Schmookler:2001:LZA,
  author =       "Martin S. Schmookler and Kevin J. Nowka",
  title =        "Leading Zero Anticipation and Detection --- a
                 Comparison of Methods",
  crossref =     "Burgess:2001:ISC",
  pages =        "7--12",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930098",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Schmookler.pdf",
  abstract =     "Design of the leading zero anticipator (LZA) or
                 detector (LZD) is pivotal to the normalization of
                 results for addition and fused multiplication-addition
                 in high-performance floating point processors. This
                 paper formalizes the analysis and describes some
                 alternative organizations and implementations from the
                 known art. It shows how choices made in the design are
                 often dependent on the overall design of the addition
                 unit, on how subtraction is handled when the exponents
                 are the same, and on how it detects and corrects for
                 the possible one-bit error of the LZA.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Schonfelder:2001:VPA
author: J. L. Schonfelder
title: Variable Precision Arithmetic: a Fortran 95 Module
journal: j-FORTRAN-FORUM
volume: 20
number: 3
pages: 2--11
month: dec
monthnumber: 12
year: 2001
DOI: https://doi.org/10.1145/570822.570823
ISSN: 1061-7264 (print), 1931-1311 (electronic) OR 10617264 (print), 19311311 (electronic)
ISSNL: 1061-7264 OR 10617264
bibdate: Wed Jun 18 16:26:45 MDT 2008
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.06.18 16:26:45 MDT
fjournal: ACM Fortran Forum
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/toc.cfm?id=J286
issue: 62
rawauthor: J. L. Schonfelder
rawtitle: Variable Precision Arithmetic: a {Fortran 95} Module
abstract:
This paper describes the design and development of a software package supporting variable precision arithmetic as a semantic extension to the core FORTRAN language. The working precision of the arithmetic supported by this package can be dynamically and arbitrarily variable. The facility exploits the data-abstraction capabilities of Fortran 95 and allows the operations to be used elementally with array operands as well as with scalars. The number system is defined in such a way as to be closed under all of the basic operations of normal arithmetic; no program-terminating numerical exceptions can occur. Precision loss situations like underflow and overflow are handled by defining special value representations that preserve as much of the numeric information as is practical and the operation semantics are defined so that these exceptional values propagate as appropriate to reflect this loss of information. The number system uses an essentially conventional variable precision floating-point representation. Where operations can be performed exactly within the currently-set working precision limit, the excess trailing zero digits are not stored, nor do they take part in future operations. This is both economical in storage and improves efficiency. By judiciously managing the working precision, arithmetic operations that are potentially exact can be performed exactly.

rawabstract:
This paper describes the design and development of a software package supporting variable precision arithmetic as a semantic extension to the core FORTRAN language. The working precision of the arithmetic supported by this package can be dynamically and arbitrarily variable. The facility exploits the data-abstraction capabilities of Fortran 95 and allows the operations to be used elementally with array operands as well as with scalars. The number system is defined in such a way as to be closed under all of the basic operations of normal arithmetic; no program-terminating numerical exceptions can occur. Precision loss situations like underflow and overflow are handled by defining special value representations that preserve as much of the numeric information as is practical and the operation semantics are defined so that these exceptional values propagate as appropriate to reflect this loss of information. The number system uses an essentially conventional variable precision floating-point representation. Where operations can be performed exactly within the currently-set working precision limit, the excess trailing zero digits are not stored, nor do they take part in future operations. This is both economical in storage and improves efficiency. By judiciously managing the working precision, arithmetic operations that are potentially exact can be performed exactly.

entry:
@Article{Schonfelder:2001:VPA,
  author =       "J. L. Schonfelder",
  title =        "Variable Precision Arithmetic: a {Fortran 95} Module",
  journal =      j-FORTRAN-FORUM,
  volume =       "20",
  number =       "3",
  pages =        "2--11",
  month =        dec,
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/570822.570823",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Wed Jun 18 16:26:45 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes the design and development of a
                 software package supporting variable precision
                 arithmetic as a semantic extension to the core FORTRAN
                 language. The working precision of the arithmetic
                 supported by this package can be dynamically and
                 arbitrarily variable. The facility exploits the
                 data-abstraction capabilities of Fortran 95 and allows
                 the operations to be used elementally with array
                 operands as well as with scalars. The number system is
                 defined in such a way as to be closed under all of the
                 basic operations of normal arithmetic; no
                 program-terminating numerical exceptions can occur.
                 Precision loss situations like underflow and overflow
                 are handled by defining special value representations
                 that preserve as much of the numeric information as is
                 practical and the operation semantics are defined so
                 that these exceptional values propagate as appropriate
                 to reflect this loss of information. The number system
                 uses an essentially conventional variable precision
                 floating-point representation. Where operations can be
                 performed exactly within the currently-set working
                 precision limit, the excess trailing zero digits are
                 not stored, nor do they take part in future operations.
                 This is both economical in storage and improves
                 efficiency. By judiciously managing the working
                 precision, arithmetic operations that are potentially
                 exact can be performed exactly.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "62",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}


bibtype: inproceedings
filename: fparith.bib
label: Seidel:2001:BMR
author: Peter-Michael Seidel and Lee D. McFearin and David W. Matula
title: Binary Multiplication Radix-$ 32 $ and Radix-$ 256 $
crossref: Burgess:2001:ISC
pages: 23--32
year: 2001
bibdate: Fri May 3 13:52:01 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:52:01 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Peter-Michael Seidel and Lee D. McFearin and David W. Matula
rawtitle: Binary Multiplication Radix-$ 32 $ and Radix-$ 256 $
entry:
@InProceedings{Seidel:2001:BMR,
  author =       "Peter-Michael Seidel and Lee D. McFearin and David W.
                 Matula",
  title =        "Binary Multiplication Radix-$ 32 $ and Radix-$ 256 $",
  crossref =     "Burgess:2001:ISC",
  pages =        "23--32",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: Seidel:2001:DFI
author: Peter-Michael Seidel and Guy Even
title: On the Design of Fast IEEE Floating-Point Adders
crossref: Burgess:2001:ISC
pages: 184--194
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel_Even.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Peter-Michael Seidel and Guy Even
rawtitle: On the Design of Fast {IEEE} Floating-Point Adders
entry:
@InProceedings{Seidel:2001:DFI,
  author =       "Peter-Michael Seidel and Guy Even",
  title =        "On the Design of Fast {IEEE} Floating-Point Adders",
  crossref =     "Burgess:2001:ISC",
  pages =        "184--194",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel_Even.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: inproceedings
filename: fparith.bib
label: Seidel:2001:EAB
author: Peter-Michael Seidel
title: Exact arithmetic based on floating-point numbers
crossref: Kraemer:2001:SCV
pages: 123--??
year: 2001
bibdate: Wed Nov 24 10:53:43 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 10:53:43 ???
acknowledgement: ack-nhfb
rawauthor: Peter-Michael Seidel
rawtitle: Exact arithmetic based on floating-point numbers
entry:
@InProceedings{Seidel:2001:EAB,
  author =       "Peter-Michael Seidel",
  title =        "Exact arithmetic based on floating-point numbers",
  crossref =     "Kraemer:2001:SCV",
  pages =        "123--??",
  year =         "2001",
  bibdate =      "Wed Nov 24 10:53:43 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Smith:2001:AFS
author: David M. Smith
journal: j-TOMS
volume: 27
number: 4
pages: 377--387
month: dec
monthnumber: 12
year: 2001
CODEN: ACMSCU
DOI: https://doi.org/10.1145/504210.504211
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Mar 13 08:49:29 MST 2002
bibsource: http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.03.13 08:49:29 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David M. Smith
title:
Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions

abstract:
A collection of Fortran 90 routines for evaluating the Gamma function and related functions using the FM multiple-precision arithmetic package.

rawabstract:
A collection of Fortran 90 routines for evaluating the Gamma function and related functions using the FM multiple-precision arithmetic package.

rawtitle:
{Algorithm 814}: {Fortran 90} software for floating-point multiple precision arithmetic, gamma and related functions

entry:
@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/504210.504211",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A collection of Fortran 90 routines for evaluating the
                 Gamma function and related functions using the FM
                 multiple-precision arithmetic package.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: misc
filename: fparith.bib
label: Steele:2001:SMFa
author: Guy L. Steele Jr.
title: System and method for floating-point computation
pages: 377--387
day: 04
month: dec
monthnumber: 12
year: 2001
bibdate: Tue Dec 23 15:06:47 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.12.23 15:06:47 ???
URL: http://www.patentstorm.us/patents/6327604/fulltext.html
acknowledgement: ack-nhfb
howpublished: US Patent 6327604
rawauthor: Guy L. {Steele Jr.}
rawtitle: System and method for floating-point computation
abstract:
A system is disclosed for performing floating point computation in connection with numbers in a base floating point representation (such as the representation defined in IEEE Std. 754) that defines a plurality of formats, including a normalized format and a de-normalized format, using a common floating point representation that defines a unitary normalized format. The system includes a base to common representation converter, a processor and a common to base representation converter. The base to common representation converter converts numbers from the base floating point representation to the common floating point representation, so that all numbers involved in a computation will be expressed in the unitary normalized format. The processor is configured to perform a mathematical operation of at least one predetermined type in connection with the converted numbers generated by the base to common representation converter to generate a floating point result in the common representation. The common to base representation converter converts numbers from the common floating point representation selectively to either the normalized or de-normalized format of the base representation.

rawabstract:
A system is disclosed for performing floating point computation in connection with numbers in a base floating point representation (such as the representation defined in IEEE Std. 754) that defines a plurality of formats, including a normalized format and a de-normalized format, using a common floating point representation that defines a unitary normalized format. The system includes a base to common representation converter, a processor and a common to base representation converter. The base to common representation converter converts numbers from the base floating point representation to the common floating point representation, so that all numbers involved in a computation will be expressed in the unitary normalized format. The processor is configured to perform a mathematical operation of at least one predetermined type in connection with the converted numbers generated by the base to common representation converter to generate a floating point result in the common representation. The common to base representation converter converts numbers from the common floating point representation selectively to either the normalized or de-normalized format of the base representation.

entry:
@Misc{Steele:2001:SMFa,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for floating-point computation",
  howpublished = "US Patent 6327604",
  day =          "04",
  month =        dec,
  year =         "2001",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6327604/fulltext.html",
  abstract =     "A system is disclosed for performing floating point
                 computation in connection with numbers in a base
                 floating point representation (such as the
                 representation defined in IEEE Std. 754) that defines a
                 plurality of formats, including a normalized format and
                 a de-normalized format, using a common floating point
                 representation that defines a unitary normalized
                 format. The system includes a base to common
                 representation converter, a processor and a common to
                 base representation converter. The base to common
                 representation converter converts numbers from the base
                 floating point representation to the common floating
                 point representation, so that all numbers involved in a
                 computation will be expressed in the unitary normalized
                 format. The processor is configured to perform a
                 mathematical operation of at least one predetermined
                 type in connection with the converted numbers generated
                 by the base to common representation converter to
                 generate a floating point result in the common
                 representation. The common to base representation
                 converter converts numbers from the common floating
                 point representation selectively to either the
                 normalized or de-normalized format of the base
                 representation.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Steele:2001:SMFb
author: Guy L. Steele Jr.
title: System and method for floating-point computation
pages: 377--387
day: 11
month: sep
monthnumber: 9
year: 2001
bibdate: Tue Dec 23 15:06:47 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.12.23 15:06:47 ???
URL: http://www.patentstorm.us/patents/6289365/fulltext.html
acknowledgement: ack-nhfb
howpublished: US Patent 6289365
rawauthor: Guy L. {Steele Jr.}
rawtitle: System and method for floating-point computation
abstract:
A system is disclosed for performing floating point computation in connection with numbers in a base floating point representation (such as the representation defined in IEEE Std. 754) that defines a plurality of formats, including a normalized format and a de-normalized format, using a common floating point representation that defines a unitary normalized format. The system includes a base to common representation converter, a processor and a common to base representation converter. The base to common representation converter converts numbers from the base floating point representation to the common floating point representation, so that all numbers involved in a computation will be expressed in the unitary normalized format. The processor is configured to perform a mathematical operation of at least one predetermined type in connection with the converted numbers generated by the base to common representation converter to generate a floating point result in the common representation. The common to base representation converter converts numbers from the common floating point representation selectively to either the normalized or denormalized format of the base representation.

rawabstract:
A system is disclosed for performing floating point computation in connection with numbers in a base floating point representation (such as the representation defined in IEEE Std. 754) that defines a plurality of formats, including a normalized format and a de-normalized format, using a common floating point representation that defines a unitary normalized format. The system includes a base to common representation converter, a processor and a common to base representation converter. The base to common representation converter converts numbers from the base floating point representation to the common floating point representation, so that all numbers involved in a computation will be expressed in the unitary normalized format. The processor is configured to perform a mathematical operation of at least one predetermined type in connection with the converted numbers generated by the base to common representation converter to generate a floating point result in the common representation. The common to base representation converter converts numbers from the common floating point representation selectively to either the normalized or denormalized format of the base representation.

entry:
@Misc{Steele:2001:SMFb,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for floating-point computation",
  howpublished = "US Patent 6289365",
  day =          "11",
  month =        sep,
  year =         "2001",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6289365/fulltext.html",
  abstract =     "A system is disclosed for performing floating point
                 computation in connection with numbers in a base
                 floating point representation (such as the
                 representation defined in IEEE Std. 754) that defines a
                 plurality of formats, including a normalized format and
                 a de-normalized format, using a common floating point
                 representation that defines a unitary normalized
                 format. The system includes a base to common
                 representation converter, a processor and a common to
                 base representation converter. The base to common
                 representation converter converts numbers from the base
                 floating point representation to the common floating
                 point representation, so that all numbers involved in a
                 computation will be expressed in the unitary normalized
                 format. The processor is configured to perform a
                 mathematical operation of at least one predetermined
                 type in connection with the converted numbers generated
                 by the base to common representation converter to
                 generate a floating point result in the common
                 representation. The common to base representation
                 converter converts numbers from the common floating
                 point representation selectively to either the
                 normalized or denormalized format of the base
                 representation.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Stine:2001:CIH
author: J. E. Stine and M. J. Schulte
title: A Case for Interval Hardware on Superscalar Processors
crossref: Kraemer:2001:SCV
pages: 53--68
year: 2001
bibdate: Tue Nov 25 12:33:34 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.11.25 12:33:34 ???
keywords: interval arithmetic
acknowledgement: ack-nhfb
rawauthor: J. E. Stine and M. J. Schulte
rawtitle: A Case for Interval Hardware on Superscalar Processors
entry:
@InProceedings{Stine:2001:CIH,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "A Case for Interval Hardware on Superscalar
                 Processors",
  crossref =     "Kraemer:2001:SCV",
  pages =        "53--68",
  year =         "2001",
  bibdate =      "Tue Nov 25 12:33:34 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic",
}


bibtype: phdthesis
filename: fparith.bib
label: Stine:2001:DIA
author: James Edward Stine, Jr.
title: Design issues for accurate and reliable arithmetic
type: Ph.D. Thesis
school: Lehigh University
address: Bethlehem, PA, USA
pages: 53--68
year: 2001
bibdate: Fri Oct 25 17:18:13 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.10.25 17:18:13 ???
acknowledgement: ack-nhfb
rawauthor: James Edward {Stine, Jr.}
rawtitle: Design issues for accurate and reliable arithmetic
URL:
http://wwwlib.umi.com/dissertations/fullcit/9995540; http://wwwlib.umi.com/dissertations/preview/9995540

abstract:
The use of floating-point data types in high-level languages is prevalent in many of today's scientific applications. However, the approximation of real numbers by finite precision floating-point numbers can produce inaccurate results due to round off error and catastrophic cancellation. Interval arithmetic provides a method for monitoring errors in numerical computations, and can provide solutions to problems that cannot be efficiently solved with traditional floating point arithmetic. Although several software tools for interval arithmetic have been developed, these tools have severe performance limitations due to a lack of hardware support for interval arithmetic. This dissertation investigates the design, development, and evaluation of hardware and instruction set support for interval arithmetic. In contrast to previous research, which employed dedicated functional units and coprocessors for interval arithmetic, this research focuses on the integration of interval arithmetic support with traditional IEEE floating point hardware. Novel algorithms and hardware designs for interval arithmetic are developed, and methods for adding interval arithmetic instructions to the instruction set architectures of conventional processors are presented. To evaluate the cost and performance of this approach, hardware designs with support for interval arithmetic have been realized using VHDL and synthesized with the Leonardo/Spectrum tool set from Exemplar. These designs are compared to conventional floating point units in terms of area and delay. Simulations of interval benchmarks both with and without interval hardware support are performed using an interval-enhanced version of the SimpleScalar tool suite and GNU's gcc compiler. The results of these simulations indicate that the proposed hardware support for interval arithmetic improves the execution time of interval operations by a factor 6.3 to 14.9.

rawabstract:
The use of floating-point data types in high-level languages is prevalent in many of today's scientific applications. However, the approximation of real numbers by finite precision floating-point numbers can produce inaccurate results due to round off error and catastrophic cancellation. Interval arithmetic provides a method for monitoring errors in numerical computations, and can provide solutions to problems that cannot be efficiently solved with traditional floating point arithmetic. Although several software tools for interval arithmetic have been developed, these tools have severe performance limitations due to a lack of hardware support for interval arithmetic. This dissertation investigates the design, development, and evaluation of hardware and instruction set support for interval arithmetic. In contrast to previous research, which employed dedicated functional units and coprocessors for interval arithmetic, this research focuses on the integration of interval arithmetic support with traditional IEEE floating point hardware. Novel algorithms and hardware designs for interval arithmetic are developed, and methods for adding interval arithmetic instructions to the instruction set architectures of conventional processors are presented. To evaluate the cost and performance of this approach, hardware designs with support for interval arithmetic have been realized using VHDL and synthesized with the Leonardo/Spectrum tool set from Exemplar. These designs are compared to conventional floating point units in terms of area and delay. Simulations of interval benchmarks both with and without interval hardware support are performed using an interval-enhanced version of the SimpleScalar tool suite and GNU's gcc compiler. The results of these simulations indicate that the proposed hardware support for interval arithmetic improves the execution time of interval operations by a factor 6.3 to 14.9.

entry:
@PhdThesis{Stine:2001:DIA,
  author =       "James Edward {Stine, Jr.}",
  title =        "Design issues for accurate and reliable arithmetic",
  type =         "{Ph.D.} Thesis",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  year =         "2001",
  bibdate =      "Fri Oct 25 17:18:13 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/9995540;
                 http://wwwlib.umi.com/dissertations/preview/9995540",
  abstract =     "The use of floating-point data types in high-level
                 languages is prevalent in many of today's scientific
                 applications. However, the approximation of real
                 numbers by finite precision floating-point numbers can
                 produce inaccurate results due to round off error and
                 catastrophic cancellation. Interval arithmetic provides
                 a method for monitoring errors in numerical
                 computations, and can provide solutions to problems
                 that cannot be efficiently solved with traditional
                 floating point arithmetic. Although several software
                 tools for interval arithmetic have been developed,
                 these tools have severe performance limitations due to
                 a lack of hardware support for interval arithmetic.
                 This dissertation investigates the design, development,
                 and evaluation of hardware and instruction set support
                 for interval arithmetic. In contrast to previous
                 research, which employed dedicated functional units and
                 coprocessors for interval arithmetic, this research
                 focuses on the integration of interval arithmetic
                 support with traditional IEEE floating point hardware.
                 Novel algorithms and hardware designs for interval
                 arithmetic are developed, and methods for adding
                 interval arithmetic instructions to the instruction set
                 architectures of conventional processors are presented.
                 To evaluate the cost and performance of this approach,
                 hardware designs with support for interval arithmetic
                 have been realized using VHDL and synthesized with the
                 Leonardo/Spectrum tool set from Exemplar. These designs
                 are compared to conventional floating point units in
                 terms of area and delay. Simulations of interval
                 benchmarks both with and without interval hardware
                 support are performed using an interval-enhanced
                 version of the SimpleScalar tool suite and GNU's gcc
                 compiler. The results of these simulations indicate
                 that the proposed hardware support for interval
                 arithmetic improves the execution time of interval
                 operations by a factor 6.3 to 14.9.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Stoffel:2001:VIM
author: Dominik Stoffel and Wolfgang Kunz
title: Verification of integer multipliers on the arithmetic bit level
crossref: IEEE:2001:IPI
pages: 183--189
year: 2001
bibdate: Fri Aug 08 08:59:39 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.08 08:59:39 ???
acknowledgement: ack-nhfb
rawauthor: Dominik Stoffel and Wolfgang Kunz
rawtitle: Verification of integer multipliers on the arithmetic bit level
abstract:
One of the most severe short-comings of currently available equivalence checkers is their inability to verify integer multipliers. In this paper, we present a bit level reverse-engineering technique that can be integrated into standard equivalence checking flows. We propose a Boolean mapping algorithm that extracts a network of half adders from the gate netlist of an addition circuit. Once the arithmetic bit level representation of the circuit is obtained, equivalence checking can be performed using simple arithmetic operations. Experimental results show the promise of our approach.

rawabstract:
One of the most severe short-comings of currently available equivalence checkers is their inability to verify integer multipliers. In this paper, we present a bit level reverse-engineering technique that can be integrated into standard equivalence checking flows. We propose a Boolean mapping algorithm that extracts a network of half adders from the gate netlist of an addition circuit. Once the arithmetic bit level representation of the circuit is obtained, equivalence checking can be performed using simple arithmetic operations. Experimental results show the promise of our approach.

entry:
@InProceedings{Stoffel:2001:VIM,
  author =       "Dominik Stoffel and Wolfgang Kunz",
  title =        "Verification of integer multipliers on the arithmetic
                 bit level",
  crossref =     "IEEE:2001:IPI",
  pages =        "183--189",
  year =         "2001",
  bibdate =      "Fri Aug 08 08:59:39 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One of the most severe short-comings of currently
                 available equivalence checkers is their inability to
                 verify integer multipliers. In this paper, we present a
                 bit level reverse-engineering technique that can be
                 integrated into standard equivalence checking flows. We
                 propose a Boolean mapping algorithm that extracts a
                 network of half adders from the gate netlist of an
                 addition circuit. Once the arithmetic bit level
                 representation of the circuit is obtained, equivalence
                 checking can be performed using simple arithmetic
                 operations. Experimental results show the promise of
                 our approach.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sun:2001:NSM
author: Fangyu Sun and Peter Kosmol
title: A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic
journal: j-J-COMPUT-APPL-MATH
volume: 130
number: 1--2
pages: 293--307
day: 1
month: may
monthnumber: 5
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:18 MST 2017
bibtimestamp: 2017.02.25 12:45:18 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042799003751
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Fangyu Sun and Peter Kosmol
rawtitle: A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

entry:
@Article{Sun:2001:NSM,
  author =       "Fangyu Sun and Peter Kosmol",
  title =        "A new simultaneous method of fourth order for finding
                 complex zeros in circular interval arithmetic",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "130",
  number =       "1--2",
  pages =        "293--307",
  day =          "1",
  month =        may,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042799003751",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: fparith.bib
label: Sunar:2001:EON
author: B. Sunar and C. K. Koc
title: An efficient optimal normal basis type II multiplier
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 1
pages: 83--87
month: jan
monthnumber: 1
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.902754
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:03:08 MDT 2011
bibtimestamp: 2011.07.05 10:03:08 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902754
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. Sunar and C. K. Koc
rawtitle: An efficient optimal normal basis type {II} multiplier
entry:
@Article{Sunar:2001:EON,
  author =       "B. Sunar and C. K. Koc",
  title =        "An efficient optimal normal basis type {II}
                 multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "1",
  pages =        "83--87",
  month =        jan,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.902754",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902754",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Takagi:2001:HAC
author: Naofumi Takagi
title: A Hardware Algorithm for Computing Reciprocal Square Root
crossref: Burgess:2001:ISC
pages: 94--100
year: 2001
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/arith15/papers/ARITH15_Takagi.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Naofumi Takagi
rawtitle: A Hardware Algorithm for Computing Reciprocal Square Root
entry:
@InProceedings{Takagi:2001:HAC,
  author =       "Naofumi Takagi",
  title =        "A Hardware Algorithm for Computing Reciprocal Square
                 Root",
  crossref =     "Burgess:2001:ISC",
  pages =        "94--100",
  year =         "2001",
  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/arith15/papers/ARITH15_Takagi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  summary =      "A hardware algorithm for computing the reciprocal
                 square root which appears frequently in multimedia and
                 graphics applications is proposed. The reciprocal
                 square root is computed by iteration of
                 carry-propagation-free additions, shifts, and
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Tasche:2001:WAC
author: Manfred Tasche and Hansmartin Zeuner
title: Worst and average case roundoff error analysis for FFT
journal: j-BIT-NUM-MATH
volume: 41
number: 3
pages: 563--581
month: jun
monthnumber: 6
year: 2001
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1023/A:1021923430250
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 15:06:04 MST 2006
bibtimestamp: 2006.01.04 15:06:04 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=563
keywords: Fast Fourier Transform (FFT); floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Manfred Tasche and Hansmartin Zeuner
rawtitle: Worst and average case roundoff error analysis for {FFT}
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3; http://www.mai.liu.se/BIT/contents/bit41.html; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Tasche:2001:WAC,
  author =       "Manfred Tasche and Hansmartin Zeuner",
  title =        "Worst and average case roundoff error analysis for
                 {FFT}",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "563--581",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021923430250",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=563",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Fast Fourier Transform (FFT); floating-point
                 arithmetic; rounding errors",
}


bibtype: inproceedings
filename: fparith.bib
label: Tenca:2001:DRL
author: Alexandre F. Tenca and Syed Ubaid Hussaini
title: A Design of Radix-$2$ On-Line Division Using LSA Organization
crossref: Burgess:2001:ISC
pages: 266--276
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Tenca.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: Alexandre F. Tenca and Syed Ubaid Hussaini
rawtitle: A Design of Radix-$2$ On-Line Division Using {LSA} Organization
entry:
@InProceedings{Tenca:2001:DRL,
  author =       "Alexandre F. Tenca and Syed Ubaid Hussaini",
  title =        "A Design of Radix-$2$ On-Line Division Using {LSA}
                 Organization",
  crossref =     "Burgess:2001:ISC",
  pages =        "266--276",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Tenca.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Tenca:2001:HRD
author: A. F. Tenca and G. Todorov and C.K. Koc
title: High-Radix Design of a Scalable Modular Multiplier
journal: j-LECT-NOTES-COMP-SCI
volume: 2162
pages: 185--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:06:06 MST 2002
bibtimestamp: 2002.02.02 13:06:06 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: A. F. Tenca and G. Todorov and {\c{C}}.K. Ko{\c{c}}
rawtitle: High-Radix Design of a Scalable Modular Multiplier
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620185.htm; http://link.springer-ny.com/link/service/series/0558/papers/2162/21620185.pdf

entry:
@Article{Tenca:2001:HRD,
  author =       "A. F. Tenca and G. Todorov and {\c{C}}.K. Ko{\c{c}}",
  title =        "High-Radix Design of a Scalable Modular Multiplier",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "185--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620185.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620185.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Thompson:2001:BPC
author: D. U. Thompson and B. A. Wooley
title: A 15-b pipelined CMOS floating-point A/D converter
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 36
number: 2
pages: 299--303
month: feb
monthnumber: 2
year: 2001
CODEN: IJSCBC
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
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 Journal of Solid-State Circuits
acknowledgement: ack-nhfb
rawauthor: D. U. Thompson and B. A. Wooley
rawtitle: A 15-b pipelined {CMOS} floating-point {A/D} converter
entry:
@Article{Thompson:2001:BPC,
  author =       "D. U. Thompson and B. A. Wooley",
  title =        "A 15-b pipelined {CMOS} floating-point {A/D}
                 converter",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "36",
  number =       "2",
  pages =        "299--303",
  month =        feb,
  year =         "2001",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  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 Journal of Solid-State Circuits",
  summary =      "A floating-point approach can be used to extend the
                 dynamic range of analog-to-digital (A/D) converters in
                 applications where large signals need not be encoded
                 with a precision greater than that required for small
                 signals. Owing to the nonuniform nature \ldots{}",
}


bibtype: manual
filename: fparith.bib
label: TI:2001:TTPa
title: TI-89 / TI-92 Plus Sierra C Assembler Reference Manual, Beta Version .02
organization: Texas Instruments
address: Post Office box 655303, Dallas, TX 75265, USA
pages: 322
year: 2001
bibdate: Thu Nov 25 09:44:52 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.25 09:44:52 ???
acknowledgement: ack-nhfb
rawtitle: {TI-89\slash TI-92 Plus Sierra C} Assembler Reference Manual, Beta Version .02
entry:
@Manual{TI:2001:TTPa,
  title =        "{TI-89\slash TI-92 Plus Sierra C} Assembler Reference
                 Manual, Beta Version .02",
  organization = "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  pages =        "322",
  year =         "2001",
  bibdate =      "Thu Nov 25 09:44:52 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: manual
filename: fparith.bib
label: TI:2001:TTPb
title: TI-89 / TI-92 Plus Developers Guide, Beta Version .02
organization: Texas Instruments
address: Post Office box 655303, Dallas, TX 75265, USA
pages: 1356
year: 2001
bibdate: Thu Nov 25 09:44:52 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.25 09:44:52 ???
acknowledgement: ack-nhfb
rawtitle: {TI-89\slash TI-92 Plus} Developers Guide, Beta Version .02
entry:
@Manual{TI:2001:TTPb,
  title =        "{TI-89\slash TI-92 Plus} Developers Guide, Beta
                 Version .02",
  organization = "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  pages =        "1356",
  year =         "2001",
  bibdate =      "Thu Nov 25 09:44:52 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Tisseur:2001:NMF
author: Francoise Tisseur
journal: j-SIAM-J-MAT-ANA-APPL
volume: 22
number: 4
pages: 1038--1057
year: 2001
CODEN: SJMAEL
DOI: https://doi.org/10.1137/S0895479899359837
ISSN: 0895-4798 (print), 1095-7162 (electronic) OR 08954798 (print), 10957162 (electronic)
ISSNL: 0895-4798 OR 08954798
MRclass: 65F15 (65F35)
MRnumber: MR1824056 (2002b:65061)
MRreviewer: Raffaella Pavani
bibdate: Tue Feb 11 14:17:49 MST 2014
bibtimestamp: 2014.02.11 14:17:49 MST
fjournal: SIAM Journal on Matrix Analysis and Applications
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/simax
onlinedate: January 2001
rawauthor: Fran{\c{c}}oise Tisseur
title:
Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems

bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/4; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib

rawtitle:
{Newton}'s Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems

entry:
@Article{Tisseur:2001:NMF,
  author =       "Fran{\c{c}}oise Tisseur",
  title =        "{Newton}'s Method in Floating Point Arithmetic and
                 Iterative Refinement of Generalized Eigenvalue
                 Problems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "4",
  pages =        "1038--1057",
  month =        "????",
  year =         "2001",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479899359837",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15 (65F35)",
  MRnumber =     "MR1824056 (2002b:65061)",
  MRreviewer =   "Raffaella Pavani",
  bibdate =      "Tue Feb 11 14:17:49 MST 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2001",
}


bibtype: article
filename: fparith.bib
label: Trichina:2001:SAM
author: Elena Trichina and Alex Tiountchik
journal: j-LECT-NOTES-COMP-SCI
volume: 2020
pages: 235--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:03:38 MST 2002
bibtimestamp: 2002.02.02 13:03:38 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Elena Trichina and Alex Tiountchik
title:
Scalable Algorithm for Montgomery Multiplication and Its Implementation on the Coarse-Grain Reconfigurable Chip

bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2020.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2020/20200235.htm; http://link.springer-ny.com/link/service/series/0558/papers/2020/20200235.pdf

rawtitle:
Scalable Algorithm for {Montgomery} Multiplication and Its Implementation on the Coarse-Grain Reconfigurable Chip

entry:
@Article{Trichina:2001:SAM,
  author =       "Elena Trichina and Alex Tiountchik",
  title =        "Scalable Algorithm for {Montgomery} Multiplication and
                 Its Implementation on the Coarse-Grain Reconfigurable
                 Chip",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2020",
  pages =        "235--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:38 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2020.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2020/20200235.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2020/20200235.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Um:2001:OAC
author: Junhyung Um and Taewhan Kim
title: An optimal allocation of carry-save-adders in arithmetic circuits
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 3
pages: 215--233
month: mar
monthnumber: 3
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.910813
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:03:09 MDT 2011
bibtimestamp: 2011.07.05 10:03:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=910813
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Junhyung Um and Taewhan Kim
rawtitle: An optimal allocation of carry-save-adders in arithmetic circuits
entry:
@Article{Um:2001:OAC,
  author =       "Junhyung Um and Taewhan Kim",
  title =        "An optimal allocation of carry-save-adders in
                 arithmetic circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "3",
  pages =        "215--233",
  month =        mar,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.910813",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=910813",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Verdonk:2001:PRIa
author: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
journal: j-TOMS
volume: 27
number: 1
pages: 92--118
month: mar
monthnumber: 3
year: 2001
CODEN: ACMSCU
DOI: https://doi.org/10.1145/382043.382404
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibsource: http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.02.06 16:43:42 MST
URL: http://www.win.ua.ac.be/~cant/ieeecc754.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
title:
A precision- and range-independent tool for testing floating-point arithmetic I: Basic operations, square root, and remainder

abstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

keywords:
arithmetic; floating-point testing; IEEE floating-point standard; multiprecision; validation; Verification

subject:
Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.0 General Subjects: Standards

rawabstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50\% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

rawtitle:
A precision- and range-independent tool for testing floating-point arithmetic {I}: {Basic} operations, square root, and remainder

entry:
@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {I}: {Basic} operations,
                 square root, and remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "This paper introduces a precision- and
                 range-independent tool for testing the compliance of
                 hardware or software implementations of
                 (multiprecision) floating-point arithmetic with the
                 principles of the IEEE standards 754 and 854. The tool
                 consists of a driver program, offering many options to
                 test only specific aspects of the IEEE standards, and a
                 large set of test vectors, encoded in a
                 precision-independent syntax to allow the testing of
                 basic and extended hardware formats as well as
                 multiprecision floating-point implementations. The
                 suite of test vectors stems on one hand from the
                 integration and fully precision- and range-independent
                 generalization of existing hardware test sets, and on
                 the other hand from the systematic testing of exact
                 rounding for all combinations of round and sticky bits
                 that can occur. The former constitutes only 50\% of the
                 resulting test set. In the latter we especially focus
                 on hard-to-round cases. In addition, the test suite
                 implicitly tests properties of floating-point
                 operations, following the idea of Paranoia, and it
                 reports which of the three IEEE-compliant underflow
                 mechanisms is used by the floating-point implementation
                 under consideration. We also check whether that
                 underflow mechanism is used consistently. The tool is
                 backward compatible with the UCBTEST package and with
                 Coonen's test syntax.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; floating-point testing; IEEE
                 floating-point standard; multiprecision; validation;
                 Verification",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
                 arithmetic\\
                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.0 General Subjects: Standards",
}


bibtype: article
filename: fparith.bib
label: Verdonk:2001:PRIb
author: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
title: A precision- and range-independent tool for testing floating-point arithmetic II: conversions
journal: j-TOMS
volume: 27
number: 1
pages: 119--140
month: mar
monthnumber: 3
year: 2001
CODEN: ACMSCU
DOI: https://doi.org/10.1145/382043.382405
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
URL: http://www.win.ua.ac.be/~cant/ieeecc754.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: decimal floating-point arithmetic; floating-point testing
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
rawtitle: A precision- and range-independent tool for testing floating-point arithmetic {II}: conversions
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
The IEEE 754 and 854 standards for floating-point arithmetic are essentially a specification of a programming environment, encompassing aspects from computer hardware, operating systems and compilers to programming languages (see especially section 8). Part I and II of this paper together describe a tool to test floating-point implementations of arbitrary precision and exponent range (hardware as well as software) for compliance with the principles outlined in the IEEE standards. The tool consists of a driver program, together with a very large set of test vectors encoded in a precision independent syntax.par In Part I we have covered the testing of the basic operations +, -, $ times $, /, the square root and remainder functions. In Part II we describe the extension of the test tool to deal with conversions between floating-point formats, conversions between floating-point and integer formats, the rounding of floating-point numbers to integral values and last but not least binary-decimal conversions. Conversions can now be tested from a floating-point format of arbitrary precision and exponent range to another arbitrary smaller (larger) floating-point format as well as to and from fixed hardware integer formats. Conversions between the bases 2 and 10 can be tested for a number of precisions ranging from single (24 bits), double (53 bits), long double or extended (64 bits) to quadruple (113 bits) precision and a proper multiprecision (240 bits) format.par We conclude Part II with some applications of our test tool and report on the results of testing various floating-point implementations, meaning various language-compiler-hardware combinations as well as multiprecision libraries.

rawabstract:
The IEEE 754 and 854 standards for floating-point arithmetic are essentially a specification of a programming environment, encompassing aspects from computer hardware, operating systems and compilers to programming languages (see especially section 8). Part I and II of this paper together describe a tool to test floating-point implementations of arbitrary precision and exponent range (hardware as well as software) for compliance with the principles outlined in the IEEE standards. The tool consists of a driver program, together with a very large set of test vectors encoded in a precision independent syntax.\par In Part I we have covered the testing of the basic operations +, -, $ \times $, /, the square root and remainder functions. In Part II we describe the extension of the test tool to deal with conversions between floating-point formats, conversions between floating-point and integer formats, the rounding of floating-point numbers to integral values and last but not least binary-decimal conversions. Conversions can now be tested from a floating-point format of arbitrary precision and exponent range to another arbitrary smaller (larger) floating-point format as well as to and from fixed hardware integer formats. Conversions between the bases 2 and 10 can be tested for a number of precisions ranging from single (24 bits), double (53 bits), long double or extended (64 bits) to quadruple (113 bits) precision and a proper multiprecision (240 bits) format.\par We conclude Part II with some applications of our test tool and report on the results of testing various floating-point implementations, meaning various language-compiler-hardware combinations as well as multiprecision libraries.

entry:
@Article{Verdonk:2001:PRIb,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {II}: conversions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "119--140",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382405",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "The IEEE 754 and 854 standards for floating-point
                 arithmetic are essentially a specification of a
                 programming environment, encompassing aspects from
                 computer hardware, operating systems and compilers to
                 programming languages (see especially section 8). Part
                 I and II of this paper together describe a tool to test
                 floating-point implementations of arbitrary precision
                 and exponent range (hardware as well as software) for
                 compliance with the principles outlined in the IEEE
                 standards. The tool consists of a driver program,
                 together with a very large set of test vectors encoded
                 in a precision independent syntax.\par

                 In Part I we have covered the testing of the basic
                 operations +, -, $ \times $, /, the square root and
                 remainder functions. In Part II we describe the
                 extension of the test tool to deal with conversions
                 between floating-point formats, conversions between
                 floating-point and integer formats, the rounding of
                 floating-point numbers to integral values and last but
                 not least binary-decimal conversions. Conversions can
                 now be tested from a floating-point format of arbitrary
                 precision and exponent range to another arbitrary
                 smaller (larger) floating-point format as well as to
                 and from fixed hardware integer formats. Conversions
                 between the bases 2 and 10 can be tested for a number
                 of precisions ranging from single (24 bits), double (53
                 bits), long double or extended (64 bits) to quadruple
                 (113 bits) precision and a proper multiprecision (240
                 bits) format.\par

                 We conclude Part II with some applications of our test
                 tool and report on the results of testing various
                 floating-point implementations, meaning various
                 language-compiler-hardware combinations as well as
                 multiprecision libraries.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "decimal floating-point arithmetic; floating-point
                 testing",
}


bibtype: inproceedings
filename: fparith.bib
label: Vergos:2001:HSP
author: H. T. Vergos and C. Efstathiou and D. Nikolos
title: High Speed Parallel-Prefix Modulo $ 2^n + 1 $ Adders for Diminished-One Operands
crossref: Burgess:2001:ISC
pages: 211--217
year: 2001
bibdate: Fri May 3 13:58:18 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database
bibtimestamp: 2002.05.03 13:58:18 MDT
URL: http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Vergos.pdf
keywords: ARITH-15
acknowledgement: ack-nhfb
rawauthor: H. T. Vergos and C. Efstathiou and D. Nikolos
rawtitle: High Speed Parallel-Prefix Modulo $ 2^{n + 1} $ Adders for Diminished-One Operands
entry:
@InProceedings{Vergos:2001:HSP,
  author =       "H. T. Vergos and C. Efstathiou and D. Nikolos",
  title =        "High Speed Parallel-Prefix Modulo $ 2^{n + 1} $ Adders
                 for Diminished-One Operands",
  crossref =     "Burgess:2001:ISC",
  pages =        "211--217",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Vergos.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}


bibtype: article
filename: fparith.bib
label: Visavakul:2001:DSS
author: Chakkapas Visavakul and Peter Y. K. Cheung and Wayne Luk
title: A Digit-Serial Structure for Reconfigurable Multipliers
journal: j-LECT-NOTES-COMP-SCI
volume: 2147
pages: 565--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:49 MST 2002
bibtimestamp: 2002.02.02 13:05:49 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Chakkapas Visavakul and Peter Y. K. Cheung and Wayne Luk
rawtitle: A Digit-Serial Structure for Reconfigurable Multipliers
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470565.htm; http://link.springer-ny.com/link/service/series/0558/papers/2147/21470565.pdf

entry:
@Article{Visavakul:2001:DSS,
  author =       "Chakkapas Visavakul and Peter Y. K. Cheung and Wayne
                 Luk",
  title =        "A Digit-Serial Structure for Reconfigurable
                 Multipliers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2147",
  pages =        "565--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470565.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2147/21470565.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Walter:2001:DIH
author: Colin D. Walter
title: Data Integrity in Hardware for Modular Arithmetic
journal: j-LECT-NOTES-COMP-SCI
volume: 1965
pages: 204--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:02:57 MST 2002
bibtimestamp: 2002.02.02 13:02:57 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Colin D. Walter
rawtitle: Data Integrity in Hardware for Modular Arithmetic
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650204.htm; http://link.springer-ny.com/link/service/series/0558/papers/1965/19650204.pdf

entry:
@Article{Walter:2001:DIH,
  author =       "Colin D. Walter",
  title =        "Data Integrity in Hardware for Modular Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1965",
  pages =        "204--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650204.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1965/19650204.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Walter:2001:PBM
author: Colin D. Walter
title: Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli
journal: j-LECT-NOTES-COMP-SCI
volume: 2271
pages: 30--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:06 MDT 2002
bibtimestamp: 2002.09.10 19:09:06 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Colin D. Walter
rawtitle: Precise Bounds for {Montgomery} Modular Multiplication and Some Potentially Insecure {RSA} Moduli
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2271.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2271/22710030.htm; http://link.springer-ny.com/link/service/series/0558/papers/2271/22710030.pdf

entry:
@Article{Walter:2001:PBM,
  author =       "Colin D. Walter",
  title =        "Precise Bounds for {Montgomery} Modular Multiplication
                 and Some Potentially Insecure {RSA} Moduli",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2271",
  pages =        "30--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:06 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2271.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2271/22710030.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2271/22710030.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Walters:2001:CUT
author: E. G. Walters and J. Schlessman and M. J. Schulte
title: Combined Unsigned and Two's Complement Hybrid Squarers
crossref: Matthews:2001:CRT
pages: 861--866
year: 2001
bibdate: Sun Mar 04 11:46:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:46:37 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2001-08.pdf
acknowledgement: ack-nhfb
rawauthor: E. G. Walters and J. Schlessman and M. J. Schulte
rawtitle: Combined Unsigned and Two's Complement Hybrid Squarers
entry:
@InProceedings{Walters:2001:CUT,
  author =       "E. G. Walters and J. Schlessman and M. J. Schulte",
  title =        "Combined Unsigned and Two's Complement Hybrid
                 Squarers",
  crossref =     "Matthews:2001:CRT",
  pages =        "861--866",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:46:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-08.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Wang:2001:LPF
author: Wei Wang and M. N. S. Swamy and M. O. Ahmad
booktitle: MWSCAS 2001, Proceedings of the 44th IEEE 2001 Midwest Symposium on Circuits and Systems
title: Low power FIR filter FPGA implementation based on distributed arithmetic and residue number system
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 102--105
year: 2001
DOI: https://doi.org/10.1109/MWSCAS.2001.986125
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Wei Wang and M. N. S. Swamy and M. O. Ahmad
rawbooktitle: {MWSCAS 2001}, Proceedings of the 44th {IEEE 2001} Midwest Symposium on Circuits and Systems
rawtitle:
Low power {FIR} filter {FPGA} implementation based on distributed arithmetic and residue number system

entry:
@InProceedings{Wang:2001:LPF,
  author =       "Wei Wang and M. N. S. Swamy and M. O. Ahmad",
  booktitle =    "{MWSCAS 2001}, Proceedings of the 44th {IEEE 2001}
                 Midwest Symposium on Circuits and Systems",
  title =        "Low power {FIR} filter {FPGA} implementation based on
                 distributed arithmetic and residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "102--105",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.2001.986125",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper, several low power techniques are
                 proposed for the FPGA implementation of a distributed
                 arithmetic and residue number system-based FIR filter.
                 Two algorithms are proposed to reduce the size of the
                 residue-to-binary converter, which is \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Wires:2001:FRR
author: K. E. Wires and M. J. Schulte and D. McCarley
title: FPGA Resource Reduction Through Truncated Multiplication
crossref: Brebner:2001:FLA
pages: 574--583
year: 2001
DOI: https://doi.org/10.1007/3-540-44687-7_59
bibdate: Sun Mar 04 11:42:02 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 11:42:02 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2001-04.pdf
acknowledgement: ack-nhfb
rawauthor: K. E. Wires and M. J. Schulte and D. McCarley
rawtitle: {FPGA} Resource Reduction Through Truncated Multiplication
entry:
@InProceedings{Wires:2001:FRR,
  author =       "K. E. Wires and M. J. Schulte and D. McCarley",
  title =        "{FPGA} Resource Reduction Through Truncated
                 Multiplication",
  crossref =     "Brebner:2001:FLA",
  pages =        "574--583",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/3-540-44687-7_59",
  bibdate =      "Sun Mar 04 11:42:02 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-04.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Wirthlin:2001:ECC
author: Michael J. Wirthlin and Brian McMurtrey
title: Efficient Constant Coefficient Multiplication Using Advanced FPGA Architectures
journal: j-LECT-NOTES-COMP-SCI
volume: 2147
pages: 555--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:49 MST 2002
bibtimestamp: 2002.02.02 13:05:49 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Michael J. Wirthlin and Brian McMurtrey
rawtitle: Efficient Constant Coefficient Multiplication Using Advanced {FPGA} Architectures
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470555.htm; http://link.springer-ny.com/link/service/series/0558/papers/2147/21470555.pdf

entry:
@Article{Wirthlin:2001:ECC,
  author =       "Michael J. Wirthlin and Brian McMurtrey",
  title =        "Efficient Constant Coefficient Multiplication Using
                 Advanced {FPGA} Architectures",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2147",
  pages =        "555--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470555.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2147/21470555.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Wright:2001:EFP
author: Stephen J. Wright
title: Effects of Finite-Precision Arithmetic on Interior-Point Methods for Nonlinear Programming
journal: j-SIAM-J-OPT
volume: 12
number: 1
pages: 36--78
month: may
monthnumber: 5
year: 2001
CODEN: SJOPE8
DOI: https://doi.org/10.1137/S1052623498347438
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 90C51 (90C30 90C33)
MRnumber: MR1870586 (2002j:90107)
MRreviewer: Levent Tun{\c{c}}el
bibdate: Sat Oct 4 12:16:05 MDT 2003
bibtimestamp: 2003.10.04 12:16:05 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/34743
fjournal: SIAM Journal on Optimization
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siopt
rawauthor: Stephen J. Wright
rawtitle: Effects of Finite-Precision Arithmetic on Interior-Point Methods for Nonlinear Programming
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/12/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database

entry:
@Article{Wright:2001:EFP,
  author =       "Stephen J. Wright",
  title =        "Effects of Finite-Precision Arithmetic on
                 Interior-Point Methods for Nonlinear Programming",
  journal =      j-SIAM-J-OPT,
  volume =       "12",
  number =       "1",
  pages =        "36--78",
  month =        may # "\slash " # oct,
  year =         "2001",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/S1052623498347438",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "90C51 (90C30 90C33)",
  MRnumber =     "MR1870586 (2002j:90107)",
  MRreviewer =   "Levent Tun{\c{c}}el",
  bibdate =      "Sat Oct 4 12:16:05 MDT 2003",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/12/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/34743",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
}


bibtype: article
filename: fparith.bib
label: Wu:2001:MMSa
author: Huapeng Wu
title: Montgomery Multiplier and Squarer in GF$ (2^m) $
journal: j-LECT-NOTES-COMP-SCI
volume: 1965
pages: 264--276
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:02:57 MST 2002
bibtimestamp: 2002.02.02 13:02:57 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Huapeng Wu
rawtitle: {Montgomery} Multiplier and Squarer in {GF$ (2^m) $}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650264.htm; http://link.springer-ny.com/link/service/series/0558/papers/1965/19650264.pdf

entry:
@Article{Wu:2001:MMSa,
  author =       "Huapeng Wu",
  title =        "{Montgomery} Multiplier and Squarer in {GF$ (2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1965",
  pages =        "264--276",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650264.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1965/19650264.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Yamauchi:2001:AOO
author: Tsukasa Yamauchi and Shogo Nakaya and Takeshi Inuo and Nobuki Kajihara
title: Arithmetic Operation Oriented Reconfigurable Chip: RHW
journal: j-LECT-NOTES-COMP-SCI
volume: 2147
pages: 618--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:05:49 MST 2002
bibtimestamp: 2002.02.02 13:05:49 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Tsukasa Yamauchi and Shogo Nakaya and Takeshi Inuo and Nobuki Kajihara
rawtitle: Arithmetic Operation Oriented Reconfigurable Chip: {RHW}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470618.htm; http://link.springer-ny.com/link/service/series/0558/papers/2147/21470618.pdf

entry:
@Article{Yamauchi:2001:AOO,
  author =       "Tsukasa Yamauchi and Shogo Nakaya and Takeshi Inuo and
                 Nobuki Kajihara",
  title =        "Arithmetic Operation Oriented Reconfigurable Chip:
                 {RHW}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2147",
  pages =        "618--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470618.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2147/21470618.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Yang:2001:MDD
author: Lie-Liang Yang and L. Hanzo
booktitle: ICC 2001. IEEE International Conference on Communications. 11--14 June 2001
title: Minimum-distance decoding of redundant residue number system codes
volume: 10
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2975--2979
year: 2001
DOI: https://doi.org/10.1109/ICC.2001.937218
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Lie-Liang Yang and L. Hanzo
rawbooktitle: {ICC 2001}. {IEEE} International Conference on Communications. 11--14 June 2001
rawtitle: Minimum-distance decoding of redundant residue number system codes
entry:
@InProceedings{Yang:2001:MDD,
  author =       "Lie-Liang Yang and L. Hanzo",
  booktitle =    "{ICC 2001}. {IEEE} International Conference on
                 Communications. 11--14 June 2001",
  title =        "Minimum-distance decoding of redundant residue number
                 system codes",
  volume =       "10",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2975--2979",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICC.2001.937218",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this contribution the conventional error-detection
                 and error-correction algorithms used for RRNS codes are
                 improved and unified in the context of a so-called
                 projection-based `minimum-distance decoding' algorithm,
                 which can efficiently detect or \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Yang:2001:RRN
author: Lie-Liang Yang and L. Hanzo
booktitle: VTC 2001 Fall. IEEE VTS 54th Vehicular Technology Conference
title: Redundant residue number system based error correction codes
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1472--1476
year: 2001
DOI: https://doi.org/10.1109/VTC.2001.956442
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Lie-Liang Yang and L. Hanzo
rawbooktitle: {VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular Technology Conference
rawtitle: Redundant residue number system based error correction codes
entry:
@InProceedings{Yang:2001:RRN,
  author =       "Lie-Liang Yang and L. Hanzo",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Redundant residue number system based error correction
                 codes",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1472--1476",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.956442",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper residue number system (RNS) arithmetic
                 and redundant residue number system (RRNS) based codes
                 as well as their properties are reviewed. We propose a
                 number of applications for RRNS codes and demonstrate
                 how RRNS codes can be employed \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Yeh:2001:RAO
author: Thomas Y. Yeh and Hong Wang
title: Redundant Arithmetic Optimizations (Research Note)
journal: j-LECT-NOTES-COMP-SCI
volume: 1900
pages: 984--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:02:44 MST 2002
bibtimestamp: 2002.02.02 13:02:44 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Thomas Y. Yeh and Hong Wang
rawtitle: Redundant Arithmetic Optimizations (Research Note)
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1900.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1900/19000984.htm; http://link.springer-ny.com/link/service/series/0558/papers/1900/19000984.pdf

entry:
@Article{Yeh:2001:RAO,
  author =       "Thomas Y. Yeh and Hong Wang",
  title =        "Redundant Arithmetic Optimizations (Research Note)",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1900",
  pages =        "984--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1900.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1900/19000984.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1900/19000984.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Yu:2001:DID
author: Sungwook Yu and E. E. Swartzlander, Jr.
title: DCT implementation with distributed arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: 50
number: 9
pages: 985--991
month: sep
monthnumber: 9
year: 2001
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.954513
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 10:03:12 MDT 2011
bibtimestamp: 2011.07.05 10:03:12 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=954513
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Sungwook Yu and E. E. {Swartzlander, Jr.}
rawtitle: {DCT} implementation with distributed arithmetic
entry:
@Article{Yu:2001:DID,
  author =       "Sungwook Yu and E. E. {Swartzlander, Jr.}",
  title =        "{DCT} implementation with distributed arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "9",
  pages =        "985--991",
  month =        sep,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.954513",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=954513",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Zhang:2001:FSM
author: Fangguo Zhang and Futai Zhang and Yumin Wang
title: Fast Scalar Multiplication on the Jacobian of a Family of Hyperelliptic Curves
journal: j-LECT-NOTES-COMP-SCI
volume: 2229
pages: 74--??
year: 2001
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Feb 2 13:07:15 MST 2002
bibtimestamp: 2002.02.02 13:07:15 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Fangguo Zhang and Futai Zhang and Yumin Wang
rawtitle: Fast Scalar Multiplication on the {Jacobian} of a Family of Hyperelliptic Curves
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290074.htm; http://link.springer-ny.com/link/service/series/0558/papers/2229/22290074.pdf

entry:
@Article{Zhang:2001:FSM,
  author =       "Fangguo Zhang and Futai Zhang and Yumin Wang",
  title =        "Fast Scalar Multiplication on the {Jacobian} of a
                 Family of Hyperelliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2229",
  pages =        "74--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:15 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290074.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2229/22290074.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Zhang:2001:NCP
author: Hong Zhang
title: Numerical condition of polynomials in different forms
journal: j-ELECTRON-TRANS-NUMER-ANAL
volume: 12
pages: 66--87
year: 2001
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: https://www.math.utah.edu/pub/tex/bib/etna.bib; 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.12.2001/pp66-87.dir/pp66-87.pdf
fjournal: Electronic Transactions on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://etna.mcs.kent.edu/
rawauthor: Hong Zhang
rawtitle: Numerical condition of polynomials in different forms
entry:
@Article{Zhang:2001:NCP,
  author =       "Hong Zhang",
  title =        "Numerical condition of polynomials in different
                 forms",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "12",
  pages =        "66--87",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  bibdate =      "Mon Sep 6 12:28:29 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/etna.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://etna.mcs.kent.edu/vol.12.2001/pp66-87.dir/pp66-87.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}


bibtype: inproceedings
filename: fparith.bib
label: Zheng:2001:ARE
author: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
title: The application of redundant encoding in iterative implementation of division and square root
crossref: Tang:2001:ICA
pages: 603--606
year: 2001
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: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
rawtitle: The application of redundant encoding in iterative implementation of division and square root
entry:
@InProceedings{Zheng:2001:ARE,
  author =       "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
  title =        "The application of redundant encoding in iterative
                 implementation of division and square root",
  crossref =     "Tang:2001:ICA",
  pages =        "603--606",
  year =         "2001",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this paper is to discuss the speed
                 improvement in division and square root computation
                 with small area penalty. The digit recurrence SRT
                 algorithm and functional iteration Newton--Raphson
                 algorithm are generally used in modern \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Zielke:2001:GLL
author: G. Zielke and V. Drygalla
title: Genaue Losung Linearer Gleichungssysteme. (German) [Exact solution of linear sets of equations]
journal: j-GAMM-MIT
volume: 26
pages: 7--107
year: 2001
ISSN: 0936-7195 OR 09367195
bibdate: Tue Nov 22 06:49:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.22 06:49:35 ???
fjournal: Mitteilungen der Gesellschaft fur Angewandte Mathematik und Mechanik
keywords: accurate floating-point summation
language: German
acknowledgement: ack-nhfb
rawauthor: G. Zielke and V. Drygalla
rawtitle:
{Genaue L{\"o}sung Linearer Gleichungssysteme}. ({German}) [Exact solution of linear sets of equations]

entry:
@Article{Zielke:2001:GLL,
  author =       "G. Zielke and V. Drygalla",
  title =        "{Genaue L{\"o}sung Linearer Gleichungssysteme}.
                 ({German}) [Exact solution of linear sets of
                 equations]",
  journal =      j-GAMM-MIT,
  volume =       "26",
  number =       "??",
  pages =        "7--107",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "0936-7195",
  bibdate =      "Tue Nov 22 06:49:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mitteilungen der Gesellschaft f{\"u}r Angewandte
                 Mathematik und Mechanik",
  keywords =     "accurate floating-point summation",
  language =     "German",
}


bibtype: techreport
filename: fparith.bib
label: Zimmermann:2001:AAC
author: Paul Zimmermann
type: Technical report
institution: Departement de formation doctorale en informatique. Ecole doctorale IAEM Lorraine, UFR STMIA
pages: 43
month: nov
monthnumber: 11
year: 2001
bibdate: Sun Sep 10 08:37:41 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.09.10 08:37:41 ???
URL: http://www.loria.fr/~zimmerma/papers/hdr.ps.gz
language: French
remark: Habilitation a diriger des recherches
acknowledgement: ack-nhfb
rawauthor: Paul Zimmermann
title:
De l'algorithmique a l'arithmetique via le calcul formel. (French) [From algorithmics to arithmetic via symbolic calculation]

address:
Batiment A, Technopole de Nancy-Brabois, 615 rue du jardin botanique, F-54602 Villers-les-Nancy Cedex, France

abstract:
This document presents my research contributions from 1988 to 2001, performed first at INRIA Rocquencourt within the Algo project (1988 to 1992), then at INRIA Lorraine and LORIA within the projects Eureca (1993-1997), PolKA (1998-2000), and Spaces (2001). Three main periods can be roughly distinguished: from 1988 to 1992 where my research focused on analysis of algorithms and random generation, from 1993 to 1997 where I worked on computer algebra and related algorithms, finally from 1998 to 2001 where I was interested in arbitrary precision floating-point arithmetic with well-defined semantics.

rawabstract:
This document presents my research contributions from 1988 to 2001, performed first at INRIA Rocquencourt within the Algo project (1988 to 1992), then at INRIA Lorraine and LORIA within the projects Eur{\'e}ca (1993-1997), PolKA (1998-2000), and Spaces (2001). Three main periods can be roughly distinguished: from 1988 to 1992 where my research focused on analysis of algorithms and random generation, from 1993 to 1997 where I worked on computer algebra and related algorithms, finally from 1998 to 2001 where I was interested in arbitrary precision floating-point arithmetic with well-defined semantics.

rawtitle:
De l'algorithmique {\`a} l'arithm{\'e}tique via le calcul formel. ({French}) [{From} algorithmics to arithmetic via symbolic calculation]

entry:
@TechReport{Zimmermann:2001:AAC,
  author =       "Paul Zimmermann",
  title =        "De l'algorithmique {\`a} l'arithm{\'e}tique via le
                 calcul formel. ({French}) [{From} algorithmics to
                 arithmetic via symbolic calculation]",
  type =         "Technical report",
  institution =  "D{\'e}partement de formation doctorale en
                 informatique. {\'E}cole doctorale IAEM Lorraine, UFR
                 STMIA",
  address =      "B{\^a}timent A, Technop{\^o}le de Nancy-Brabois, 615
                 rue du jardin botanique, F-54602 Villers-l{\`e}s-Nancy
                 Cedex, France",
  pages =        "43",
  month =        nov,
  year =         "2001",
  bibdate =      "Sun Sep 10 08:37:41 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/hdr.ps.gz",
  abstract =     "This document presents my research contributions from
                 1988 to 2001, performed first at INRIA Rocquencourt
                 within the Algo project (1988 to 1992), then at INRIA
                 Lorraine and LORIA within the projects Eur{\'e}ca
                 (1993-1997), PolKA (1998-2000), and Spaces (2001).
                 Three main periods can be roughly distinguished: from
                 1988 to 1992 where my research focused on analysis of
                 algorithms and random generation, from 1993 to 1997
                 where I worked on computer algebra and related
                 algorithms, finally from 1998 to 2001 where I was
                 interested in arbitrary precision floating-point
                 arithmetic with well-defined semantics.",
  acknowledgement = ack-nhfb,
  language =     "French",
  remark =       "Habilitation {\`a} diriger des recherches",
}


bibtype: techreport
filename: fparith.bib
label: Zimmermann:2001:APA
author: Paul Zimmermann
title: Arithmetique en precision arbitraire. (French) [Arbitrary-precision arithmetic]
type: Research Report
number: 4272
institution: inst-LORIA-INRIA-LORRAINE
address: inst-LORIA-INRIA-LORRAINE:adr
pages: 25
day: 29
month: sep
monthnumber: 9
year: 2001
ISSN: 0249-6399 OR 02496399
bibdate: Sun Sep 10 08:43:26 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.09.10 08:43:26 ???
URL: http://www.loria.fr/~zimmerma/papers/RR4272.ps.gz
language: French
acknowledgement: ack-nhfb
rawauthor: Paul Zimmermann
rawtitle: Arithm{\'e}tique en pr{\'e}cision arbitraire. ({French}) [Arbitrary-precision arithmetic]
abstract:
This paper surveys the available algorithms for integer or floating-point arbitrary precision calculations. After a brief discussion about possible memory representations, known algorithms for multiplication, division, square root, greatest common divisor, input and output, are presented, together with their complexity and usage. For each operation, we present the naive algorithm, the asymptotically optimal one, and also intermediate ``divide and conquer'' algorithms, which often are very useful. For floating-points computations, some general-purpose methods are presented for algebraic, elementary, hypergeometric and special functions.

rawabstract:
This paper surveys the available algorithms for integer or floating-point arbitrary precision calculations. After a brief discussion about possible memory representations, known algorithms for multiplication, division, square root, greatest common divisor, input and output, are presented, together with their complexity and usage. For each operation, we present the naive algorithm, the asymptotically optimal one, and also intermediate ``divide and conquer'' algorithms, which often are very useful. For floating-points computations, some general-purpose methods are presented for algebraic, elementary, hypergeometric and special functions.

entry:
@TechReport{Zimmermann:2001:APA,
  author =       "Paul Zimmermann",
  title =        "Arithm{\'e}tique en pr{\'e}cision arbitraire.
                 ({French}) [Arbitrary-precision arithmetic]",
  type =         "Research Report",
  number =       "4272",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "25",
  day =          "29",
  month =        sep,
  year =         "2001",
  ISSN =         "0249-6399",
  bibdate =      "Sun Sep 10 08:43:26 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/RR4272.ps.gz",
  abstract =     "This paper surveys the available algorithms for
                 integer or floating-point arbitrary precision
                 calculations. After a brief discussion about possible
                 memory representations, known algorithms for
                 multiplication, division, square root, greatest common
                 divisor, input and output, are presented, together with
                 their complexity and usage. For each operation, we
                 present the naive algorithm, the asymptotically optimal
                 one, and also intermediate ``divide and conquer''
                 algorithms, which often are very useful. For
                 floating-points computations, some general-purpose
                 methods are presented for algebraic, elementary,
                 hypergeometric and special functions.",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: misc
filename: fparith.bib
label: Ziv:2001:APM
author: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
title: Accurate Portable Mathematical Library (IBM APMathLib)
publisher: pub-IBM
address: pub-IBM:adr
pages: 25
day: 20
month: dec
monthnumber: 12
year: 2001
bibdate: Wed Nov 24 08:06:54 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 08:06:54 ???
URL: ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz; http://oss.software.ibm.com/mathlib/
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
rawtitle: Accurate Portable Mathematical Library ({IBM APMathLib})
entry:
@Misc{Ziv:2001:APM,
  author =       "Abraham Ziv and Moshe Olshansky and Ealan Henis and
                 Anna Reitman",
  title =        "Accurate Portable Mathematical Library ({IBM
                 APMathLib})",
  howpublished = "World-Wide Web document",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  day =          "20",
  month =        dec,
  year =         "2001",
  bibdate =      "Wed Nov 24 08:06:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
                 http://oss.software.ibm.com/mathlib/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Agarwal:2002:FPN
author: R. C. Agarwal and R. F. Enenkel and F. G. Gustavson and A. Kothari and M. Zubair
title: Fast pseudorandom-number generators with modulus $ 2^k $ or $ 2^k - 1 $ using fused multiply--add
journal: j-IBM-JRD
volume: 46
number: 1
pages: 97--116
month: jan
monthnumber: 1
year: 2002
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.461.0097
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Mon Mar 18 17:27:08 MST 2002
bibsource: http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.03.18 17:27:08 MST
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: R. C. Agarwal and R. F. Enenkel and F. G. Gustavson and A. Kothari and M. Zubair
rawtitle: Fast pseudorandom-number generators with modulus $ 2^k $ or $ 2^{k - 1} $ using fused multiply--add
URL:
http://www.research.ibm.com/journal/rd/461/agarwal.html; http://www.research.ibm.com/journal/rd/461/agarwal.pdf

abstract:
Many numerically intensive computations done in a scientific computing environment require uniformly distributed pseudorandom numbers in the range $ (0, 1) $ and $ ( - 1, 1) $. For multiplicative congruential generators with modulus $ 2^k $, $ k leq 52 $, and period $ 2^k - 2 $, we show that the cost per random number for these two distributions is 3 and 3.125 multiply-adds on RS/6000 processors. Our code, on the IBM POWER2 Model 590, produces more than 40 million uniformly distributed pseudorandom numbers per second for both ranges $ (0, 1) $ and $ ( - 1, 1) $. Additionally, our code sustains the 40 million per second rate for data out of cache. The Numerical Aerodynamic Simulation (NAS) parallel benchmarks use a linear congruential generator with modulus 246. Our result is about 50 times faster than the generic implementation given in the benchmarks. The extra-accuracy fused multiply-add instruction of RS/6000 machines combined with a few algorithmic innovations gives rise to the 50-fold increase. If IEEE 64-bit arithmetic is used with our Fortran code on POWER and PowerPC architectures, the results we obtain are bit-wise identical to the generic algorithms. The paper gives several illustrations of a general technique called the Algorithm and Architecture approach. We demonstrate herein that programmer-controlled unrolling of loops is equivalent to ``customized vectorization of RISC-type code.'' Customized vectorization is more powerful than ordinary vectorization, and it is only possible on RISC-type machines. We illustrate its use to show that RS/6000 processors can compute the distribution $ ( - 1, 1) $ at the rate of 3.125 multiply-adds. We also specify a linear congruential generator that is related to the multiplicative congruential generator referred to above. It has a full period of 2k, where 2k is the modulus. The cost per random number [in the range $ (0, 1) $ ] for this generator is four multiply-adds on RS/6000 processors. Our code, on the IBM POWER2 Model 590, for this generator produces more than 30 million uniformly distributed pseudorandom numbers per second for the range $ (0, 1) $. We show that this generator is ``embarrassingly parallel,'' or EP. Using the Algorithm and Architecture approach, we describe a new concept called ``generalized unrolling.'' Finally, we present a multiplicative congruential generator for which the modulus is not a power of $2$. Such a generator, as well as one with modulus $ 2^k $, is selectable as the generator used in the RANDOM_NUMBER intrinsic function of IBM XL Fortran and XL High Performance Fortran. All of the generators reported here are EP. Using an IBM SP2 machine with 250 wide nodes, it is possible to compute more than ten billion uniform random numbers in a second.

rawabstract:
Many numerically intensive computations done in a scientific computing environment require uniformly distributed pseudorandom numbers in the range $ (0, 1) $ and $ ( - 1, 1) $. For multiplicative congruential generators with modulus $ 2^k $, $ k \leq 52 $, and period $ 2^k - 2 $, we show that the cost per random number for these two distributions is 3 and 3.125 multiply-adds on RS/6000 processors. Our code, on the IBM POWER2 Model 590, produces more than 40 million uniformly distributed pseudorandom numbers per second for both ranges $ (0, 1) $ and $ ( - 1, 1) $. Additionally, our code sustains the 40 million per second rate for data out of cache. The Numerical Aerodynamic Simulation (NAS) parallel benchmarks use a linear congruential generator with modulus 246. Our result is about 50 times faster than the generic implementation given in the benchmarks. The extra-accuracy fused multiply-add instruction of RS/6000 machines combined with a few algorithmic innovations gives rise to the 50-fold increase. If IEEE 64-bit arithmetic is used with our Fortran code on POWER and PowerPC architectures, the results we obtain are bit-wise identical to the generic algorithms. The paper gives several illustrations of a general technique called the Algorithm and Architecture approach. We demonstrate herein that programmer-controlled unrolling of loops is equivalent to ``customized vectorization of RISC-type code.'' Customized vectorization is more powerful than ordinary vectorization, and it is only possible on RISC-type machines. We illustrate its use to show that RS/6000 processors can compute the distribution $ ( - 1, 1) $ at the rate of 3.125 multiply-adds. We also specify a linear congruential generator that is related to the multiplicative congruential generator referred to above. It has a full period of 2k, where 2k is the modulus. The cost per random number [in the range $ (0, 1) $ ] for this generator is four multiply-adds on RS/6000 processors. Our code, on the IBM POWER2 Model 590, for this generator produces more than 30 million uniformly distributed pseudorandom numbers per second for the range $ (0, 1) $. We show that this generator is ``embarrassingly parallel,'' or EP. Using the Algorithm and Architecture approach, we describe a new concept called ``generalized unrolling.'' Finally, we present a multiplicative congruential generator for which the modulus is not a power of $2$. Such a generator, as well as one with modulus $ 2^k $, is selectable as the generator used in the RANDOM_NUMBER intrinsic function of IBM XL Fortran and XL High Performance Fortran. All of the generators reported here are EP. Using an IBM SP2 machine with 250 wide nodes, it is possible to compute more than ten billion uniform random numbers in a second.

entry:
@Article{Agarwal:2002:FPN,
  author =       "R. C. Agarwal and R. F. Enenkel and F. G. Gustavson
                 and A. Kothari and M. Zubair",
  title =        "Fast pseudorandom-number generators with modulus $ 2^k
                 $ or $ 2^{k - 1} $ using fused multiply--add",
  journal =      j-IBM-JRD,
  volume =       "46",
  number =       "1",
  pages =        "97--116",
  month =        jan,
  year =         "2002",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.461.0097",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Mar 18 17:27:08 MST 2002",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/461/agarwal.html;
                 http://www.research.ibm.com/journal/rd/461/agarwal.pdf",
  abstract =     "Many numerically intensive computations done in a
                 scientific computing environment require uniformly
                 distributed pseudorandom numbers in the range $ (0, 1)
                 $ and $ ( - 1, 1) $. For multiplicative congruential
                 generators with modulus $ 2^k $, $ k \leq 52 $, and
                 period $ 2^k - 2 $, we show that the cost per random
                 number for these two distributions is 3 and 3.125
                 multiply-adds on RS/6000 processors. Our code, on the
                 IBM POWER2 Model 590, produces more than 40 million
                 uniformly distributed pseudorandom numbers per second
                 for both ranges $ (0, 1) $ and $ ( - 1, 1) $.
                 Additionally, our code sustains the 40 million per
                 second rate for data out of cache. The Numerical
                 Aerodynamic Simulation (NAS) parallel benchmarks use a
                 linear congruential generator with modulus 246. Our
                 result is about 50 times faster than the generic
                 implementation given in the benchmarks. The
                 extra-accuracy fused multiply-add instruction of
                 RS/6000 machines combined with a few algorithmic
                 innovations gives rise to the 50-fold increase. If IEEE
                 64-bit arithmetic is used with our Fortran code on
                 POWER and PowerPC architectures, the results we obtain
                 are bit-wise identical to the generic algorithms. The
                 paper gives several illustrations of a general
                 technique called the Algorithm and Architecture
                 approach. We demonstrate herein that
                 programmer-controlled unrolling of loops is equivalent
                 to ``customized vectorization of RISC-type code.''
                 Customized vectorization is more powerful than ordinary
                 vectorization, and it is only possible on RISC-type
                 machines. We illustrate its use to show that RS/6000
                 processors can compute the distribution $ ( - 1, 1) $
                 at the rate of 3.125 multiply-adds. We also specify a
                 linear congruential generator that is related to the
                 multiplicative congruential generator referred to
                 above. It has a full period of 2k, where 2k is the
                 modulus. The cost per random number [in the range $ (0,
                 1) $ ] for this generator is four multiply-adds on
                 RS/6000 processors. Our code, on the IBM POWER2 Model
                 590, for this generator produces more than 30 million
                 uniformly distributed pseudorandom numbers per second
                 for the range $ (0, 1) $. We show that this generator
                 is ``embarrassingly parallel,'' or EP. Using the
                 Algorithm and Architecture approach, we describe a new
                 concept called ``generalized unrolling.'' Finally, we
                 present a multiplicative congruential generator for
                 which the modulus is not a power of $2$. Such a
                 generator, as well as one with modulus $ 2^k $, is
                 selectable as the generator used in the RANDOM_NUMBER
                 intrinsic function of IBM XL Fortran and XL High
                 Performance Fortran. All of the generators reported
                 here are EP. Using an IBM SP2 machine with 250 wide
                 nodes, it is possible to compute more than ten billion
                 uniform random numbers in a second.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  ordernumber =  "G322-0230",
}


bibtype: article
filename: fparith.bib
label: Akbarpour:2002:FCS
author: Behzad Akbarpour and Abdelkader Dekdouk and Sofiene Tahar
title: Formalization of Cadence SPW Fixed-Point Arithmetic in HOL
journal: j-LECT-NOTES-COMP-SCI
volume: 2335
pages: 185--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:38 MDT 2002
bibtimestamp: 2002.09.10 19:09:38 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Behzad Akbarpour and Abdelkader Dekdouk and Sofi{\`e}ne Tahar
rawtitle: Formalization of Cadence {SPW} Fixed-Point Arithmetic in {HOL}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2335.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2335/23350185.htm; http://link.springer-ny.com/link/service/series/0558/papers/2335/23350185.pdf

entry:
@Article{Akbarpour:2002:FCS,
  author =       "Behzad Akbarpour and Abdelkader Dekdouk and
                 Sofi{\`e}ne Tahar",
  title =        "Formalization of Cadence {SPW} Fixed-Point Arithmetic
                 in {HOL}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2335",
  pages =        "185--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:38 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2335.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2335/23350185.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2335/23350185.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Akkas:2002:CIF
author: A. Akkas
title: A Combined Interval and Floating-point Comparator / Selector
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 208--217
year: 2002
bibdate: Fri Jun 11 05:39:44 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.06.11 05:39:44 ???
URL: http://home.ku.edu.tr/~ahakkas/publications/comparator.pdf
acknowledgement: ack-nhfb
rawauthor: A. Akkas
rawtitle: A Combined Interval and Floating-point Comparator\slash Selector
booktitle:
IEEE 13th International Conference on Application-specific Systems, Architectures, and Processors, San Jose, USA, July, 2002

rawbooktitle:
{IEEE 13th} International Conference on Application-specific Systems, Architectures, and Processors, San Jose, {USA}, July, 2002

entry:
@InProceedings{Akkas:2002:CIF,
  author =       "A. Akkas",
  booktitle =    "{IEEE 13th} International Conference on
                 Application-specific Systems, Architectures, and
                 Processors, San Jose, {USA}, July, 2002",
  title =        "A Combined Interval and Floating-point
                 Comparator\slash Selector",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "208--217",
  year =         "2002",
  bibdate =      "Fri Jun 11 05:39:44 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home.ku.edu.tr/~ahakkas/publications/comparator.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: fparith.bib
label: Akkas:2002:ISE
author: Ahmet Akkas
title: Instruction Set Enhancements for Reliable Computations
type: Ph.D. Thesis
school: Lehigh University
address: Bethlehem, PA, USA
pages: 159
year: 2002
bibdate: Tue Nov 25 12:43:51 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.11.25 12:43:51 ???
remark: Dissertation Abstracts International, Volume: 62-12, Section: B, page: 5799.
acknowledgement: ack-nhfb
advisor: Michael J. Schulte
rawauthor: Ahmet Akkas
rawtitle: Instruction Set Enhancements for Reliable Computations
URL:
http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3036247

abstract:
Although there have been significant advances in VLSI technology and numerical computing, floating-point computations still suffer from undetected errors due to rounding and catastrophic cancellation. Fast computers let programmers write numerically intensive programs, but computed results can be far from the true results due to the accumulation of errors in arithmetic operations. Therefore, accurate and reliable computations have become more important.par Interval arithmetic is one technique for accurate and reliable computing. With interval arithmetic, each data value is represented by two floating-point numbers which correspond to the endpoints of an interval, such that the true result is guaranteed to lie on this interval. Since interval arithmetic represents ranges of numbers, it also provides the ability to solve problems that cannot be efficiently solved using floating-point arithmetic. Although interval arithmetic provides an efficient method for monitoring and controlling errors in floating-point computations, it is not yet used widely because it is not sufficiently fast.par This dissertation investigates instruction set enhancements for interval arithmetic. Existing interval arithmetic programs are examined to determine bottlenecks in interval computations. Then, a variety of instruction set enhancements are proposed to overcome these bottlenecks. The efficiency of the proposed enhancements are evaluated using an interval-enhanced compiler and a superscalar processor simulator. Hardware modifications to support these enhancements are evaluated, and a novel design for a combined Interval and Floating-point Comparator is presented.par This dissertation also investigates instruction set enhancements for extended precision arithmetic. In particular, instruction set support for quadruple precision arithmetic is examined. Hardware modifications needed to support quadruple precision arithmetic on superscalar processor is evaluated to determine which extensions can be most efficiently incorporated into superscalar processor designs. Furthermore, a technique for performing parallel double precision multiplication using quadruple precision hardware is proposed.

rawabstract:
Although there have been significant advances in VLSI technology and numerical computing, floating-point computations still suffer from undetected errors due to rounding and catastrophic cancellation. Fast computers let programmers write numerically intensive programs, but computed results can be far from the true results due to the accumulation of errors in arithmetic operations. Therefore, accurate and reliable computations have become more important.\par Interval arithmetic is one technique for accurate and reliable computing. With interval arithmetic, each data value is represented by two floating-point numbers which correspond to the endpoints of an interval, such that the true result is guaranteed to lie on this interval. Since interval arithmetic represents ranges of numbers, it also provides the ability to solve problems that cannot be efficiently solved using floating-point arithmetic. Although interval arithmetic provides an efficient method for monitoring and controlling errors in floating-point computations, it is not yet used widely because it is not sufficiently fast.\par This dissertation investigates instruction set enhancements for interval arithmetic. Existing interval arithmetic programs are examined to determine bottlenecks in interval computations. Then, a variety of instruction set enhancements are proposed to overcome these bottlenecks. The efficiency of the proposed enhancements are evaluated using an interval-enhanced compiler and a superscalar processor simulator. Hardware modifications to support these enhancements are evaluated, and a novel design for a combined Interval and Floating-point Comparator is presented.\par This dissertation also investigates instruction set enhancements for extended precision arithmetic. In particular, instruction set support for quadruple precision arithmetic is examined. Hardware modifications needed to support quadruple precision arithmetic on superscalar processor is evaluated to determine which extensions can be most efficiently incorporated into superscalar processor designs. Furthermore, a technique for performing parallel double precision multiplication using quadruple precision hardware is proposed.

entry:
@PhdThesis{Akkas:2002:ISE,
  author =       "Ahmet Akkas",
  title =        "Instruction Set Enhancements for Reliable
                 Computations",
  type =         "{Ph.D.} Thesis",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "159",
  year =         "2002",
  bibdate =      "Tue Nov 25 12:43:51 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3036247",
  abstract =     "Although there have been significant advances in VLSI
                 technology and numerical computing, floating-point
                 computations still suffer from undetected errors due to
                 rounding and catastrophic cancellation. Fast computers
                 let programmers write numerically intensive programs,
                 but computed results can be far from the true results
                 due to the accumulation of errors in arithmetic
                 operations. Therefore, accurate and reliable
                 computations have become more important.\par

                 Interval arithmetic is one technique for accurate and
                 reliable computing. With interval arithmetic, each data
                 value is represented by two floating-point numbers
                 which correspond to the endpoints of an interval, such
                 that the true result is guaranteed to lie on this
                 interval. Since interval arithmetic represents ranges
                 of numbers, it also provides the ability to solve
                 problems that cannot be efficiently solved using
                 floating-point arithmetic. Although interval arithmetic
                 provides an efficient method for monitoring and
                 controlling errors in floating-point computations, it
                 is not yet used widely because it is not sufficiently
                 fast.\par

                 This dissertation investigates instruction set
                 enhancements for interval arithmetic. Existing interval
                 arithmetic programs are examined to determine
                 bottlenecks in interval computations. Then, a variety
                 of instruction set enhancements are proposed to
                 overcome these bottlenecks. The efficiency of the
                 proposed enhancements are evaluated using an
                 interval-enhanced compiler and a superscalar processor
                 simulator. Hardware modifications to support these
                 enhancements are evaluated, and a novel design for a
                 combined Interval and Floating-point Comparator is
                 presented.\par

                 This dissertation also investigates instruction set
                 enhancements for extended precision arithmetic. In
                 particular, instruction set support for quadruple
                 precision arithmetic is examined. Hardware
                 modifications needed to support quadruple precision
                 arithmetic on superscalar processor is evaluated to
                 determine which extensions can be most efficiently
                 incorporated into superscalar processor designs.
                 Furthermore, a technique for performing parallel double
                 precision multiplication using quadruple precision
                 hardware is proposed.",
  acknowledgement = ack-nhfb,
  advisor =      "Michael J. Schulte",
  remark =       "Dissertation Abstracts International, Volume: 62-12,
                 Section: B, page: 5799.",
}


bibtype: article
filename: fparith.bib
label: Alvarez:2002:IRF
author: C. Alvarez and J. Corbal and E. Salami and M. Valero
title: Initial Results on Fuzzy Floating Point Computation for Multimedia Processors
journal: j-IEEE-COMPUT-ARCHIT-LETT
volume: 1
number: 1
pages: 1--1
month: jan
monthnumber: 1
year: 2002
DOI: https://doi.org/10.1109/L-CA.2002.6
ISSN: 1556-6056 (print), 1556-6064 (electronic) OR 15566056 (print), 15566064 (electronic)
ISSNL: 1556-6056 OR 15566056
bibdate: Fri Jun 21 05:49:19 2019
bibtimestamp: 2019.06.21 05:49:19 ???
fjournal: IEEE Computer Architecture Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208
rawauthor: C. Alvarez and J. Corbal and E. Salami and M. Valero
rawtitle: Initial Results on Fuzzy Floating Point Computation for Multimedia Processors
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib

abstract:
During the recent years the market of mid low end portable systems such as PDAs or mobile digital phones have experimented a revolution in both selling volume and features as handheld devices incorporate Multimedia applications. This fact brings to an increase in the computational demands of the devices while still having the limitation of power and energy consumption. Instruction memoization is a promising technique to help alleviate the problem of power consumption of expensive functional units such as the floating point one. Unfortunately this technique could be energy inefficient for low end systems due to the additional power consumption of the relatively big tables required. In this paper we present a novel way of understanding multimedia floating point operations based on the fuzzy computation paradigm losses in the computation precision may exchange performance for negligible errors in the output. Exploiting the implicit characteristics of media FP computation we propose a new technique called fuzzy memoization. Fuzzy memoization expands the capabilities of classic memoization by attaching entries with similar inputs to the same output. We present a case of study for a SH like processor and report good performance and power delay improvements with feasible hardware requirements

keywords:
Delay; Energy consumption; Fuzzy systems; Handheld computers; Joining processes; Mobile computing; Multimedia systems; Performance loss; Personal digital assistants; Portable computers

rawabstract:
During the recent years the market of mid low end portable systems such as PDAs or mobile digital phones have experimented a revolution in both selling volume and features as handheld devices incorporate Multimedia applications. This fact brings to an increase in the computational demands of the devices while still having the limitation of power and energy consumption. Instruction memoization is a promising technique to help alleviate the problem of power consumption of expensive functional units such as the floating point one. Unfortunately this technique could be energy inefficient for low end systems due to the additional power consumption of the relatively big tables required. In this paper we present a novel way of understanding multimedia floating point operations based on the fuzzy computation paradigm losses in the computation precision may exchange performance for negligible errors in the output. Exploiting the implicit characteristics of media FP computation we propose a new technique called fuzzy memoization. Fuzzy memoization expands the capabilities of classic memoization by attaching entries with similar inputs to the same output. We present a case of study for a SH like processor and report good performance and power delay improvements with feasible hardware requirements

entry:
@Article{Alvarez:2002:IRF,
  author =       "C. Alvarez and J. Corbal and E. Salami and M. Valero",
  title =        "Initial Results on Fuzzy Floating Point Computation
                 for Multimedia Processors",
  journal =      j-IEEE-COMPUT-ARCHIT-LETT,
  volume =       "1",
  number =       "1",
  pages =        "1--1",
  month =        jan,
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/L-CA.2002.6",
  ISSN =         "1556-6056 (print), 1556-6064 (electronic)",
  ISSN-L =       "1556-6056",
  bibdate =      "Fri Jun 21 05:49:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib",
  abstract =     "During the recent years the market of mid low end
                 portable systems such as PDAs or mobile digital phones
                 have experimented a revolution in both selling volume
                 and features as handheld devices incorporate Multimedia
                 applications. This fact brings to an increase in the
                 computational demands of the devices while still having
                 the limitation of power and energy consumption.
                 Instruction memoization is a promising technique to
                 help alleviate the problem of power consumption of
                 expensive functional units such as the floating point
                 one. Unfortunately this technique could be energy
                 inefficient for low end systems due to the additional
                 power consumption of the relatively big tables
                 required. In this paper we present a novel way of
                 understanding multimedia floating point operations
                 based on the fuzzy computation paradigm losses in the
                 computation precision may exchange performance for
                 negligible errors in the output. Exploiting the
                 implicit characteristics of media FP computation we
                 propose a new technique called fuzzy memoization. Fuzzy
                 memoization expands the capabilities of classic
                 memoization by attaching entries with similar inputs to
                 the same output. We present a case of study for a SH
                 like processor and report good performance and power
                 delay improvements with feasible hardware
                 requirements",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Architecture Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
  keywords =     "Delay; Energy consumption; Fuzzy systems; Handheld
                 computers; Joining processes; Mobile computing;
                 Multimedia systems; Performance loss; Personal digital
                 assistants; Portable computers",
}


bibtype: article
filename: fparith.bib
label: Anonymous:2002:AIVf
author: Anonymous
title: Author index volume 279 (2002)
journal: j-THEOR-COMP-SCI
volume: 279
number: 1-2
pages: 97
month: may
monthnumber: 5
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:08:56 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:08:56 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Anonymous
rawtitle: Author index volume 279 (2002)
entry:
@Article{Anonymous:2002:AIVf,
  author =       "Anonymous",
  title =        "Author index volume 279 (2002)",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "97",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: techreport
filename: fparith.bib
label: Anonymous:2002:OFP
author: Anonymous
title: OpenVMS floating-point arithmetic on the Itanium architecture
institution: inst-HP
address: inst-HP:adr
pages: 97
month: sep
monthnumber: 9
year: 2002
bibdate: Tue Nov 18 15:23:17 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.11.18 15:23:17 ???
URL: http://sysdoc.doors.ch/HP/openvms_ipf_floating_point_wp.pdf
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: {OpenVMS} floating-point arithmetic on the {Itanium} architecture
entry:
@TechReport{Anonymous:2002:OFP,
  author =       "Anonymous",
  title =        "{OpenVMS} floating-point arithmetic on the {Itanium}
                 architecture",
  institution =  inst-HP,
  address =      inst-HP:adr,
  month =        sep,
  year =         "2002",
  bibdate =      "Tue Nov 18 15:23:17 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://sysdoc.doors.ch/HP/openvms_ipf_floating_point_wp.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: manual
filename: fparith.bib
label: ARM:2002:VVF
title: VFP9-S Vector Floating-point Coprocessor (r0p2) Technical Reference Manual
organization: ARM Limited
address: Sunnyvale, CA, USA
pages: xvi + 156
year: 2002
bibdate: Fri May 27 17:59:08 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.05.27 17:59:08 ???
URL: http://www.arm.com/pdfs/VFP-S_Vector_Floating_Point_Tech_Manual.pdf
acknowledgement: ack-nhfb
rawtitle: {VFP9-S} Vector Floating-point Coprocessor (r0p2) Technical Reference Manual
remark:
From the manual, p. 1-7: ``The FMAC family of instructions (FMAC, FNMAC, FMSC, and FNMSC) perform a chained multiply and accumulate operation. The product is computed, rounded according to the specified rounding mode and destination precision, and checked for exceptions before the accumulate operation is performed. The accumulate operation is also rounded according to the specified rounding mode and destination precision, and checked for exceptions. The final result is identical to the equivalent sequence of operations executed in sequence.''par From p. 1-12: ``For instance, the VFP9-S coprocessor does not process subnormal input values directly. To provide correct handling of subnormal inputs according to the IEEE 754 standard, a trap is made to support code to process the operation. Using the support code for processing this operation can require hundreds of cycles.''par From p. 2-2: ``The VFP9-S register file contains thirty-two 32-bit registers organized in four banks. Each register can store either a single-precision floating-point number or an integer.''par From p. 3-5: ``Any SNaN passed as input to an operation causes an Invalid Operation exception, which is passed to a user trap handler, if present. If a user trap handler is not present, then a default QNaN is created.''par From p. 3-7: ``In Flush-to-Zero mode, results that are tiny before rounding, as described in the IEEE 754 standard, are flushed to a positive zero, and the UFC flag, FPSCR[3], is set. Support code is not involved. ldots When the VFP9-S coprocessor is not in Flush-to-Zero mode, any operation with a risk of producing a tiny result, as described in the IEEE 754 standard, bounces to support code. If the operation does not produce a tiny result, it returns the computed result, and the UFC flag, FPSCR[3], is not set. The IXC flag, FPSCR[4], is set if the operation is inexact. If the operation produces a tiny result, the result is a subnormal or zero value, and the UFC flag, FPSCR[3], is set.

entry:
@Manual{ARM:2002:VVF,
  title =        "{VFP9-S} Vector Floating-point Coprocessor (r0p2)
                 Technical Reference Manual",
  organization = "ARM Limited",
  address =      "Sunnyvale, CA, USA",
  pages =        "xvi + 156",
  year =         "2002",
  bibdate =      "Fri May 27 17:59:08 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.arm.com/pdfs/VFP-S_Vector_Floating_Point_Tech_Manual.pdf",
  acknowledgement = ack-nhfb,
  remark =       "From the manual, p. 1-7: ``The FMAC family of
                 instructions (FMAC, FNMAC, FMSC, and FNMSC) perform a
                 chained multiply and accumulate operation. The product
                 is computed, rounded according to the specified
                 rounding mode and destination precision, and checked
                 for exceptions before the accumulate operation is
                 performed. The accumulate operation is also rounded
                 according to the specified rounding mode and
                 destination precision, and checked for exceptions. The
                 final result is identical to the equivalent sequence of
                 operations executed in sequence.''\par

                 From p. 1-12: ``For instance, the VFP9-S coprocessor
                 does not process subnormal input values directly. To
                 provide correct handling of subnormal inputs according
                 to the IEEE 754 standard, a trap is made to support
                 code to process the operation. Using the support code
                 for processing this operation can require hundreds of
                 cycles.''\par

                 From p. 2-2: ``The VFP9-S register file contains
                 thirty-two 32-bit registers organized in four banks.
                 Each register can store either a single-precision
                 floating-point number or an integer.''\par

                 From p. 3-5: ``Any SNaN passed as input to an operation
                 causes an Invalid Operation exception, which is passed
                 to a user trap handler, if present. If a user trap
                 handler is not present, then a default QNaN is
                 created.''\par

                 From p. 3-7: ``In Flush-to-Zero mode, results that are
                 tiny before rounding, as described in the IEEE 754
                 standard, are flushed to a positive zero, and the UFC
                 flag, FPSCR[3], is set. Support code is not involved.
                 \ldots{} When the VFP9-S coprocessor is not in
                 Flush-to-Zero mode, any operation with a risk of
                 producing a tiny result, as described in the IEEE 754
                 standard, bounces to support code. If the operation
                 does not produce a tiny result, it returns the computed
                 result, and the UFC flag, FPSCR[3], is not set. The IXC
                 flag, FPSCR[4], is set if the operation is inexact. If
                 the operation produces a tiny result, the result is a
                 subnormal or zero value, and the UFC flag, FPSCR[3], is
                 set.",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2002:AOS
author: M. G. Arnold
booktitle: 2002 IEEE Workshop on Multimedia Signal Processing
title: Avoiding oddification to simplify MPEG-1 decoding with LNS
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 125--129
year: 2002
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
acknowledgement: ack-nhfb
rawauthor: M. G. Arnold
rawbooktitle: 2002 {IEEE} Workshop on Multimedia Signal Processing
rawtitle: Avoiding oddification to simplify {MPEG}-1 decoding with {LNS}
entry:
@InProceedings{Arnold:2002:AOS,
  author =       "M. G. Arnold",
  booktitle =    "2002 {IEEE} Workshop on Multimedia Signal Processing",
  title =        "Avoiding oddification to simplify {MPEG}-1 decoding
                 with {LNS}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "125--129",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Low-precision logarithmic number system (LNS)
                 arithmetic can reduce the power consumption for MPEG
                 decoding compared to conventional fixed-point
                 techniques. Although this introduces small numeric
                 errors, which violate the IEEE-1180 standard for the
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2002:ICL
author: M. G. Arnold
booktitle: IEEE International Symposium on Circuits and Systems: ISCAS 2002, 26--29 May 2002
title: Improved cotransformation for LNS subtraction
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: II-752--II-755
year: 2002
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
acknowledgement: ack-nhfb
rawauthor: M. G. Arnold
rawbooktitle: {IEEE} International Symposium on Circuits and Systems: {ISCAS 2002}, 26--29 May 2002
rawtitle: Improved cotransformation for {LNS} subtraction
entry:
@InProceedings{Arnold:2002:ICL,
  author =       "M. G. Arnold",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS 2002}, 26--29 May 2002",
  title =        "Improved cotransformation for {LNS} subtraction",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-752--II-755",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Two co-transformations have been proposed previously
                 to avoid interpolation difficulties for logarithmic
                 subtraction: Arnold's and Coleman's. We show these two
                 are closely related, but that Arnold's is considerably
                 more accurate in the worst case. \ldots{}",
}


bibtype: phdthesis
filename: fparith.bib
label: Arnold:2002:LNS
author: Mark Gordon Arnold
title: Logarithmic Number Systems for MPEG and Multimedia Applications
type: Ph.D. thesis
school: University of Manchester
address: Manchester, UK
pages: xiv + 358
month: apr
monthnumber: 4
year: 2002
bibdate: Fri Dec 01 07:16:52 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.01 07:16:52 ???
URL: https://www.proquest.com/pqdtglobal/docview/2780144113
acknowledgement: ack-nhfb
advisor: Colin Donald Walter
rawauthor: Mark Gordon Arnold
rawtitle: Logarithmic Number Systems for {MPEG} and Multimedia Applications
entry:
@PhdThesis{Arnold:2002:LNS,
  author =       "Mark Gordon Arnold",
  title =        "Logarithmic Number Systems for {MPEG} and Multimedia
                 Applications",
  type =         "{Ph.D.} thesis",
  school =       "University of Manchester",
  address =      "Manchester, UK",
  pages =        "xiv + 358",
  month =        apr,
  year =         "2002",
  bibdate =      "Fri Dec 01 07:16:52 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.proquest.com/pqdtglobal/docview/2780144113",
  acknowledgement = ack-nhfb,
  advisor =      "Colin Donald Walter",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2002:RPC
author: Mark G. Arnold
title: Reduced Power Consumption for MPEG Decoding with LNS
crossref: Schulte:2002:PII
pages: 65--75
year: 2002
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
keywords: LNS (logarithmic number system)
acknowledgement: ack-nhfb
rawauthor: Mark G. Arnold
rawtitle: Reduced Power Consumption for {MPEG} Decoding with {LNS}
entry:
@InProceedings{Arnold:2002:RPC,
  author =       "Mark G. Arnold",
  title =        "Reduced Power Consumption for {MPEG} Decoding with
                 {LNS}",
  crossref =     "Schulte:2002:PII",
  pages =        "65--75",
  year =         "2002",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "LNS (logarithmic number system)",
  summary =      "By reducing the accuracy of the logarithmic number
                 system (LNS) it is possible to achieve lower power
                 consumption for multimedia applications, such as MPEG,
                 without significantly lowering the visual quality of
                 the output. An LNS wordsize of 8 to 10 \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Bailey:2002:AAP
author: David H. Bailey and Yozo Hida and Xiaoye S. Li and Brandon Thompson
title: ARPREC: An arbitrary precision computation package
type: Technical Report
number: LBNL-53651
institution: Lawrence Berkeley National Laboratory
address: Berkeley, CA, USA
pages: 65--75
month: sep
monthnumber: 9
year: 2002
DOI: https://doi.org/10.2172/817634
bibdate: Fri Jan 31 15:28:44 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.01.31 15:28:44 ???
URL: https://pubarchive.lbl.gov/islandora/object/ir:121949
acknowledgement: ack-nhfb
rawauthor: David H. Bailey and Yozo Hida and Xiaoye S. Li and Brandon Thompson
rawtitle: {ARPREC}: An arbitrary precision computation package
entry:
@TechReport{Bailey:2002:AAP,
  author =       "David H. Bailey and Yozo Hida and Xiaoye S. Li and
                 Brandon Thompson",
  title =        "{ARPREC}: An arbitrary precision computation package",
  type =         "Technical Report",
  number =       "LBNL-53651",
  institution =  "Lawrence Berkeley National Laboratory",
  address =      "Berkeley, CA, USA",
  month =        sep,
  year =         "2002",
  DOI =          "https://doi.org/10.2172/817634",
  bibdate =      "Fri Jan 31 15:28:44 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://pubarchive.lbl.gov/islandora/object/ir:121949",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bailey:2002:HPC
author: David H. Bailey and David Broadhurst and Yozo Hida and Xiaoye S. Li and Brandon Thompson
title: High Performance Computing Meets Experimental Mathematics
crossref: IEEE:2002:STI
pages: ??--??
year: 2002
bibdate: Wed Nov 26 07:34:20 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.26 07:34:20 ???
URL: http://www.sc-2002.org/paperpdfs/pap.pap124.pdf
acknowledgement: ack-nhfb
rawauthor: David H. Bailey and David Broadhurst and Yozo Hida and Xiaoye S. Li and Brandon Thompson
rawtitle: High Performance Computing Meets Experimental Mathematics
abstract:
In this paper we describe some novel applications of high performance computing in a discipline now known as experimental mathematics. The paper reviews some recent published work, and then presents some new results that have not yet appeared in the literature. A key technique involved in this research is the PSLQ integer relation algorithm (recently named one of ten algorithms of the century by Computing in Science and Engineering). This algorithm permits one to recognize a numeric constant in terms of the formula that it satisfies. We present a variant of PSLQ that is well-suited for parallel computation, and give several examples of new mathematical results that we have found using it. Two of these computations were performed on highly parallel computers, since they are not feasible on conventional systems. We also describe a new software package for performing arbitrary precision arithmetic, which is required in this research.

rawabstract:
In this paper we describe some novel applications of high performance computing in a discipline now known as experimental mathematics. The paper reviews some recent published work, and then presents some new results that have not yet appeared in the literature. A key technique involved in this research is the PSLQ integer relation algorithm (recently named one of ten algorithms of the century by Computing in Science and Engineering). This algorithm permits one to recognize a numeric constant in terms of the formula that it satisfies. We present a variant of PSLQ that is well-suited for parallel computation, and give several examples of new mathematical results that we have found using it. Two of these computations were performed on highly parallel computers, since they are not feasible on conventional systems. We also describe a new software package for performing arbitrary precision arithmetic, which is required in this research.

entry:
@InProceedings{Bailey:2002:HPC,
  author =       "David H. Bailey and David Broadhurst and Yozo Hida and
                 Xiaoye S. Li and Brandon Thompson",
  title =        "High Performance Computing Meets Experimental
                 Mathematics",
  crossref =     "IEEE:2002:STI",
  pages =        "??--??",
  year =         "2002",
  bibdate =      "Wed Nov 26 07:34:20 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sc-2002.org/paperpdfs/pap.pap124.pdf",
  abstract =     "In this paper we describe some novel applications of
                 high performance computing in a discipline now known as
                 experimental mathematics. The paper reviews some recent
                 published work, and then presents some new results that
                 have not yet appeared in the literature. A key
                 technique involved in this research is the PSLQ integer
                 relation algorithm (recently named one of ten
                 algorithms of the century by Computing in Science and
                 Engineering). This algorithm permits one to recognize a
                 numeric constant in terms of the formula that it
                 satisfies. We present a variant of PSLQ that is
                 well-suited for parallel computation, and give several
                 examples of new mathematical results that we have found
                 using it. Two of these computations were performed on
                 highly parallel computers, since they are not feasible
                 on conventional systems. We also describe a new
                 software package for performing arbitrary precision
                 arithmetic, which is required in this research.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Barrio:2002:REB
author: Roberto Barrio
journal: j-J-COMPUT-APPL-MATH
volume: 138
number: 2
pages: 185--204
day: 15
month: jan
monthnumber: 1
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:23 MST 2017
bibtimestamp: 2017.02.25 12:45:23 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270100382X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Roberto Barrio
title:
Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

rawtitle:
Rounding error bounds for the {Clenshaw} and {Forsythe} algorithms for the evaluation of orthogonal polynomial series

entry:
@Article{Barrio:2002:REB,
  author =       "Roberto Barrio",
  title =        "Rounding error bounds for the {Clenshaw} and
                 {Forsythe} algorithms for the evaluation of orthogonal
                 polynomial series",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "138",
  number =       "2",
  pages =        "185--204",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:23 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270100382X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: fparith.bib
label: Belanovic:2002:LPF
author: Pavle Belanovic and Miriam Leeser
title: A Library of Parameterized Floating-Point Modules and Their Use
journal: j-LECT-NOTES-COMP-SCI
volume: 2438
pages: 657--666
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:10:28 MDT 2002
bibtimestamp: 2002.09.10 19:10:28 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Pavle Belanovic and Miriam Leeser
rawtitle: A Library of Parameterized Floating-Point Modules and Their Use
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380657.htm; http://link.springer-ny.com/link/service/series/0558/papers/2438/24380657.pdf

entry:
@Article{Belanovic:2002:LPF,
  author =       "Pavle Belanovic and Miriam Leeser",
  title =        "A Library of Parameterized Floating-Point Modules and
                 Their Use",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "657--666",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380657.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380657.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Bertot:2002:PGS
author: Yves Bertot and Nicolas Magaud and Paul Zimmermann
title: A Proof of GMP Square Root
journal: j-J-AUTOM-REASON
volume: 29
number: 3--4
pages: 225--252
month: sep
monthnumber: 9
year: 2002
CODEN: JAREEW
DOI: https://doi.org/10.1023/A:1021987403425
ISSN: 0168-7433 (print), 1573-0670 (electronic) OR 01687433 (print), 15730670 (electronic)
ISSNL: 0168-7433 OR 01687433
bibdate: Sat Feb 08 08:59:09 2020
bibtimestamp: 2020.02.08 08:59:09 ???
URL: https://link.springer.com/article/10.1023/A:1021987403425
fjournal: Journal of Automated Reasoning
keywords: GNU Multiple Precision library
acknowledgement: ack-nhfb
ajournal: J. Autom. Reason.
journalURL: http://link.springer.com/journal/10817
rawauthor: Yves Bertot and Nicolas Magaud and Paul Zimmermann
rawtitle: A Proof of {GMP} Square Root
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/jautomreason.bib

entry:
@Article{Bertot:2002:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A Proof of {GMP} Square Root",
  journal =      j-J-AUTOM-REASON,
  volume =       "29",
  number =       "3--4",
  pages =        "225--252",
  month =        sep,
  year =         "2002",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1023/A:1021987403425",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Feb 08 08:59:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1023/A:1021987403425",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "GNU Multiple Precision library",
}


bibtype: article
filename: fparith.bib
label: Beuchat:2002:SMB
author: Jean-Luc Beuchat and Arnaud Tisserand
title: Small Multiplier-Based Multiplication and Division Operators for Virtex-II Devices
journal: j-LECT-NOTES-COMP-SCI
volume: 2438
pages: 513--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:10:28 MDT 2002
bibtimestamp: 2002.09.10 19:10:28 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Jean-Luc Beuchat and Arnaud Tisserand
rawtitle: Small Multiplier-Based Multiplication and Division Operators for Virtex-{II} Devices
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380513.htm; http://link.springer-ny.com/link/service/series/0558/papers/2438/24380513.pdf

entry:
@Article{Beuchat:2002:SMB,
  author =       "Jean-Luc Beuchat and Arnaud Tisserand",
  title =        "Small Multiplier-Based Multiplication and Division
                 Operators for Virtex-{II} Devices",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "513--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380513.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380513.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Blackford:2002:USB
title: An updated set of Basic Linear Algebra Subprograms (BLAS)
journal: j-TOMS
volume: 28
number: 2
pages: 135--151
month: jun
monthnumber: 6
year: 2002
CODEN: ACMSCU
DOI: https://doi.org/10.1145/567806.567807
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 9 11:16:50 MST 2002
bibtimestamp: 2002.11.09 11:16:50 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawtitle: An updated set of {Basic Linear Algebra Subprograms (BLAS)}
author:
L. Susan Blackford and James Demmel and Jack Dongarra and Iain Duff and Sven Hammarling and Greg Henry and Michael Heroux and Linda Kaufman and Andrew Lumsdaine and Antoine Petitet and Roldan Pozo and Karin Remington and R. Clint Whaley

bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
This paper expands the specification of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS.par Numerical linear algebra, particularly the solution of linear systems of equations, linear least squares problems, eigenvalue problems and singular value problems, is fundamental to most calculations in scientific computing, and is often the computationally intense part of such calculations. Designers of computer programs involving linear algebraic operations have frequently chosen to implement certain low level operations, such as the dot product or the matrix vector product, as separate subprograms. This may be observed both in many published codes and in codes written for specific applications at many computer installations.par A major aim of the standards defined in this paper is to enable linear algebra libraries (both public domain and commercial) to interoperate efficiently, reliably and easily.

rawabstract:
This paper expands the specification of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS.\par Numerical linear algebra, particularly the solution of linear systems of equations, linear least squares problems, eigenvalue problems and singular value problems, is fundamental to most calculations in scientific computing, and is often the computationally intense part of such calculations. Designers of computer programs involving linear algebraic operations have frequently chosen to implement certain low level operations, such as the dot product or the matrix vector product, as separate subprograms. This may be observed both in many published codes and in codes written for specific applications at many computer installations.\par A major aim of the standards defined in this paper is to enable linear algebra libraries (both public domain and commercial) to interoperate efficiently, reliably and easily.

rawauthor:
L. Susan Blackford and James Demmel and Jack Dongarra and Iain Duff and Sven Hammarling and Greg Henry and Michael Heroux and Linda Kaufman and Andrew Lumsdaine and Antoine Petitet and Roldan Pozo and Karin Remington and R. Clint Whaley

entry:
@Article{Blackford:2002:USB,
  author =       "L. Susan Blackford and James Demmel and Jack Dongarra
                 and Iain Duff and Sven Hammarling and Greg Henry and
                 Michael Heroux and Linda Kaufman and Andrew Lumsdaine
                 and Antoine Petitet and Roldan Pozo and Karin Remington
                 and R. Clint Whaley",
  title =        "An updated set of {Basic Linear Algebra Subprograms
                 (BLAS)}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "135--151",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567807",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper expands the specification of a set of
                 kernel routines for linear algebra, historically called
                 the Basic Linear Algebra Subprograms and commonly known
                 as the BLAS.\par

                 Numerical linear algebra, particularly the solution of
                 linear systems of equations, linear least squares
                 problems, eigenvalue problems and singular value
                 problems, is fundamental to most calculations in
                 scientific computing, and is often the computationally
                 intense part of such calculations. Designers of
                 computer programs involving linear algebraic operations
                 have frequently chosen to implement certain low level
                 operations, such as the dot product or the matrix
                 vector product, as separate subprograms. This may be
                 observed both in many published codes and in codes
                 written for specific applications at many computer
                 installations.\par

                 A major aim of the standards defined in this paper is
                 to enable linear algebra libraries (both public domain
                 and commercial) to interoperate efficiently, reliably
                 and easily.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: fparith.bib
label: Boldo:2002:FRF
author: Sylvie Boldo and Marc Daumas
title: Faithful rounding without fused multiply and accumulate
pages: ??--??
year: 2002
bibdate: Tue Nov 23 10:31:01 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 10:31:01 ???
URL: http://scan2002.lip6.fr/abstracts/boldo.pdf
acknowledgement: ack-nhfb
rawauthor: Sylvie Boldo and Marc Daumas
rawtitle: Faithful rounding without fused multiply and accumulate
booktitle:
10th IMACS-GAMM International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, SCAN-2002, September 24--27, Paris, France

rawbooktitle:
10th {IMACS-GAMM} International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, {SCAN-2002}, September 24--27, Paris, France

entry:
@InProceedings{Boldo:2002:FRF,
  author =       "Sylvie Boldo and Marc Daumas",
  booktitle =    "10th {IMACS-GAMM} International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics, {SCAN-2002}, September 24--27, Paris,
                 France",
  title =        "Faithful rounding without fused multiply and
                 accumulate",
  publisher =    "????",
  address =      "????",
  bookpages =    "????",
  pages =        "??--??",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Nov 23 10:31:01 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://scan2002.lip6.fr/abstracts/boldo.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Boldo:2002:IAO
author: Sylvie Boldo
title: Introduction a l'arithmetique des ordinateurs. (French) [Introduction to computer arithmetic]
publisher: Ecole Normale Superieure de Lyon
address: 69364 Lyon Cedex 07, France
pages: ??--??
year: 2002
bibdate: Tue Nov 23 10:51:50 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 10:51:50 ???
note: Presented in 2002 at the ``Forum des jeunes mathematiciennes et des jeunes informaticiennes''.
URL: http://perso.ens-lyon.fr/sylvie.boldo/doc/FetM.ps
language: French
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Sylvie Boldo
rawnote: Presented in 2002 at the ``Forum des jeunes math{\`e}maticiennes et des jeunes informaticiennes''.
rawtitle:
Introduction {\`a} l'arithm{\`e}tique des ordinateurs. ({French}) [Introduction to computer arithmetic]

entry:
@Misc{Boldo:2002:IAO,
  author =       "Sylvie Boldo",
  title =        "Introduction {\`a} l'arithm{\`e}tique des ordinateurs.
                 ({French}) [Introduction to computer arithmetic]",
  howpublished = "World-Wide Web document",
  publisher =    "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  year =         "2002",
  bibdate =      "Tue Nov 23 10:51:50 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Presented in 2002 at the ``Forum des jeunes
                 math{\`e}maticiennes et des jeunes
                 informaticiennes''.",
  URL =          "http://perso.ens-lyon.fr/sylvie.boldo/doc/FetM.ps",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: techreport
filename: fparith.bib
label: Boldo:2002:NSC
author: Sylvie Boldo and Marc Daumas
title: Necessary and sufficient conditions for exact floating point operations
type: Research Report
number: 2002-44
institution: Ecole Normale Superieure de Lyon
address: 69364 Lyon Cedex 07, France
pages: ??--??
month: nov
monthnumber: 11
year: 2002
bibdate: Tue Nov 23 10:54:25 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 10:54:25 ???
URL: ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4644.pdf
acknowledgement: ack-nhfb
rawauthor: Sylvie Boldo and Marc Daumas
rawtitle: Necessary and sufficient conditions for exact floating point operations
entry:
@TechReport{Boldo:2002:NSC,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "Necessary and sufficient conditions for exact floating
                 point operations",
  type =         "Research Report",
  number =       "2002-44",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  month =        nov,
  year =         "2002",
  bibdate =      "Tue Nov 23 10:54:25 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4644.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Boldo:2002:PSVa
author: Sylvie Boldo and Marc Daumas
title: Properties of the Subtraction Valid for any Floating Point System
type: Research Report
number: 2002-23
institution: Ecole Normale Superieure de Lyon
address: 69364 Lyon Cedex 07, France
pages: ??--??
month: jun
monthnumber: 6
year: 2002
bibdate: Tue Nov 23 11:08:31 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 11:08:31 ???
acknowledgement: ack-nhfb
rawauthor: Sylvie Boldo and Marc Daumas
rawtitle: Properties of the Subtraction Valid for any Floating Point System
URL:
ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-23.ps.gz; ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4473.pdf

entry:
@TechReport{Boldo:2002:PSVa,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "Properties of the Subtraction Valid for any Floating
                 Point System",
  type =         "Research Report",
  number =       "2002-23",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  month =        jun,
  year =         "2002",
  bibdate =      "Tue Nov 23 11:08:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-23.ps.gz;
                 ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4473.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Boldo:2002:PSVb
author: Sylvie Boldo and Marc Daumas
editor: Rance Cleaveland and Hubert Garavel
title: Properties of the Subtraction Valid for any Floating Point System
publisher: Universidad de Malaga, Spain
address: Malaga, Spain
pages: 137--149
year: 2002
bibdate: Tue Nov 23 10:14:59 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.23 10:14:59 ???
URL: http://www.inrialpes.fr/vasy/fmics/workshop-7/proceedings.pdf
acknowledgement: ack-nhfb
bookpages: v + 217
rawauthor: Sylvie Boldo and Marc Daumas
raweditor: Rance Cleaveland and Hubert Garavel
rawtitle: Properties of the Subtraction Valid for any Floating Point System
booktitle:
7th International ERCIM Workshop on Formal Methods for Industrial Critical Systems (FMICS 02): University of Malaga, Spain July 12--13, 2002

note:
Available as Technical Report ITI-2002-5, Dpto. de Lenguajes y Ciencias de la Computacion, Universidad de Malaga, Spain

rawbooktitle:
7th International {ERCIM} Workshop on Formal Methods for Industrial Critical Systems {(FMICS 02)}: University of M{\'a}laga, Spain July 12--13, 2002

rawnote:
Available as Technical Report ITI-2002-5, Dpto. de Lenguajes y Ciencias de la Computaci{\'o}n, Universidad de M{\'a}laga, Spain

entry:
@InProceedings{Boldo:2002:PSVb,
  author =       "Sylvie Boldo and Marc Daumas",
  editor =       "Rance Cleaveland and Hubert Garavel",
  booktitle =    "7th International {ERCIM} Workshop on Formal Methods
                 for Industrial Critical Systems {(FMICS 02)}:
                 University of M{\'a}laga, Spain July 12--13, 2002",
  title =        "Properties of the Subtraction Valid for any Floating
                 Point System",
  publisher =    "Universidad de M{\'a}laga, Spain",
  address =      "M{\'a}laga, Spain",
  bookpages =    "v + 217",
  pages =        "137--149",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Nov 23 10:14:59 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Available as Technical Report ITI-2002-5, Dpto. de
                 Lenguajes y Ciencias de la Computaci{\'o}n, Universidad
                 de M{\'a}laga, Spain",
  URL =          "http://www.inrialpes.fr/vasy/fmics/workshop-7/proceedings.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Cardarilli:2002:RNS
author: G. C. Cardarilli and A. Del Re and A. Nannarelli and M. Re
booktitle: ISCAS 2002, IEEE International Symposium on Circuits and Systems, 26--29 May 2002
title: Residue number system reconfigurable datapath
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: II-756--II-759
year: 2002
DOI: https://doi.org/10.1109/ISCAS.2002.1011463
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: G. C. Cardarilli and A. Del Re and A. Nannarelli and M. Re
rawbooktitle: {ISCAS 2002}, {IEEE} International Symposium on Circuits and Systems, 26--29 May 2002
rawtitle: Residue number system reconfigurable datapath
entry:
@InProceedings{Cardarilli:2002:RNS,
  author =       "G. C. Cardarilli and A. Del Re and A. Nannarelli and
                 M. Re",
  booktitle =    "{ISCAS 2002}, {IEEE} International Symposium on
                 Circuits and Systems, 26--29 May 2002",
  title =        "Residue number system reconfigurable datapath",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-756--II-759",
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2002.1011463",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper we describe a possible approach to
                 implement a reconfigurable datapath for digital signal
                 processing. The datapath should be programmable in
                 terms of dynamic range, type and sequence of
                 operations. We chose to implement it in the \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chesneaux:2002:FRN
author: Jean-Marie Chesneaux and Christiane Frougny and Jean-Michel Muller
title: Foreword: Real Numbers
journal: j-THEOR-COMP-SCI
volume: 279
number: 1-2
pages: 1--2
month: may
monthnumber: 5
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:08:56 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:08:56 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Jean-Marie Chesneaux and Christiane Frougny and Jean-Michel Muller
rawtitle: Foreword: Real Numbers
entry:
@Article{Chesneaux:2002:FRN,
  author =       "Jean-Marie Chesneaux and Christiane Frougny and
                 Jean-Michel Muller",
  title =        "Foreword: Real Numbers",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "1--2",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: article
filename: fparith.bib
label: Chiricescu:2002:MM
author: Silviu Chiricescu and Michael Schuette and Robin Glinton and Herman Schmit
title: Morphable Multipliers
journal: j-LECT-NOTES-COMP-SCI
volume: 2438
pages: 647--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:10:28 MDT 2002
bibtimestamp: 2002.09.10 19:10:28 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Silviu Chiricescu and Michael Schuette and Robin Glinton and Herman Schmit
rawtitle: Morphable Multipliers
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380647.htm; http://link.springer-ny.com/link/service/series/0558/papers/2438/24380647.pdf

entry:
@Article{Chiricescu:2002:MM,
  author =       "Silviu Chiricescu and Michael Schuette and Robin
                 Glinton and Herman Schmit",
  title =        "Morphable Multipliers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "647--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380647.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380647.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Chotin:2002:FPU
author: R. Chotin and H. Mehrez
booktitle: 9th International Conference on Electronics, Circuits and Systems, 2002
title: A floating-point unit using stochastic arithmetic compliant with the IEEE-754 standard
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 603--606
year: 2002
bibdate: Sat Jul 16 17:14:11 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 17:14:11 MDT
acknowledgement: ack-nhfb
rawauthor: R. Chotin and H. Mehrez
rawbooktitle: 9th International Conference on Electronics, Circuits and Systems, 2002
rawtitle: A floating-point unit using stochastic arithmetic compliant with the {IEEE-754} standard
entry:
@InProceedings{Chotin:2002:FPU,
  author =       "R. Chotin and H. Mehrez",
  booktitle =    "9th International Conference on Electronics, Circuits
                 and Systems, 2002",
  title =        "A floating-point unit using stochastic arithmetic
                 compliant with the {IEEE-754} standard",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--606",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper, we present CESTAC, a method to control
                 round-off errors in floating-point scientific
                 computation, based on stochastic arithmetic. The real
                 time use of this method suffers from a bottleneck of
                 software calculations. This paper gives a \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Col:2002:ALC
author: Marie-Andree Jacob-Da Col
title: About local configurations in arithmetic planes
journal: j-THEOR-COMP-SCI
volume: 283
number: 1
pages: 183--201
month: jun
monthnumber: 6
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:08:57 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:08:57 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Marie-Andr{\'e}e Jacob-Da Col
rawtitle: About local configurations in arithmetic planes
entry:
@Article{Col:2002:ALC,
  author =       "Marie-Andr{\'e}e Jacob-Da Col",
  title =        "About local configurations in arithmetic planes",
  journal =      j-THEOR-COMP-SCI,
  volume =       "283",
  number =       "1",
  pages =        "183--201",
  month =        jun,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: inproceedings
filename: fparith.bib
label: Conway:2002:NOH
author: Richard Conway and Thomas Conway and John Nelson
title: New One-Hot RNS Structures for High-Speed Signal Processing
crossref: Luk:2002:PSA
pages: 381--392
year: 2002
bibdate: Fri Jun 24 18:17:01 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 18:17:01 ???
URL: http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=452053
keywords: One-Hot Residue Number System (OHRNS); Residue Number System (RNS)
acknowledgement: ack-nhfb
rawauthor: Richard Conway and Thomas Conway and John Nelson
rawtitle: New One-Hot {RNS} Structures for High-Speed Signal Processing
abstract:
New efficient structures using the one-hot residue number system (OHRNS) are presented. Normally the RNS uses a binary representation for the residues, though recently there has been renewed interest in the OHRNS, which uses a simple, but novel representation for the residues. The basic component of the OHRNS is the barrel shifter, making the OHRNS suitable for very high speed applications. The first of the new structures presented reduces the power dissipation in OHRNS adder trees. A modification to the normal barrel shifter is proposed, which reduces the power dissipated by as much as 30%. This improvement is obtained through the use of the modified barrel shifter and the appropriate connection of active-low and active-high stages. This overall power reduction offers the possibility of using the OHRNS in place of a typical full adder based tree in high speed DSP applications. A new storage register for one-hot representations is detailed, which overcomes the problem of having to use a large number of registers. A new architecture is presented for fast OHRNS sign detection. Sign detection is complex and slow to perform in the RNS. A mixed radix conversion (MRC) is typically used for sign detection in the OHRNS. The new sign detection architecture is based on a new property of the Chinese Remainder Theorem (CRT) and is significantly faster than the MRC approach for large moduli sets. Simulation results using SPICE are detailed for the new structures.

rawabstract:
New efficient structures using the one-hot residue number system (OHRNS) are presented. Normally the RNS uses a binary representation for the residues, though recently there has been renewed interest in the OHRNS, which uses a simple, but novel representation for the residues. The basic component of the OHRNS is the barrel shifter, making the OHRNS suitable for very high speed applications. The first of the new structures presented reduces the power dissipation in OHRNS adder trees. A modification to the normal barrel shifter is proposed, which reduces the power dissipated by as much as 30\%. This improvement is obtained through the use of the modified barrel shifter and the appropriate connection of active-low and active-high stages. This overall power reduction offers the possibility of using the OHRNS in place of a typical full adder based tree in high speed DSP applications. A new storage register for one-hot representations is detailed, which overcomes the problem of having to use a large number of registers. A new architecture is presented for fast OHRNS sign detection. Sign detection is complex and slow to perform in the RNS. A mixed radix conversion (MRC) is typically used for sign detection in the OHRNS. The new sign detection architecture is based on a new property of the Chinese Remainder Theorem (CRT) and is significantly faster than the MRC approach for large moduli sets. Simulation results using SPICE are detailed for the new structures.

entry:
@InProceedings{Conway:2002:NOH,
  author =       "Richard Conway and Thomas Conway and John Nelson",
  title =        "New One-Hot {RNS} Structures for High-Speed Signal
                 Processing",
  crossref =     "Luk:2002:PSA",
  pages =        "381--392",
  year =         "2002",
  bibdate =      "Fri Jun 24 18:17:01 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=452053",
  abstract =     "New efficient structures using the one-hot residue
                 number system (OHRNS) are presented. Normally the RNS
                 uses a binary representation for the residues, though
                 recently there has been renewed interest in the OHRNS,
                 which uses a simple, but novel representation for the
                 residues. The basic component of the OHRNS is the
                 barrel shifter, making the OHRNS suitable for very high
                 speed applications. The first of the new structures
                 presented reduces the power dissipation in OHRNS adder
                 trees. A modification to the normal barrel shifter is
                 proposed, which reduces the power dissipated by as much
                 as 30\%. This improvement is obtained through the use
                 of the modified barrel shifter and the appropriate
                 connection of active-low and active-high stages. This
                 overall power reduction offers the possibility of using
                 the OHRNS in place of a typical full adder based tree
                 in high speed DSP applications. A new storage register
                 for one-hot representations is detailed, which
                 overcomes the problem of having to use a large number
                 of registers. A new architecture is presented for fast
                 OHRNS sign detection. Sign detection is complex and
                 slow to perform in the RNS. A mixed radix conversion
                 (MRC) is typically used for sign detection in the
                 OHRNS. The new sign detection architecture is based on
                 a new property of the Chinese Remainder Theorem (CRT)
                 and is significantly faster than the MRC approach for
                 large moduli sets. Simulation results using SPICE are
                 detailed for the new structures.",
  acknowledgement = ack-nhfb,
  keywords =     "One-Hot Residue Number System (OHRNS); Residue Number
                 System (RNS)",
}


bibtype: article
filename: fparith.bib
label: Conway:2002:SRI
author: T. Conway
title: Static register implementation for one hot residue number systems
journal: j-ELECT-LETTERS
volume: 38
number: 2
pages: 63--64
day: 17
month: jan
monthnumber: 1
year: 2002
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:20020050
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Fri Nov 9 11:38:59 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:59 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=21138
fjournal: Electronics Letters
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: T. Conway
rawtitle: Static register implementation for one hot residue number systems
entry:
@Article{Conway:2002:SRI,
  author =       "T. Conway",
  title =        "Static register implementation for one hot residue
                 number systems",
  journal =      j-ELECT-LETTERS,
  volume =       "38",
  number =       "2",
  pages =        "63--64",
  day =          "17",
  month =        jan,
  year =         "2002",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20020050",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=21138",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A method of implementing static registers for one-hot
                 residue number systems is described. The method
                 overcomes the high power dissipation problems
                 associated with conventional flip-flops and clock
                 distribution. The proposed design relies on the low
                 \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Cornea:2002:SCI
author: Marius Cornea and John Harrison and Ping Tak Peter Tang
title: Scientific computing on Itanium-based systems
publisher: pub-INTEL
address: pub-INTEL:adr
pages: xvii + 406
year: 2002
ISBN: 0-9712887-7-1 OR 0971288771
ISBN13: 978-0-9712887-7-5 OR 9780971288775
LCCN: QA76.8.I83 C67 2002
bibdate: Sat Dec 06 15:02:26 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 2003.12.06 15:02:26 ???
URL: http://www.intel.com/intelpress/sum_scientific.htm
acknowledgement: ack-nhfb
rawauthor: Marius Cornea and John Harrison and Ping Tak Peter Tang
rawtitle: Scientific computing on {Itanium}-based systems
abstract:
Written for professionals who need to write, port, or maintain reliable, accurate, and efficient numerical software for the Itanium architecture, Scientific Computing on Itanium-based Systems shows you how to construct key numerical infrastructure and application programs.par This book describes the crucial techniques required for stability and reliability in developing numerical kernels and applications. Through numerous tested examples, the authors explain how you can get the most from the 64-bit architecture. This combination of explanation with example helps you to make difficult computations more easily and to increase the performance of your numerical software.par This book provides examples to solve problems encountered in scientific and engineering computations, such as:par * Polynomial evaluation * Complex arithmetic * Quad-precision arithmetic * Software pipelining, to include register rotation and modulo-scheduled loop support * SIMD instructions * Interval arithmetic * Fast-Fourier Transformation (FFT) algorithms * Numerical linear algebra and basic linear algebra subprograms(BLAS) * Vector Math Library (VML) * Cryptography

rawabstract:
Written for professionals who need to write, port, or maintain reliable, accurate, and efficient numerical software for the Itanium architecture, Scientific Computing on Itanium-based Systems shows you how to construct key numerical infrastructure and application programs.\par This book describes the crucial techniques required for stability and reliability in developing numerical kernels and applications. Through numerous tested examples, the authors explain how you can get the most from the 64-bit architecture. This combination of explanation with example helps you to make difficult computations more easily and to increase the performance of your numerical software.\par This book provides examples to solve problems encountered in scientific and engineering computations, such as:\par * Polynomial evaluation\\ * Complex arithmetic\\ * Quad-precision arithmetic\\ * Software pipelining, to include register rotation and modulo-scheduled loop support\\ * SIMD instructions\\ * Interval arithmetic\\ * Fast-Fourier Transformation (FFT) algorithms\\ * Numerical linear algebra and basic linear algebra subprograms(BLAS)\\ * Vector Math Library (VML)\\ * Cryptography

entry:
@Book{Cornea:2002:SCI,
  author =       "Marius Cornea and John Harrison and Ping Tak Peter
                 Tang",
  title =        "Scientific computing on {Itanium}-based systems",
  publisher =    pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "xvii + 406",
  year =         "2002",
  ISBN =         "0-9712887-7-1",
  ISBN-13 =      "978-0-9712887-7-5",
  LCCN =         "QA76.8.I83 C67 2002",
  bibdate =      "Sat Dec 06 15:02:26 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$69.95",
  URL =          "http://www.intel.com/intelpress/sum_scientific.htm",
  abstract =     "Written for professionals who need to write, port, or
                 maintain reliable, accurate, and efficient numerical
                 software for the Itanium architecture, Scientific
                 Computing on Itanium-based Systems shows you how to
                 construct key numerical infrastructure and application
                 programs.\par

                 This book describes the crucial techniques required for
                 stability and reliability in developing numerical
                 kernels and applications. Through numerous tested
                 examples, the authors explain how you can get the most
                 from the 64-bit architecture. This combination of
                 explanation with example helps you to make difficult
                 computations more easily and to increase the
                 performance of your numerical software.\par

                 This book provides examples to solve problems
                 encountered in scientific and engineering computations,
                 such as:\par

                 * Polynomial evaluation\\
                 * Complex arithmetic\\
                 * Quad-precision arithmetic\\
                 * Software pipelining, to include register rotation and
                 modulo-scheduled loop support\\
                 * SIMD instructions\\
                 * Interval arithmetic\\
                 * Fast-Fourier Transformation (FFT) algorithms\\
                 * Numerical linear algebra and basic linear algebra
                 subprograms(BLAS)\\
                 * Vector Math Library (VML)\\
                 * Cryptography",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Cowlishaw:2002:DPD
author: Michael F. Cowlishaw
title: Densely Packed Decimal Encoding
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 149
number: 3
pages: 102--104
year: 2002
CODEN: ICDTEA
DOI: https://doi.org/10.1049/ip-cdt:20020407
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Fri Jun 07 11:08:45 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.06.07 11:08:45 ???
fjournal: IEE Proceedings. Computers and Digital Techniques
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Michael F. Cowlishaw
rawtitle: Densely Packed Decimal Encoding
entry:
@Article{Cowlishaw:2002:DPD,
  author =       "Michael F. Cowlishaw",
  title =        "Densely Packed Decimal Encoding",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "149",
  number =       "3",
  pages =        "102--104",
  year =         "2002",
  CODEN =        "ICDTEA",
  DOI =          "https://doi.org/10.1049/ip-cdt:20020407",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Jun 07 11:08:45 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: misc
filename: fparith.bib
label: Cowlishaw:2002:TB
author: M. F. Cowlishaw
title: The `telco' benchmark
institution: IBM Hursley Laboratory
address: Hursley, UK
pages: 3
year: 2002
bibdate: Fri Nov 28 11:14:02 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:14:02 ???
URL: http://www2.hursley.ibm.com/decimal/telco.html
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
howpublished: World-Wide Web document.
rawauthor: M. F. Cowlishaw
rawtitle: The `telco' benchmark
entry:
@Misc{Cowlishaw:2002:TB,
  author =       "M. F. Cowlishaw",
  title =        "The `telco' benchmark",
  howpublished = "World-Wide Web document.",
  institution =  "IBM Hursley Laboratory",
  address =      "Hursley, UK",
  pages =        "3",
  year =         "2002",
  bibdate =      "Fri Nov 28 11:14:02 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www2.hursley.ibm.com/decimal/telco.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: techreport
filename: fparith.bib
label: Crandall:2002:OPF
author: R. E. Crandall and J. Papadopoulos
title: Octuple-precision floating point on Apple G4
type: Report
institution: Advanced Computation Group, Apple Computer
address: Cupertino, CA, USA
pages: 8
day: 8
month: may
monthnumber: 5
year: 2002
bibdate: Tue Mar 19 09:06:09 2013
bibtimestamp: 2013.03.19 09:06:09 ???
URL: http://images.apple.com/acg/pdf/oct3a.pdf
acknowledgement: ack-nhfb
rawauthor: R. E. Crandall and J. Papadopoulos
rawtitle: Octuple-precision floating point on {Apple G4}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Crandall:2002:OPF,
  author =       "R. E. Crandall and J. Papadopoulos",
  title =        "Octuple-precision floating point on {Apple G4}",
  type =         "Report",
  institution =  "Advanced Computation Group, Apple Computer",
  address =      "Cupertino, CA, USA",
  pages =        "8",
  day =          "8",
  month =        may,
  year =         "2002",
  bibdate =      "Tue Mar 19 09:06:09 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://images.apple.com/acg/pdf/oct3a.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Daumas:2002:ASN
author: Marc Daumas and Philippe Langlois
title: Additive symmetries: the non-negative case
journal: j-THEOR-COMP-SCI
volume: 291
number: 2
pages: 143--157
month: nov
monthnumber: 11
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:15:29 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:15:29 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Marc Daumas and Philippe Langlois
rawtitle: Additive symmetries: the non-negative case
entry:
@Article{Daumas:2002:ASN,
  author =       "Marc Daumas and Philippe Langlois",
  title =        "Additive symmetries: the non-negative case",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "143--157",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: inproceedings
filename: fparith.bib
label: deDinechin:2002:MTJ
author: Florent de Dinechin and Jeremie Detrey
title: Multipartite Tables in JBits for the Evaluation of Functions on FPGA's
crossref: IEEE:2002:IRA
pages: 154--160
year: 2002
bibdate: Fri Jun 24 20:27:42 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 20:27:42 ???
URL: http://www.ens-lyon.fr/LIP/Arenaire/News/JBits/
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and J{\'e}r{\'e}mie Detrey
rawtitle: Multipartite Tables in {JBits} for the Evaluation of Functions on {FPGA}'s
abstract:
This paper presents the implementation, on Virtex FPGAs, of a core generator for arbitrary numeric functions in fixed-point format. The cores use the state-of-theart multipartite table method, which allows input and output precisions in the range of 8 to 24 bits on current Virtex chips. The implementation uses the JBits API to embed elaborate optimisation techniques in the description of the hardware.

rawabstract:
This paper presents the implementation, on Virtex FPGAs, of a core generator for arbitrary numeric functions in fixed-point format. The cores use the state-of-theart multipartite table method, which allows input and output precisions in the range of 8 to 24 bits on current Virtex chips. The implementation uses the JBits API to embed elaborate optimisation techniques in the description of the hardware.

entry:
@InProceedings{deDinechin:2002:MTJ,
  author =       "Florent de Dinechin and J{\'e}r{\'e}mie Detrey",
  title =        "Multipartite Tables in {JBits} for the Evaluation of
                 Functions on {FPGA}'s",
  crossref =     "IEEE:2002:IRA",
  pages =        "154--160",
  year =         "2002",
  bibdate =      "Fri Jun 24 20:27:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Arenaire/News/JBits/",
  abstract =     "This paper presents the implementation, on Virtex
                 FPGAs, of a core generator for arbitrary numeric
                 functions in fixed-point format. The cores use the
                 state-of-theart multipartite table method, which allows
                 input and output precisions in the range of 8 to 24
                 bits on current Virtex chips. The implementation uses
                 the JBits API to embed elaborate optimisation
                 techniques in the description of the hardware.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Defour:2002:SCSa
author: David Defour and Florent de Dinechin
title: Software Carry-Save for Fast Multiple-Precision Algorithms
type: Research Report
number: 2002-08
institution: Ecole Normale Superieure de Lyon
address: 69364 Lyon Cedex 07, France
pages: 12
month: feb
monthnumber: 2
year: 2002
bibdate: Wed Nov 24 07:47:53 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.24 07:47:53 ???
acknowledgement: ack-nhfb
rawauthor: David Defour and Florent de Dinechin
rawtitle: Software Carry-Save for Fast Multiple-Precision Algorithms
URL:
ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-08.ps.gz; http://www.ens-lyon.fr/LIP/Arenaire/Ware/SCSLib/

entry:
@TechReport{Defour:2002:SCSa,
  author =       "David Defour and Florent de Dinechin",
  title =        "Software Carry-Save for Fast Multiple-Precision
                 Algorithms",
  type =         "Research Report",
  number =       "2002-08",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "12",
  month =        feb,
  year =         "2002",
  bibdate =      "Wed Nov 24 07:47:53 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-08.ps.gz;
                 http://www.ens-lyon.fr/LIP/Arenaire/Ware/SCSLib/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Defour:2002:SCSb
author: David Defour and Florent de Dinechin
title: Software Carry-Save for Fast Multiple-Precision Algorithms
crossref: Cohen:2002:MSP
pages: 29--39
year: 2002
bibdate: Fri Jun 24 19:59:47 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.06.24 19:59:47 ???
acknowledgement: ack-nhfb
rawauthor: David Defour and Florent de Dinechin
rawtitle: Software Carry-Save for Fast Multiple-Precision Algorithms
entry:
@InProceedings{Defour:2002:SCSb,
  author =       "David Defour and Florent de Dinechin",
  title =        "Software Carry-Save for Fast Multiple-Precision
                 Algorithms",
  crossref =     "Cohen:2002:MSP",
  pages =        "29--39",
  year =         "2002",
  bibdate =      "Fri Jun 24 19:59:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxbooktitle =  "35th International Congress of Mathematical Software,
                 Beijing, China, 2002",
  xxnote =       "Check: 1st or 35th congress??",
}


bibtype: inproceedings
filename: fparith.bib
label: Demmel:2002:AEA
author: J. Demmel and P. Koev
title: Accurate and Efficient Algorithms for Floating Point Computation
crossref: Li:2002:PIC
pages: 16
year: 2002
bibdate: Mon Apr 25 07:13:09 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.25 07:13:09 ???
URL: http://math.mit.edu/~plamen/files/ICIAM_main.pdf
acknowledgement: ack-nhfb
rawauthor: J. Demmel and P. Koev
rawtitle: Accurate and Efficient Algorithms for Floating Point Computation
entry:
@InProceedings{Demmel:2002:AEA,
  author =       "J. Demmel and P. Koev",
  title =        "Accurate and Efficient Algorithms for Floating Point
                 Computation",
  crossref =     "Li:2002:PIC",
  pages =        "16",
  year =         "2002",
  bibdate =      "Mon Apr 25 07:13:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.mit.edu/~plamen/files/ICIAM_main.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Demmel:2002:AFP
author: James Demmel and Yozo Hida
title: Accurate floating-point summation
type: Report
institution: Computer Science Division and Mathematics Department, University of California, Berkeley
address: Berkeley, CA, USA
pages: 16
day: 8
month: may
monthnumber: 5
year: 2002
bibdate: Wed May 08 15:15:07 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.08 15:15:07 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: James Demmel and Yozo Hida
rawtitle: Accurate floating-point summation
URL:
http://www.cs.berkeley.edu/~demmel/AccurateSummation.pdf; http://www.cs.berkeley.edu/~demmel/AccurateSummation.ps

abstract:
We present and analyze several simple algorithms for accurately summing $n$ floating point numbers $ S = sum _i = 1^n s_i $ independent of how much cancellation occurs in the sum. Let $f$ be the number of significant bits in the $ s_i $. We assume a register is available with $ F > f $ significant bits. Then assuming that (1) $ n leq floor 2^F - f / (1 - 2^-f) + 1 $, (2) rounding is to nearest, (3) no overflow occurs, and (4) all underflow is gradual,then simply summing the $ s_i $ in decreasing order of magnitude yields $S$ rounded to within just over 1.5 units in its last place. If $ S = 0 $, then it is computed exactly. If we increase $n$ slightly to $ floor 2^F - f / (1 - 2^-f) + 3 $ then all accuracy can be lost. This result extends work of Priest and others who considered double precision only $ (F geq 2 f) $. We apply this result to the floating point formats in the (proposed revision of the) IEEE floating point standard. For example, a dot product of IEEE single precision vectors $ sum _i = 1^n x_i dot y_i $ computed using double precision and sorting is guaranteed correct to nearly $ 1.5 $ ulps as long as $ n leq 33 $. If double extended is used $n$ can be as large as $ 65537 $. We also show how sorting may be avoided while retaining accuracy.

rawabstract:
We present and analyze several simple algorithms for accurately summing $n$ floating point numbers $ S = \sum_{i = 1}^n s_i $ independent of how much cancellation occurs in the sum. Let $f$ be the number of significant bits in the $ s_i $. We assume a register is available with $ F > f $ significant bits. Then assuming that (1) $ n \leq \floor {2^{F - f} / (1 - 2^{-f})} + 1 $, (2) rounding is to nearest, (3) no overflow occurs, and (4) all underflow is gradual,then simply summing the $ s_i $ in decreasing order of magnitude yields $S$ rounded to within just over 1.5 units in its last place. If $ S = 0 $, then it is computed exactly. If we increase $n$ slightly to $ \floor {2^{F - f} / (1 - 2^{-f})} + 3 $ then all accuracy can be lost. This result extends work of Priest and others who considered double precision only $ (F \geq 2 f) $. We apply this result to the floating point formats in the (proposed revision of the) IEEE floating point standard. For example, a dot product of IEEE single precision vectors $ \sum_{i = 1}^n x_i \dot {}y_i $ computed using double precision and sorting is guaranteed correct to nearly $ 1.5 $ ulps as long as $ n \leq 33 $. If double extended is used $n$ can be as large as $ 65537 $. We also show how sorting may be avoided while retaining accuracy.

entry:
@TechReport{Demmel:2002:AFP,
  author =       "James Demmel and Yozo Hida",
  title =        "Accurate floating-point summation",
  type =         "Report",
  institution =  "Computer Science Division and Mathematics Department,
                 University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "8",
  month =        may,
  year =         "2002",
  bibdate =      "Wed May 08 15:15:07 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~demmel/AccurateSummation.pdf;
                 http://www.cs.berkeley.edu/~demmel/AccurateSummation.ps",
  abstract =     "We present and analyze several simple algorithms for
                 accurately summing $n$ floating point numbers $ S =
                 \sum_{i = 1}^n s_i $ independent of how much
                 cancellation occurs in the sum. Let $f$ be the number
                 of significant bits in the $ s_i $. We assume a
                 register is available with $ F > f $ significant bits.
                 Then assuming that (1) $ n \leq \floor {2^{F - f} / (1
                 - 2^{-f})} + 1 $, (2) rounding is to nearest, (3) no
                 overflow occurs, and (4) all underflow is gradual,then
                 simply summing the $ s_i $ in decreasing order of
                 magnitude yields $S$ rounded to within just over 1.5
                 units in its last place. If $ S = 0 $, then it is
                 computed exactly. If we increase $n$ slightly to $
                 \floor {2^{F - f} / (1 - 2^{-f})} + 3 $ then all
                 accuracy can be lost. This result extends work of
                 Priest and others who considered double precision only
                 $ (F \geq 2 f) $. We apply this result to the floating
                 point formats in the (proposed revision of the) IEEE
                 floating point standard. For example, a dot product of
                 IEEE single precision vectors $ \sum_{i = 1}^n x_i \dot
                 {}y_i $ computed using double precision and sorting is
                 guaranteed correct to nearly $ 1.5 $ ulps as long as $
                 n \leq 33 $. If double extended is used $n$ can be as
                 large as $ 65537 $. We also show how sorting may be
                 avoided while retaining accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: incollection
filename: fparith.bib
label: Demmel:2002:CAF
author: J. Demmel and Plamen Koev and Ben Diament
title: The Complexity of Accurate Floating Point Computation
crossref: Li:2002:PIC
volume: III (1--3)
pages: 16
year: 2002
MRclass: 65G30 (65Y20)
MRnumber: MR1957571 (2004b:65060)
bibdate: Mon Apr 25 06:44:54 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.25 06:44:54 ???
acknowledgement: ack-nhfb
rawauthor: J. Demmel and Plamen Koev and Ben Diament
rawtitle: The Complexity of Accurate Floating Point Computation
URL:
http://www.cs.berkeley.edu/~demmel/ICM_final.pdf; http://www.fernuni-hagen.de/MATHPHYS/veselic/abstracts/abs_demmel.html

abstract:
We consider the complexity of accurately evaluating floating point expressions, by which we mean getting some guaranteed relative accuracy, and identify a class of expressions where this can be done in polynomial time in the size of the expression and data. We also have a simple expression not in this class for which we have strong evidence that it cannot be evaluated accurately in polynomial time. We extend these results to the accurate computations of certain matrix computations including inverses, LU decompositions, and the SVD.par If time permits, we will also present a recent result where we show that the complexity of approximate condition estimation is as large as ``verifying'' matrix multiplication. Together with the widely-believed conjecture that verifying that A*B=0 cannot be done more cheaply than by multiplying A*B, this implies that all fast condition estimators in widespread use have counterexamples, i.e. matrices for which their estimates are arbitrarily wrong.

remark:
Also presented at the Householder Symposium on Numerical Linear Algebra June 17--21, 2002 Peebles Hotel Hydro, Scotland, and the IV International Workshop on Accurate Solution of Eigenvalue Problems Split, Croatia, June 24--27, 2002.

rawabstract:
We consider the complexity of accurately evaluating floating point expressions, by which we mean getting some guaranteed relative accuracy, and identify a class of expressions where this can be done in polynomial time in the size of the expression and data. We also have a simple expression not in this class for which we have strong evidence that it cannot be evaluated accurately in polynomial time. We extend these results to the accurate computations of certain matrix computations including inverses, LU decompositions, and the SVD.\par If time permits, we will also present a recent result where we show that the complexity of approximate condition estimation is as large as ``verifying'' matrix multiplication. Together with the widely-believed conjecture that verifying that A*B=0 cannot be done more cheaply than by multiplying A*B, this implies that all fast condition estimators in widespread use have counterexamples, i.e. matrices for which their estimates are arbitrarily wrong.

entry:
@InCollection{Demmel:2002:CAF,
  author =       "J. Demmel and Plamen Koev and Ben Diament",
  title =        "The Complexity of Accurate Floating Point
                 Computation",
  crossref =     "Li:2002:PIC",
  volume =       "III (1--3)",
  year =         "2002",
  MRclass =      "65G30 (65Y20)",
  MRnumber =     "MR1957571 (2004b:65060)",
  bibdate =      "Mon Apr 25 06:44:54 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~demmel/ICM_final.pdf;
                 http://www.fernuni-hagen.de/MATHPHYS/veselic/abstracts/abs_demmel.html",
  abstract =     "We consider the complexity of accurately evaluating
                 floating point expressions, by which we mean getting
                 some guaranteed relative accuracy, and identify a class
                 of expressions where this can be done in polynomial
                 time in the size of the expression and data. We also
                 have a simple expression not in this class for which we
                 have strong evidence that it cannot be evaluated
                 accurately in polynomial time. We extend these results
                 to the accurate computations of certain matrix
                 computations including inverses, LU decompositions, and
                 the SVD.\par

                 If time permits, we will also present a recent result
                 where we show that the complexity of approximate
                 condition estimation is as large as ``verifying''
                 matrix multiplication. Together with the
                 widely-believed conjecture that verifying that A*B=0
                 cannot be done more cheaply than by multiplying A*B,
                 this implies that all fast condition estimators in
                 widespread use have counterexamples, i.e. matrices for
                 which their estimates are arbitrarily wrong.",
  acknowledgement = ack-nhfb,
  pagecount =    "10",
  remark =       "Also presented at the Householder Symposium on
                 Numerical Linear Algebra June 17--21, 2002 Peebles
                 Hotel Hydro, Scotland, and the IV International
                 Workshop on Accurate Solution of Eigenvalue Problems
                 Split, Croatia, June 24--27, 2002.",
}


bibtype: techreport
filename: fparith.bib
label: Devillers:2002:FPE
author: Olivier Devillers and Philippe Guigue
title: Finite Precision Elementary Geometric Constructions
type: Technical report
number: RR 4559
institution: Unite de recherche INRIA Sophia Antipolis
address: 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France
pages: 17
month: sep
monthnumber: 9
year: 2002
bibdate: Tue Nov 13 21:54:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.13 21:54:25 ???
URL: http://www-sop.inria.fr/rapports/sophia/RR-4559.html
keywords: computational geometry; Floating point filter; robustness, floating point arithmetic
acknowledgement: ack-nhfb
rawauthor: Olivier Devillers and Philippe Guigue
rawtitle: Finite Precision Elementary Geometric Constructions
abstract:
In this paper we propose a new approach for the robust computation of the nearest integer lattice points of some specific geometric constructions (intersection of two planar segments, circumcenter of a planar triangle and of a spatial tetrahedron). Given that the data and the final results of the geometric constructions are stored using single precision floating point representation (typically fixed size integers), the proposed algorithms first perform the geometric construction in IEEE double precision floating point arithmetic, the rounding error is estimated, and only if the error estimation indicates that the result of the floating point computation may be wrong, the computation is repeated with exact arithmetic. The basic advantage is that exact computations are in most cases avoided, thus reducing both the storage and the required computation time.

rawabstract:
In this paper we propose a new approach for the robust computation of the nearest integer lattice points of some specific geometric constructions (intersection of two planar segments, circumcenter of a planar triangle and of a spatial tetrahedron). Given that the data and the final results of the geometric constructions are stored using single precision floating point representation (typically fixed size integers), the proposed algorithms first perform the geometric construction in IEEE double precision floating point arithmetic, the rounding error is estimated, and only if the error estimation indicates that the result of the floating point computation may be wrong, the computation is repeated with exact arithmetic. The basic advantage is that exact computations are in most cases avoided, thus reducing both the storage and the required computation time.

entry:
@TechReport{Devillers:2002:FPE,
  author =       "Olivier Devillers and Philippe Guigue",
  title =        "Finite Precision Elementary Geometric Constructions",
  type =         "Technical report",
  number =       "RR 4559",
  institution =  "Unit{\'e} de recherche INRIA Sophia Antipolis",
  address =      "2004, route des Lucioles, BP 93, 06902 Sophia
                 Antipolis C{\'e}dex, France",
  pages =        "17",
  month =        sep,
  year =         "2002",
  bibdate =      "Tue Nov 13 21:54:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www-sop.inria.fr/rapports/sophia/RR-4559.html",
  abstract =     "In this paper we propose a new approach for the robust
                 computation of the nearest integer lattice points of
                 some specific geometric constructions (intersection of
                 two planar segments, circumcenter of a planar triangle
                 and of a spatial tetrahedron). Given that the data and
                 the final results of the geometric constructions are
                 stored using single precision floating point
                 representation (typically fixed size integers), the
                 proposed algorithms first perform the geometric
                 construction in IEEE double precision floating point
                 arithmetic, the rounding error is estimated, and only
                 if the error estimation indicates that the result of
                 the floating point computation may be wrong, the
                 computation is repeated with exact arithmetic. The
                 basic advantage is that exact computations are in most
                 cases avoided, thus reducing both the storage and the
                 required computation time.",
  acknowledgement = ack-nhfb,
  keywords =     "computational geometry; Floating point filter;
                 robustness, floating point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Dido:2002:FFP
author: J. Dido and N. Geraudie and L. Loiseau and O. Payeur and Y. Savaria and D. Poirier
title: A flexible floating-point format for optimizing data-paths and operators in FPGA based DSPs
crossref: Trimberger:2002:FTA
pages: 50--55
year: 2002
DOI: https://doi.org/10.1145/503048.503056
bibdate: Sat Oct 9 12:34:43 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.09 12:34:43 ???
acknowledgement: ack-nhfb
rawauthor: J. Dido and N. Geraudie and L. Loiseau and O. Payeur and Y. Savaria and D. Poirier
rawtitle: A flexible floating-point format for optimizing data-paths and operators in {FPGA} based {DSPs}
abstract:
Video signal processing requires complex algorithms performing many basic operations on a video stream. To perform these calculations in real-time in a FPGA, we must use innovative structures to meet speed requirements while managing complexity. As part of a project aiming at the development of a video noise reducer, we developed an optimized processing stream that required some floating-point calculations. This paper presents the rationale for developing a floating-point unit, justifies the data representation used, its implementation in a Xilinx VirtexE FPGA and reports the performance we obtained. A divider using this representation is also presented, with its implementation and performances in the same FPGA.

rawabstract:
Video signal processing requires complex algorithms performing many basic operations on a video stream. To perform these calculations in real-time in a FPGA, we must use innovative structures to meet speed requirements while managing complexity. As part of a project aiming at the development of a video noise reducer, we developed an optimized processing stream that required some floating-point calculations. This paper presents the rationale for developing a floating-point unit, justifies the data representation used, its implementation in a Xilinx VirtexE FPGA and reports the performance we obtained. A divider using this representation is also presented, with its implementation and performances in the same FPGA.

entry:
@InProceedings{Dido:2002:FFP,
  author =       "J. Dido and N. Geraudie and L. Loiseau and O. Payeur
                 and Y. Savaria and D. Poirier",
  title =        "A flexible floating-point format for optimizing
                 data-paths and operators in {FPGA} based {DSPs}",
  crossref =     "Trimberger:2002:FTA",
  pages =        "50--55",
  year =         "2002",
  DOI =          "https://doi.org/10.1145/503048.503056",
  bibdate =      "Sat Oct 9 12:34:43 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Video signal processing requires complex algorithms
                 performing many basic operations on a video stream. To
                 perform these calculations in real-time in a FPGA, we
                 must use innovative structures to meet speed
                 requirements while managing complexity. As part of a
                 project aiming at the development of a video noise
                 reducer, we developed an optimized processing stream
                 that required some floating-point calculations. This
                 paper presents the rationale for developing a
                 floating-point unit, justifies the data representation
                 used, its implementation in a Xilinx VirtexE FPGA and
                 reports the performance we obtained. A divider using
                 this representation is also presented, with its
                 implementation and performances in the same FPGA.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Elia:2002:ISC
author: M. Elia and M. Leone
title: On the inherent space complexity of fast parallel multipliers for $ mathrm GF(2^m) $
journal: j-IEEE-TRANS-COMPUT
volume: 51
number: 3
pages: 346--351
month: mar
monthnumber: 3
year: 2002
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.990131
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 09:41:49 MDT 2011
bibtimestamp: 2011.07.05 09:41:49 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=990131
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Elia and M. Leone
rawtitle: On the inherent space complexity of fast parallel multipliers for {$ \mathrm {GF}(2^m) $}
entry:
@Article{Elia:2002:ISC,
  author =       "M. Elia and M. Leone",
  title =        "On the inherent space complexity of fast parallel
                 multipliers for {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "3",
  pages =        "346--351",
  month =        mar,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.990131",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:41:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=990131",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Erle:2002:PSD
author: Mark A. Erle and Michael J. Schulte and J. G. Linebarger
title: Potential Speedup with Decimal Floating-Point Hardware
crossref: Matthews:2002:PTS
pages: 1073--1077
year: 2002
bibdate: Thu Mar 24 13:47:20 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.03.24 13:47:20 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2002-05.pdf
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Mark A. Erle and Michael J. Schulte and J. G. Linebarger
rawtitle: Potential Speedup with Decimal Floating-Point Hardware
abstract:
This paper addresses the potential speedup achieved by using decimal floating-point hardware, instead of software routines, on a high-performance superscalar architecture. Software routines were written to perform decimal addition, subtraction, multiplication, and division. Cycle counts were then measured for each instruction using the Simplescalar simulator. After this, new hardware algorithms were developed, existing hardware algorithms were analyzed, and cycle counts were estimated for the same set of instructions using specialized decimal floating-point hardware. This data was then used to show the potential speedup obtained for programs with different instruction mixes and a recently developed benchmark.

rawabstract:
This paper addresses the potential speedup achieved by using decimal floating-point hardware, instead of software routines, on a high-performance superscalar architecture. Software routines were written to perform decimal addition, subtraction, multiplication, and division. Cycle counts were then measured for each instruction using the Simplescalar simulator. After this, new hardware algorithms were developed, existing hardware algorithms were analyzed, and cycle counts were estimated for the same set of instructions using specialized decimal floating-point hardware. This data was then used to show the potential speedup obtained for programs with different instruction mixes and a recently developed benchmark.

entry:
@InProceedings{Erle:2002:PSD,
  author =       "Mark A. Erle and Michael J. Schulte and J. G.
                 Linebarger",
  title =        "Potential Speedup with Decimal Floating-Point
                 Hardware",
  crossref =     "Matthews:2002:PTS",
  pages =        "1073--1077",
  year =         "2002",
  bibdate =      "Thu Mar 24 13:47:20 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2002-05.pdf",
  abstract =     "This paper addresses the potential speedup achieved by
                 using decimal floating-point hardware, instead of
                 software routines, on a high-performance superscalar
                 architecture. Software routines were written to perform
                 decimal addition, subtraction, multiplication, and
                 division. Cycle counts were then measured for each
                 instruction using the Simplescalar simulator. After
                 this, new hardware algorithms were developed, existing
                 hardware algorithms were analyzed, and cycle counts
                 were estimated for the same set of instructions using
                 specialized decimal floating-point hardware. This data
                 was then used to show the potential speedup obtained
                 for programs with different instruction mixes and a
                 recently developed benchmark.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Etiemble:2002:CAH
author: Daniel Etiemble
title: Computer arithmetic and hardware: ``off the shelf'' microprocessors versus ``custom hardware''
journal: j-THEOR-COMP-SCI
volume: 279
number: 1--2
pages: 3--27
month: may
monthnumber: 5
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:08:56 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:08:56 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Daniel Etiemble
rawtitle: Computer arithmetic and hardware: ``off the shelf'' microprocessors versus ``custom hardware''
abstract:
This paper discusses the relationship between computer arithmetic and hardware implementation. First, we examine the impact of computer arithmetic on the overall performance of today's microprocessors. By comparing their evolution over the last 10 years, we show that the performance of arithmetic operators is far less critical than the performance of the memory hierarchy or the branch predictors. We then discuss the potential for improvement in arithmetic performance, both for pipelined and non-pipelined operations. We then examine the possible impact of new technologies, such as MMX technology or asynchronous control of microprocessors, on computer arithmetic. Finally, we show that programmable logic devices now permit a cost-effective implementation of specific arithmetic number representations, such as serial arithmetic or logarithmic representations.

rawabstract:
This paper discusses the relationship between computer arithmetic and hardware implementation. First, we examine the impact of computer arithmetic on the overall performance of today's microprocessors. By comparing their evolution over the last 10 years, we show that the performance of arithmetic operators is far less critical than the performance of the memory hierarchy or the branch predictors. We then discuss the potential for improvement in arithmetic performance, both for pipelined and non-pipelined operations. We then examine the possible impact of new technologies, such as MMX technology or asynchronous control of microprocessors, on computer arithmetic. Finally, we show that programmable logic devices now permit a cost-effective implementation of specific arithmetic number representations, such as serial arithmetic or logarithmic representations.

entry:
@Article{Etiemble:2002:CAH,
  author =       "Daniel Etiemble",
  title =        "Computer arithmetic and hardware: ``off the shelf''
                 microprocessors versus ``custom hardware''",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1--2",
  pages =        "3--27",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper discusses the relationship between computer
                 arithmetic and hardware implementation. First, we
                 examine the impact of computer arithmetic on the
                 overall performance of today's microprocessors. By
                 comparing their evolution over the last 10 years, we
                 show that the performance of arithmetic operators is
                 far less critical than the performance of the memory
                 hierarchy or the branch predictors. We then discuss the
                 potential for improvement in arithmetic performance,
                 both for pipelined and non-pipelined operations. We
                 then examine the possible impact of new technologies,
                 such as MMX technology or asynchronous control of
                 microprocessors, on computer arithmetic. Finally, we
                 show that programmable logic devices now permit a
                 cost-effective implementation of specific arithmetic
                 number representations, such as serial arithmetic or
                 logarithmic representations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: article
filename: fparith.bib
label: Gaffar:2002:ACF
author: Altaf Abdul Gaffar and Wayne Luk and Peter Y. K. Cheung and Nabeel Shirazi and James Hwang
title: Automating Customisation of Floating-Point Designs
journal: j-LECT-NOTES-COMP-SCI
volume: 2438
pages: 523--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:10:28 MDT 2002
bibtimestamp: 2002.09.10 19:10:28 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Altaf Abdul Gaffar and Wayne Luk and Peter Y. K. Cheung and Nabeel Shirazi and James Hwang
rawtitle: Automating Customisation of Floating-Point Designs
URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380523.htm; http://link.springer-ny.com/link/service/series/0558/papers/2438/24380523.pdf

entry:
@Article{Gaffar:2002:ACF,
  author =       "Altaf Abdul Gaffar and Wayne Luk and Peter Y. K.
                 Cheung and Nabeel Shirazi and James Hwang",
  title =        "Automating Customisation of Floating-Point Designs",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "523--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380523.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380523.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Galbraith:2002:ASC
author: S. D. Galbraith and S. M. Paulus and N. P. Smart
title: Arithmetic on superelliptic curves
journal: j-MATH-COMPUT
volume: 71
number: 237
pages: 393--405
month: jan
monthnumber: 1
year: 2002
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Thu Jan 31 06:16:28 MST 2002
bibsource: http://www.ams.org/mcom/2002-71-237; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.01.31 06:16:28 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: S. D. Galbraith and S. M. Paulus and N. P. Smart
rawtitle: Arithmetic on superelliptic curves
URL:
http://www.ams.org/journal-getitem?pii=S0025-5718-00-01297-7; http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.dvi; http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.pdf; http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.ps; http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.tex

entry:
@Article{Galbraith:2002:ASC,
  author =       "S. D. Galbraith and S. M. Paulus and N. P. Smart",
  title =        "Arithmetic on superelliptic curves",
  journal =      j-MATH-COMPUT,
  volume =       "71",
  number =       "237",
  pages =        "393--405",
  month =        jan,
  year =         "2002",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu Jan 31 06:16:28 MST 2002",
  bibsource =    "http://www.ams.org/mcom/2002-71-237;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/journal-getitem?pii=S0025-5718-00-01297-7;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.dvi;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.pdf;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.ps;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.tex",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: inproceedings
filename: fparith.bib
label: Garcia:2002:CBB
author: E. Garcia and M. J. Schulte
title: A Combined 16-Bit Binary and Dual Galois Field Multiplier
crossref: IEEE:2002:IWS
pages: 63--68
year: 2002
bibdate: Sun Mar 04 17:49:09 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.03.04 17:49:09 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2002-04.pdf
acknowledgement: ack-nhfb
rawauthor: E. Garcia and M. J. Schulte
rawtitle: A Combined 16-Bit Binary and Dual {Galois} Field Multiplier
entry:
@InProceedings{Garcia:2002:CBB,
  author =       "E. Garcia and M. J. Schulte",
  title =        "A Combined 16-Bit Binary and Dual {Galois} Field
                 Multiplier",
  crossref =     "IEEE:2002:IWS",
  pages =        "63--68",
  year =         "2002",
  bibdate =      "Sun Mar 04 17:49:09 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2002-04.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Geiselmann:2002:NRE
author: W. Geiselmann and J. Muller-Quade and R. Steinwandt
journal: j-IEEE-TRANS-COMPUT
volume: 51
number: 12
pages: 1460--1461
month: dec
monthnumber: 12
year: 2002
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2002.1146713
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 09:42:01 MDT 2011
bibtimestamp: 2011.07.05 09:42:01 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146713
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: W. Geiselmann and J. Muller-Quade and R. Steinwandt
title:
On ``A new representation of elements of finite fields $ mathrm GF(2^m) $ yielding small complexity arithmetic circuits''

rawtitle:
On {``A new representation of elements of finite fields $ \mathrm {GF}(2^m) $ yielding small complexity arithmetic circuits''}

entry:
@Article{Geiselmann:2002:NRE,
  author =       "W. Geiselmann and J. Muller-Quade and R. Steinwandt",
  title =        "On {``A new representation of elements of finite
                 fields $ \mathrm {GF}(2^m) $ yielding small complexity
                 arithmetic circuits''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "12",
  pages =        "1460--1461",
  month =        dec,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1146713",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:42:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146713",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Glossner:2002:JED
author: C. John Glossner and Michael Schulte and Stamatis Vassiliadis
title: A Java-Enabled DSP
journal: j-LECT-NOTES-COMP-SCI
volume: 2268
pages: 307--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:05 MDT 2002
bibtimestamp: 2002.09.10 19:09:05 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: C. John Glossner and Michael Schulte and Stamatis Vassiliadis
rawtitle: A {Java}-Enabled {DSP}
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2268.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2268/22680307.htm; http://link.springer-ny.com/link/service/series/0558/papers/2268/22680307.pdf; http://mesa.ece.wisc.edu/publications/cp_2002-01.pdf

entry:
@Article{Glossner:2002:JED,
  author =       "C. John Glossner and Michael Schulte and Stamatis
                 Vassiliadis",
  title =        "A {Java}-Enabled {DSP}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2268",
  pages =        "307--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:05 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2268.htm;
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  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2268/22680307.htm;
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  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: incollection
filename: fparith.bib
label: Goldberg:2002:CA
author: David Goldberg
title: Computer Arithmetic
crossref: Hennessy:2002:CAQ
chapter: H
pages: H-1--H-74
year: 2002
bibdate: Fri May 31 16:10:43 2002
bibsource: http://www.mkp.com/CA3; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.31 16:10:43 ???
URL: http://books.elsevier.com/companions/1558605967/appendices/1558605967-appendix-h.pdf
acknowledgement: ack-nhfb
rawauthor: David Goldberg
rawtitle: Computer Arithmetic
note:
The complete Appendix H is not in the printed book; it is available only at the book's Web site: path =http://www.mkp.com/CA3=.

rawnote:
The complete Appendix H is not in the printed book; it is available only at the book's Web site: \path=http://www.mkp.com/CA3=.

entry:
@InCollection{Goldberg:2002:CA,
  author =       "David Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:2002:CAQ",
  chapter =      "H",
  pages =        "H-1--H-74",
  year =         "2002",
  bibdate =      "Fri May 31 16:10:43 2002",
  bibsource =    "http://www.mkp.com/CA3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The complete Appendix H is not in the printed book; it
                 is available only at the book's Web site:
                 \path=http://www.mkp.com/CA3=.",
  URL =          "http://books.elsevier.com/companions/1558605967/appendices/1558605967-appendix-h.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Gonzalez:2002:NME
title: A New Methodology for Efficient Synchronization of RNS-Based VLSI Systems
journal: j-LECT-NOTES-COMP-SCI
volume: 2451
pages: 188--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:10:32 MDT 2002
bibtimestamp: 2002.09.10 19:10:32 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawtitle: A New Methodology for Efficient Synchronization of {RNS}-Based {VLSI} Systems
author:
Daniel Gonzalez and Antonio Garcia and Graham A. Jullien and Javier Ramirez and Luis Parrilla and Antonio Lloris

bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510188.htm; http://link.springer-ny.com/link/service/series/0558/papers/2451/24510188.pdf

rawauthor:
Daniel Gonz{\'a}lez and Antonio Garc{\'\i}a and Graham A. Jullien and Javier Ram{\'\i}rez and Luis Parrilla and Antonio Lloris

entry:
@Article{Gonzalez:2002:NME,
  author =       "Daniel Gonz{\'a}lez and Antonio Garc{\'\i}a and Graham
                 A. Jullien and Javier Ram{\'\i}rez and Luis Parrilla
                 and Antonio Lloris",
  title =        "A New Methodology for Efficient Synchronization of
                 {RNS}-Based {VLSI} Systems",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2451",
  pages =        "188--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:32 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm;
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  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510188.htm;
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  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Gottwald:2002:NBL
author: G. A. Gottwald and M. Nicol
title: On the nature of Benford's Law
journal: j-PHYSICA-A
volume: 303
pages: 387--396
year: 2002
CODEN: PHYADX
ISSN: 0378-4371 (print), 1873-2119 (electronic) OR 03784371 (print), 18732119 (electronic)
ISSNL: 0378-4371 OR 03784371
bibdate: Thu Feb 15 16:32:55 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 16:32:55 ???
fjournal: Physica A. Statistical Mechanics and its Applications
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784371
rawauthor: G. A. Gottwald and M. Nicol
rawtitle: On the nature of {Benford's Law}
entry:
@Article{Gottwald:2002:NBL,
  author =       "G. A. Gottwald and M. Nicol",
  title =        "On the nature of {Benford's Law}",
  journal =      j-PHYSICA-A,
  volume =       "303",
  number =       "??",
  pages =        "387--396",
  month =        "????",
  year =         "2002",
  CODEN =        "PHYADX",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 15 16:32:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Goubault:2002:APF
author: Eric Goubault and Matthieu Martel and Sylvie Putot
title: Asserting the Precision of Floating-Point Computations: a Simple Abstract Interpreter
journal: j-LECT-NOTES-COMP-SCI
volume: 2305
pages: 209--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:22 MDT 2002
bibtimestamp: 2002.09.10 19:09:22 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Eric Goubault and Matthieu Martel and Sylvie Putot
rawtitle: Asserting the Precision of Floating-Point Computations: a Simple Abstract Interpreter
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2305.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2305/23050209.htm; http://link.springer-ny.com/link/service/series/0558/papers/2305/23050209.pdf

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  author =       "Eric Goubault and Matthieu Martel and Sylvie Putot",
  title =        "Asserting the Precision of Floating-Point
                 Computations: a Simple Abstract Interpreter",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2305",
  pages =        "209--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:22 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2305.htm;
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  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2305/23050209.htm;
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  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
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bibtype: article
filename: fparith.bib
label: Guo:2002:RIB
author: Linfeng Guo and Yan Meng
title: Round-up of integer bit allocation
journal: j-ELECT-LETTERS
volume: 38
number: 10
pages: 466--467
day: 9
month: may
monthnumber: 5
year: 2002
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 11:25:05 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:05 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: Linfeng Guo and Yan Meng
rawtitle: Round-up of integer bit allocation
entry:
@Article{Guo:2002:RIB,
  author =       "Linfeng Guo and Yan Meng",
  title =        "Round-up of integer bit allocation",
  journal =      j-ELECT-LETTERS,
  volume =       "38",
  number =       "10",
  pages =        "466--467",
  day =          "9",
  month =        may,
  year =         "2002",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A non-iterative algorithm is presented for the
                 round-up procedure of integer bit allocation. The
                 round-up algorithm will give the optimum result without
                 the disadvantages of the traditional iterative
                 \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Hamacher:2002: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: Fifth
pages: xx + 805
year: 2002
ISBN: 0-07-232086-9 OR 0072320869
ISBN13: 978-0-07-232086-2 OR 9780072320862
LCCN: QA76.9.C643 .H36 2002
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:2002: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 =      "Fifth",
  pages =        "xx + 805",
  year =         "2002",
  ISBN =         "0-07-232086-9",
  ISBN-13 =      "978-0-07-232086-2",
  LCCN =         "QA76.9.C643 .H36 2002",
  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: article
filename: fparith.bib
label: Hanrot:2002:DRF
author: G. Hanrot and J. Rivat and G. Tenenbaum and P. Zimmermann
title: Density results on floating-point invertible numbers
journal: j-THEOR-COMP-SCI
volume: 291
number: 2
pages: 135--141
month: nov
monthnumber: 11
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:15:29 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:15:29 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: G. Hanrot and J. Rivat and G. Tenenbaum and P. Zimmermann
rawtitle: Density results on floating-point invertible numbers
entry:
@Article{Hanrot:2002:DRF,
  author =       "G. Hanrot and J. Rivat and G. Tenenbaum and P.
                 Zimmermann",
  title =        "Density results on floating-point invertible numbers",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "135--141",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: techreport
filename: fparith.bib
label: Hanrot:2002:LNM
author: G. Hanrot and P. Zimmermann
title: A long note on Mulders' short product
type: Technical Report
number: RR-4654
institution: inst-LORIA-INRIA-LORRAINE
address: inst-LORIA-INRIA-LORRAINE:adr
pages: 12
month: nov
monthnumber: 11
year: 2002
bibdate: Sun Sep 10 08:17:26 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.09.10 08:17:26 ???
note: See cite Mulders:2000:SMD
acknowledgement: ack-nhfb
rawauthor: G. Hanrot and P. Zimmermann
rawnote: See \cite{Mulders:2000:SMD}
rawtitle: A long note on {Mulders}' short product
abstract:
The short product of two power series is the meaningful part of the product of these objects, i.e., $ sum _i + j < n a_i b_j x^i + j $. In [2], Mulders gives an algorithm to compute a short product faster than the full product in the case of Karatsuba's multiplication [1]. This algorithm work by selecting a cutoff point $k$ and performing a full $ k times k $ product and two $ (n - k) times (n - k) $ short products recursively. Mulders also gives an heuristically optimal cutoff point $ beta n $. In this paper, we determine the optimal cutoff point in Mulders' algorithm. We also give a slightly more general description of Mulders' method.

rawabstract:
The short product of two power series is the meaningful part of the product of these objects, i.e., $ \sum_{i + j < n} a_i b_j x^{i + j} $. In [2], Mulders gives an algorithm to compute a short product faster than the full product in the case of Karatsuba's multiplication [1]. This algorithm work by selecting a cutoff point $k$ and performing a full $ k \times k $ product and two $ (n - k) \times (n - k) $ short products recursively. Mulders also gives an heuristically optimal cutoff point $ \beta n $. In this paper, we determine the optimal cutoff point in Mulders' algorithm. We also give a slightly more general description of Mulders' method.

entry:
@TechReport{Hanrot:2002:LNM,
  author =       "G. Hanrot and P. Zimmermann",
  title =        "A long note on {Mulders}' short product",
  type =         "Technical Report",
  number =       "RR-4654",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "12",
  month =        nov,
  year =         "2002",
  bibdate =      "Sun Sep 10 08:17:26 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Mulders:2000:SMD}",
  abstract =     "The short product of two power series is the
                 meaningful part of the product of these objects, i.e.,
                 $ \sum_{i + j < n} a_i b_j x^{i + j} $. In [2], Mulders
                 gives an algorithm to compute a short product faster
                 than the full product in the case of Karatsuba's
                 multiplication [1]. This algorithm work by selecting a
                 cutoff point $k$ and performing a full $ k \times k $
                 product and two $ (n - k) \times (n - k) $ short
                 products recursively. Mulders also gives an
                 heuristically optimal cutoff point $ \beta n $. In this
                 paper, we determine the optimal cutoff point in
                 Mulders' algorithm. We also give a slightly more
                 general description of Mulders' method.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Heckmann:2002:CLF
author: Reinhold Heckmann
title: Contractivity of linear fractional transformations
journal: j-THEOR-COMP-SCI
volume: 279
number: 1-2
pages: 65--82
month: may
monthnumber: 5
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:08:56 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:08:56 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Reinhold Heckmann
rawtitle: Contractivity of linear fractional transformations
entry:
@Article{Heckmann:2002:CLF,
  author =       "Reinhold Heckmann",
  title =        "Contractivity of linear fractional transformations",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "65--82",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: article
filename: fparith.bib
label: Helms:2002:IPM
author: D. Helms and E. Schmidt and A. Schulz and A. Stammermann and W. Nebel
title: An Improved Power Macro-Model for Arithmetic Datapath Components
journal: j-LECT-NOTES-COMP-SCI
volume: 2451
pages: 16--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:10:32 MDT 2002
bibtimestamp: 2002.09.10 19:10:32 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: D. Helms and E. Schmidt and A. Schulz and A. Stammermann and W. Nebel
rawtitle: An Improved Power Macro-Model for Arithmetic Datapath Components
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510016.htm; http://link.springer-ny.com/link/service/series/0558/papers/2451/24510016.pdf

entry:
@Article{Helms:2002:IPM,
  author =       "D. Helms and E. Schmidt and A. Schulz and A.
                 Stammermann and W. Nebel",
  title =        "An Improved Power Macro-Model for Arithmetic Datapath
                 Components",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2451",
  pages =        "16--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:32 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510016.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2451/24510016.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: fparith.bib
label: Hertling:2002:LBR
author: Peter Hertling
title: A lower bound for range enclosure in interval arithmetic
journal: j-THEOR-COMP-SCI
volume: 279
number: 1-2
pages: 83--95
month: may
monthnumber: 5
year: 2002
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Wed Nov 20 18:08:56 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.11.20 18:08:56 MST
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Peter Hertling
rawtitle: A lower bound for range enclosure in interval arithmetic
entry:
@Article{Hertling:2002:LBR,
  author =       "Peter Hertling",
  title =        "A lower bound for range enclosure in interval
                 arithmetic",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "83--95",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}


bibtype: article
filename: fparith.bib
label: Hiasat:2002:HSR
author: A. A. Hiasat
title: High-speed and reduced-area modular adder structures for RNS
journal: j-IEEE-TRANS-COMPUT
volume: 51
number: 1
pages: 84--89
month: jan
monthnumber: 1
year: 2002
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.980018
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 5 09:41:46 MDT 2011
bibtimestamp: 2011.07.05 09:41:46 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=980018
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. A. Hiasat
rawtitle: High-speed and reduced-area modular adder structures for {RNS}
entry:
@Article{Hiasat:2002:HSR,
  author =       "A. A. Hiasat",
  title =        "High-speed and reduced-area modular adder structures
                 for {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "1",
  pages =        "84--89",
  month =        jan,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.980018",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:41:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=980018",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Higham:2002:ASN
author: Nicholas J. Higham
title: Accuracy and Stability of Numerical Algorithms
publisher: pub-SIAM
address: pub-SIAM:adr
edition: Second
pages: xxx + 680
year: 2002
DOI: https://doi.org/10.1137/1.9780898718027
ISBN: 0-89871-521-0 (hardcover), 0-89871-802-3 (e-book) OR 0898715210 (hardcover), 0898718023 (ebook)
LCCN: QA297 .H53 2002
MRclass: 65G50 (65-02)
MRnumber: MR1927606 (2003g:65064)
bibdate: Wed Oct 30 14:20:02 2002
bibtimestamp: 2002.10.30 14:20:02 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: Nicholas J. Higham
rawtitle: Accuracy and Stability of Numerical Algorithms
ISBN13:
978-0-89871-521-7 (hardcover), 978-0-89871-802-7 (e-book) OR 9780898715217 (hardcover), 9780898718027 (ebook)

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

abstract:
booktitle Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing $ L U $ factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

TOC:
List of Figures List of Tables Preface to Second Edition Preface to First Edition About the Dedication 1: Principles of Finite Precision Computation 2: Floating Point Arithmetic 3: Basics 4: Summation 5: Polynomials 6: Norms 7: Perturbation Theory for Linear Systems 8: Triangular Systems 9: $ L U $ Factorization and Linear Equations 10: Cholesky Factorization 11: Symmetric Indefinite and Skew-Symmetric Systems 12: Iterative Refinement 13: Block LU Factorization 14: Matrix Inversion 15: Condition Number Estimation 16: The Sylvester Equation 17: Stationary Iterative Methods 18: Matrix Powers 19: QR Factorization 20: The Least Squares Problem 21: Underdetermined Systems 22: Vandermonde Systems 23: Fast Matrix Multiplication 24: The Fast Fourier Transform and Applications 25: Nonlinear Systems and Newton's Method 26: Automatic Error Analysis 27: Software Issues in Floating Point Arithmetic 28: A Gallery of Test Matrices Appendix A: Solutions to Problems Appendix B: Acquiring Software Appendix C: Program Libraries Appendix D: The Matrix Computation Toolbox Bibliography Name Index Subject Index

rawabstract:
\booktitle{Accuracy and Stability of Numerical Algorithms} gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing $ L U $ factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

rawTOC:
List of Figures \\ List of Tables \\ Preface to Second Edition \\ Preface to First Edition \\ About the Dedication \\ 1: Principles of Finite Precision Computation \\ 2: Floating Point Arithmetic \\ 3: Basics \\ 4: Summation \\ 5: Polynomials \\ 6: Norms \\ 7: Perturbation Theory for Linear Systems \\ 8: Triangular Systems \\ 9: $ L U $ Factorization and Linear Equations \\ 10: Cholesky Factorization \\ 11: Symmetric Indefinite and Skew-Symmetric Systems \\ 12: Iterative Refinement \\ 13: Block LU Factorization \\ 14: Matrix Inversion \\ 15: Condition Number Estimation \\ 16: The Sylvester Equation \\ 17: Stationary Iterative Methods \\ 18: Matrix Powers \\ 19: QR Factorization \\ 20: The Least Squares Problem \\ 21: Underdetermined Systems \\ 22: Vandermonde Systems \\ 23: Fast Matrix Multiplication \\ 24: The Fast Fourier Transform and Applications \\ 25: Nonlinear Systems and Newton's Method \\ 26: Automatic Error Analysis \\ 27: Software Issues in Floating Point Arithmetic \\ 28: A Gallery of Test Matrices \\ Appendix A: Solutions to Problems \\ Appendix B: Acquiring Software \\ Appendix C: Program Libraries \\ Appendix D: The Matrix Computation Toolbox \\ Bibliography \\ Name Index \\ Subject Index

entry:
@Book{Higham:2002:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xxx + 680",
  year =         "2002",
  DOI =          "https://doi.org/10.1137/1.9780898718027",
  ISBN =         "0-89871-521-0 (hardcover), 0-89871-802-3 (e-book)",
  ISBN-13 =      "978-0-89871-521-7 (hardcover), 978-0-89871-802-7
                 (e-book)",
  LCCN =         "QA297 .H53 2002",
  MRclass =      "65G50 (65-02)",
  MRnumber =     "MR1927606 (2003g:65064)",
  bibdate =      "Wed Oct 30 14:20:02 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "\booktitle{Accuracy and Stability of Numerical
                 Algorithms} gives a thorough, up-to-date treatment of
                 the behavior of numerical algorithms in finite
                 precision arithmetic. It combines algorithmic
                 derivations, perturbation theory, and rounding error
                 analysis, all enlivened by historical perspective and
                 informative quotations. This second edition expands and
                 updates the coverage of the first edition (1996) and
                 includes numerous improvements to the original
                 material. Two new chapters treat symmetric indefinite
                 systems and skew-symmetric systems, and nonlinear
                 systems and Newton's method. Twelve new sections
                 include coverage of additional error bounds for
                 Gaussian elimination, rank revealing $ L U $
                 factorizations, weighted and constrained least squares
                 problems, and the fused multiply-add operation found on
                 some modern computer architectures.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  tableofcontents = "List of Figures \\
                 List of Tables \\
                 Preface to Second Edition \\
                 Preface to First Edition \\
                 About the Dedication \\
                 1: Principles of Finite Precision Computation \\
                 2: Floating Point Arithmetic \\
                 3: Basics \\
                 4: Summation \\
                 5: Polynomials \\
                 6: Norms \\
                 7: Perturbation Theory for Linear Systems \\
                 8: Triangular Systems \\
                 9: $ L U $ Factorization and Linear Equations \\
                 10: Cholesky Factorization \\
                 11: Symmetric Indefinite and Skew-Symmetric Systems \\
                 12: Iterative Refinement \\
                 13: Block LU Factorization \\
                 14: Matrix Inversion \\
                 15: Condition Number Estimation \\
                 16: The Sylvester Equation \\
                 17: Stationary Iterative Methods \\
                 18: Matrix Powers \\
                 19: QR Factorization \\
                 20: The Least Squares Problem \\
                 21: Underdetermined Systems \\
                 22: Vandermonde Systems \\
                 23: Fast Matrix Multiplication \\
                 24: The Fast Fourier Transform and Applications \\
                 25: Nonlinear Systems and Newton's Method \\
                 26: Automatic Error Analysis \\
                 27: Software Issues in Floating Point Arithmetic \\
                 28: A Gallery of Test Matrices \\
                 Appendix A: Solutions to Problems \\
                 Appendix B: Acquiring Software \\
                 Appendix C: Program Libraries \\
                 Appendix D: The Matrix Computation Toolbox \\
                 Bibliography \\
                 Name Index \\
                 Subject Index",
}


