# bibtab

bibtype: article
filename: fparith.bib
label: Dunham:1990:FFE
author: C. B. Dunham
title: Feasibility of `Perfect' Function Evaluation
journal: j-SIGNUM
volume: 25
number: 4
pages: 25--26
month: oct
monthnumber: 10
year: 1990
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:30 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:30 ???
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: C. B. Dunham
rawtitle: Feasibility of `Perfect' Function Evaluation
entry:
@Article{Dunham:1990:FFE,
  author =       "C. B. Dunham",
  title =        "Feasibility of `Perfect' Function Evaluation",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "4",
  pages =        "25--26",
  month =        oct,
  year =         "1990",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: fparith.bib
label: Edenfield:1990:PPD
title: The 68040 Processor. Part 1, Design and Implementation
journal: j-IEEE-MICRO
volume: 10
number: 1
pages: 66--78
month: jan
monthnumber: 1
year: 1990
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.46770
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
fjournal: IEEE Micro
acknowledgement: ack-nj
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawtitle: The 68040 Processor. {Part} 1, Design and Implementation
author:
R. W. Edenfield and M. G. Gallup and W. B. Ledbetter, Jr. and R. C. McGarity and E. E. Quintana and R. A. Reininger

rawauthor:
R. W. Edenfield and M. G. Gallup and W. B. {Ledbetter, Jr.} and R. C. McGarity and E. E. Quintana and R. A. Reininger

entry:
@Article{Edenfield:1990:PPD,
  author =       "R. W. Edenfield and M. G. Gallup and W. B. {Ledbetter,
                 Jr.} and R. C. McGarity and E. E. Quintana and R. A.
                 Reininger",
  title =        "The 68040 Processor. {Part} 1, Design and
                 Implementation",
  journal =      j-IEEE-MICRO,
  volume =       "10",
  number =       "1",
  pages =        "66--78",
  month =        jan # "\slash " # feb,
  year =         "1990",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.46770",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1990:FMC
author: M. D. Ercegovac and T. Lang
title: Fast multiplication without carry-propagate addition
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 11
pages: 1385--1390
month: nov
monthnumber: 11
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.61047
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:05 MDT 2011
bibtimestamp: 2011.07.07 14:20:05 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61047
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: Fast multiplication without carry-propagate addition
entry:
@Article{Ercegovac:1990:FMC,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Fast multiplication without carry-propagate addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "11",
  pages =        "1385--1390",
  month =        nov,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.61047",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61047",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1990:RSR
author: M. D. Ercegovac and T. Lang
title: Radix-$4$ square root without initial PLA
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1016--1024
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57040
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:03 MDT 2011
bibtimestamp: 2011.07.07 14:20:03 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: Radix-$4$ square root without initial {PLA}
entry:
@Article{Ercegovac:1990:RSR,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Radix-$4$ square root without initial {PLA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1016--1024",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57040",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1990:SRD
author: M. D. Ercegovac and T. Lang
title: Simple radix-$4$ division with operands scaling
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 9
pages: 1204--1208
month: sep
monthnumber: 9
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57060
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:04 MDT 2011
bibtimestamp: 2011.07.07 14:20:04 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57060
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: Simple radix-$4$ division with operands scaling
entry:
@Article{Ercegovac:1990:SRD,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Simple radix-$4$ division with operands scaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "9",
  pages =        "1204--1208",
  month =        sep,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57060",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57060",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Fussichen:1990:GAM
author: Kenneth Fussichen
title: Getting Ada into the mainstream in the 1990's
crossref: ACM:1990:PDB
pages: 428--428
year: 1990
DOI: https://doi.org/10.1145/255471.255572
bibdate: Thu Aug 07 18:17:35 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 18:17:35 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Kenneth Fussichen
rawtitle: Getting {Ada} into the mainstream in the 1990's
abstract:
Ada offers a great deal to the MIS community. There are a number of language features that provide attractive tools to the programmer. Ada's support for Object Orientation is far superior to that currently afforded by IBM mainframe languages such as COBOL and PL/1. This translates into more maintainable code, which is the key to MIS Ada acceptance.par Unfortunately, Ada introduces problems that do not currently exist in MIS. Decimal arithmetic and string manipulation adequate to support reporting are inherently non-existent. I/O support is inadequate as are DBMS bindings. Conversions are forced on non-ASCII hosts. The compiler has the option of reordering fields within records, rendering non-Ada utilities useless. There is an inexcusable lack of understanding of the targeted market.

rawabstract:
Ada offers a great deal to the MIS community. There are a number of language features that provide attractive tools to the programmer. Ada's support for Object Orientation is far superior to that currently afforded by IBM mainframe languages such as COBOL and PL/1. This translates into more maintainable code, which is the key to MIS Ada acceptance.\par Unfortunately, Ada introduces problems that do not currently exist in MIS. Decimal arithmetic and string manipulation adequate to support reporting are inherently non-existent. I/O support is inadequate as are DBMS bindings. Conversions are forced on non-ASCII hosts. The compiler has the option of reordering fields within records, rendering non-Ada utilities useless. There is an inexcusable lack of understanding of the targeted market.

entry:
@InProceedings{Fussichen:1990:GAM,
  author =       "Kenneth Fussichen",
  title =        "Getting {Ada} into the mainstream in the 1990's",
  crossref =     "ACM:1990:PDB",
  pages =        "428--428",
  year =         "1990",
  DOI =          "https://doi.org/10.1145/255471.255572",
  bibdate =      "Thu Aug 07 18:17:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Ada offers a great deal to the MIS community. There
                 are a number of language features that provide
                 attractive tools to the programmer. Ada's support for
                 Object Orientation is far superior to that currently
                 afforded by IBM mainframe languages such as COBOL and
                 PL/1. This translates into more maintainable code,
                 which is the key to MIS Ada
                 acceptance.\par

                 Unfortunately, Ada introduces problems that do not
                 currently exist in MIS. Decimal arithmetic and string
                 manipulation adequate to support reporting are
                 inherently non-existent. I/O support is inadequate as
                 are DBMS bindings. Conversions are forced on non-ASCII
                 hosts. The compiler has the option of reordering fields
                 within records, rendering non-Ada utilities useless.
                 There is an inexcusable lack of understanding of the
                 targeted market.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Gallant:1990:MCI
author: John Gallant and Bill Travis
title: Math coprocessor ICs: Floating-point chips boost muP performance
journal: j-EDN
volume: 35
number: 12
pages: 63--??
month: jun
monthnumber: 6
year: 1990
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: EDN
acknowledgement: ack-nhfb
rawauthor: John Gallant and Bill Travis
rawtitle: Math coprocessor {ICs}: Floating-point chips boost {muP} performance
abstract:
Floating-point arithmetic exacts huge penalties in CPU computation time. Dedicated coprocessor ICs execute this onerous task automatically and efficiently.

rawabstract:
Floating-point arithmetic exacts huge penalties in CPU computation time. Dedicated coprocessor ICs execute this onerous task automatically and efficiently.

entry:
@Article{Gallant:1990:MCI,
  author =       "John Gallant and Bill Travis",
  title =        "Math coprocessor {ICs}: Floating-point chips boost
                 {muP} performance",
  journal =      j-EDN,
  volume =       "35",
  number =       "12",
  pages =        "63--??",
  month =        jun,
  year =         "1990",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating-point arithmetic exacts huge penalties in CPU
                 computation time. Dedicated coprocessor ICs execute
                 this onerous task automatically and efficiently.",
  acknowledgement = ack-nhfb,
  fjournal =     "EDN",
}


bibtype: techreport
filename: fparith.bib
label: Gay:1990:CRB
author: David M. Gay
title: Correctly Rounded Binary-Decimal and Decimal-Binary Conversions
type: Numerical Analysis Manuscript
number: 90-10
institution: AT&T Bell Laboratories
pages: 16
month: nov
monthnumber: 11
year: 1990
bibdate: Sat Apr 28 18:42:55 2001
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.04.28 18:42:55 ???
keywords: correct rounding; decimal floating-point arithmetic
acknowledgement: ack-nj
rawauthor: David M. Gay
rawtitle: Correctly Rounded Binary-Decimal and Decimal-Binary Conversions
URL:
http://cm.bell-labs.com/cm/cs/doc/90/4-10.ps.gz; http://www.ampl.com/ampl/REFS/rounding.ps.gz; http://www.netlib.org/fp/dtoa.c; http://www.netlib.org/fp/g_fmt.c; http://www.netlib.org/fp/gdtoa.tgz; http://www.netlib.org/fp/rnd_prod.s

entry:
@TechReport{Gay:1990:CRB,
  author =       "David M. Gay",
  title =        "Correctly Rounded Binary-Decimal and Decimal-Binary
                 Conversions",
  type =         "Numerical Analysis Manuscript",
  number =       "90-10",
  institution =  "AT\&T Bell Laboratories",
  pages =        "16",
  month =        nov # " 30",
  year =         "1990",
  bibdate =      "Sat Apr 28 18:42:55 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://cm.bell-labs.com/cm/cs/doc/90/4-10.ps.gz;
                 http://www.ampl.com/ampl/REFS/rounding.ps.gz;
                 http://www.netlib.org/fp/dtoa.c;
                 http://www.netlib.org/fp/g_fmt.c;
                 http://www.netlib.org/fp/gdtoa.tgz;
                 http://www.netlib.org/fp/rnd_prod.s",
  acknowledgement = ack-nj,
  keywords =     "correct rounding; decimal floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Gibson:1990:CII
author: D. H. Gibson
title: Considerations for including IEEE floating point in large systems
crossref: SHARE:1990:PSE
pages: 47--62
year: 1990
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
keywords: Application portability; Floating-point arithmetic; IEEE Std 754 floating point; SHARE
acknowledgement: ack-nhfb
affiliation: IBM Corp., Poughkeepsie, NY, USA
thesaurus: Digital arithmetic; Standards
rawauthor: D. H. Gibson
rawtitle: Considerations for including {IEEE} floating point in large systems
abstract:
International standards such as ANSI/IEEE Std 754-1985 floating-point arithmetic provide the potential for application portability. The paper, beginning with a 1984 SHARE requirements statement, sets forth certain considerations for including IEEE Std 754 floating point in large systems. A tutorial is presented on IEEE Std 754 floating-point arithmetic. The considerations for integrating IEEE into a large system along with an existing floating point representation are discussed in three categories: architectural; implementation; usage. Related topics are identified and discussed. The paper concludes with a summary of the considerations. (11 Refs.)

rawabstract:
International standards such as ANSI/IEEE Std 754-1985 floating-point arithmetic provide the potential for application portability. The paper, beginning with a 1984 SHARE requirements statement, sets forth certain considerations for including IEEE Std 754 floating point in large systems. A tutorial is presented on IEEE Std 754 floating-point arithmetic. The considerations for integrating IEEE into a large system along with an existing floating point representation are discussed in three categories: architectural; implementation; usage. Related topics are identified and discussed. The paper concludes with a summary of the considerations. (11 Refs.)

entry:
@InProceedings{Gibson:1990:CII,
  author =       "D. H. Gibson",
  title =        "Considerations for including {IEEE} floating point in
                 large systems",
  crossref =     "SHARE:1990:PSE",
  pages =        "47--62",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "International standards such as ANSI/IEEE Std 754-1985
                 floating-point arithmetic provide the potential for
                 application portability. The paper, beginning with a
                 1984 SHARE requirements statement, sets forth certain
                 considerations for including IEEE Std 754 floating
                 point in large systems. A tutorial is presented on IEEE
                 Std 754 floating-point arithmetic. The considerations
                 for integrating IEEE into a large system along with an
                 existing floating point representation are discussed in
                 three categories: architectural; implementation; usage.
                 Related topics are identified and discussed. The paper
                 concludes with a summary of the considerations. (11
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Poughkeepsie, NY, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Application portability; Floating-point arithmetic;
                 IEEE Std 754 floating point; SHARE",
  thesaurus =    "Digital arithmetic; Standards",
}


bibtype: article
filename: fparith.bib
label: Glass:1990:MC
author: L. B. Glass
title: Math coprocessors
journal: j-BYTE
volume: 15
number: 1
pages: 337--348
month: jan
monthnumber: 1
year: 1990
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Thu Sep 12 17:47:21 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.12 17:47:21 MDT
fjournal: BYTE Magazine
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic; Microprocessor chips; Satellite computers
rawauthor: L. B. Glass
rawtitle: Math coprocessors
keywords:
Cyrix 83D87; Floating-point maths; IEEE 754 floating-point standard; Integrated Information Technology; Intel 80287; Intel 80387; Intel 8087; Maths coprocessors; Motorola 68881; Motorola 68882; NP-3C87; Weitek Abacus 3167

entry:
@Article{Glass:1990:MC,
  author =       "L. B. Glass",
  title =        "Math coprocessors",
  journal =      j-BYTE,
  volume =       "15",
  number =       "1",
  pages =        "337--348",
  month =        jan,
  year =         "1990",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:47:21 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); C5130 (Microprocessor chips); C5230
                 (Digital arithmetic methods)",
  fjournal =     "BYTE Magazine",
  keywords =     "Cyrix 83D87; Floating-point maths; IEEE 754
                 floating-point standard; Integrated Information
                 Technology; Intel 80287; Intel 80387; Intel 8087; Maths
                 coprocessors; Motorola 68881; Motorola 68882; NP-3C87;
                 Weitek Abacus 3167",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Satellite
                 computers",
}


bibtype: incollection
filename: fparith.bib
label: Goldberg:1990:CA
author: D. Goldberg
title: Computer Arithmetic
crossref: Hennessy:1990:CAQ
chapter: A
pages: A-1--A-66
year: 1990
bibdate: Fri Dec 08 13:04:21 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:04:21 ???
acknowledgement: ack-nj
rawauthor: D. Goldberg
rawtitle: Computer Arithmetic
entry:
@InCollection{Goldberg:1990:CA,
  author =       "D. Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:1990:CAQ",
  chapter =      "A",
  pages =        "A-1--A-66",
  year =         "1990",
  bibdate =      "Fri Dec 08 13:04:21 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Goodman:1990:SMR
author: R. H. Goodman
title: Some Models of Relative Error in Products
journal: j-APPL-NUM-MATH
volume: 6
number: 3
pages: 209--220
month: mar
monthnumber: 3
year: 1990
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Thu Sep 1 10:14:16 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:14:16 ???
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/01689274
rawauthor: R. H. Goodman
rawtitle: Some Models of Relative Error in Products
entry:
@Article{Goodman:1990:SMR,
  author =       "R. H. Goodman",
  title =        "Some Models of Relative Error in Products",
  journal =      j-APPL-NUM-MATH,
  volume =       "6",
  number =       "3",
  pages =        "209--220",
  month =        mar,
  year =         "1990",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Sep 1 10:14:16 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}


bibtype: mastersthesis
filename: fparith.bib
label: Goodreau:1990:DIF
author: Michael S. Goodreau
title: The design and implementation of a floating-point format conversion integrated circuit
type: Thesis (M.S.E.E.)
school: University of Washington
address: Seattle, WA, USA
pages: ix + 113
year: 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Michael S. Goodreau
rawtitle: The design and implementation of a floating-point format conversion integrated circuit
keywords:
Electronic digital computers --- Programming.; Floating-point arithmetic.; Integrated circuits --- Design and construction.

entry:
@MastersThesis{Goodreau:1990:DIF,
  author =       "Michael S. Goodreau",
  title =        "The design and implementation of a floating-point
                 format conversion integrated circuit",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Washington",
  address =      "Seattle, WA, USA",
  pages =        "ix + 113",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; Integrated circuits ---
                 Design and construction.",
}


bibtype: incollection
filename: fparith.bib
label: Gries:1990:BDO
author: David Gries
title: Binary to Decimal, One More Time
crossref: Feijen:1990:BOB
chapter: 16
pages: 141--148
year: 1990
DOI: https://doi.org/10.1007/978-1-4612-4476-9_17
bibdate: Sat Sep 03 09:41:32 1994
bibtimestamp: 1994.09.03 09:41:32 ???
URL: https://link.springer.com/chapter/10.1007/978-1-4612-4476-9_17
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: David Gries
rawtitle: Binary to Decimal, One More Time
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/texbook3.bib

note:
This paper presents an alternate proof of Knuth's algorithm cite Knuth:1990:SPW for conversion between decimal and fixed-point binary numbers.

rawnote:
This paper presents an alternate proof of Knuth's algorithm \cite{Knuth:1990:SPW} for conversion between decimal and fixed-point binary numbers.

entry:
@InCollection{Gries:1990:BDO,
  author =       "David Gries",
  title =        "Binary to Decimal, One More Time",
  crossref =     "Feijen:1990:BOB",
  chapter =      "16",
  pages =        "141--148",
  year =         "1990",
  DOI =          "https://doi.org/10.1007/978-1-4612-4476-9_17",
  bibdate =      "Sat Sep 03 09:41:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
  note =         "This paper presents an alternate proof of Knuth's
                 algorithm \cite{Knuth:1990:SPW} for conversion between
                 decimal and fixed-point binary numbers.",
  URL =          "https://link.springer.com/chapter/10.1007/978-1-4612-4476-9_17",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Gu:1990:TIT
author: Li Zhen Gu and Xing Yuan Chen
journal: Journal of Tsinghua University
volume: 30
number: 3
pages: 31--38
year: 1990
MRclass: 65D20 (65-04)
MRnumber: 92a:65070
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
acknowledgement: ack-nhfb
ajournal: J. Tsinghua Univ.
rawauthor: Li Zhen Gu and Xing Yuan Chen
title:
Table-driven implementation of the trigonometric functions using IEEE floating point operations. (Chinese)

rawtitle:
Table-driven implementation of the trigonometric functions using {IEEE} floating point operations. ({Chinese})

entry:
@Article{Gu:1990:TIT,
  author =       "Li Zhen Gu and Xing Yuan Chen",
  title =        "Table-driven implementation of the trigonometric
                 functions using {IEEE} floating point operations.
                 ({Chinese})",
  journal =      "Journal of Tsinghua University",
  volume =       "30",
  number =       "3",
  pages =        "31--38",
  year =         "1990",
  MRclass =      "65D20 (65-04)",
  MRnumber =     "92a:65070",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Tsinghua Univ.",
}


bibtype: book
filename: fparith.bib
label: Hamacher:1990: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: Third
pages: xx + 617
year: 1990
ISBN: 0-07-025685-3 OR 0070256853
ISBN13: 978-0-07-025685-9 OR 9780070256859
LCCN: QA76.9.A73 H351 1990
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:1990: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 =      "Third",
  pages =        "xx + 617",
  year =         "1990",
  ISBN =         "0-07-025685-3",
  ISBN-13 =      "978-0-07-025685-9",
  LCCN =         "QA76.9.A73 H351 1990",
  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: Hashemian:1990:SRA
author: R. Hashemian
title: Square Rooting Algorithms for Integer and Floating-Point Numbers
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1025--1029
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57041
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:03 MDT 2011
bibtimestamp: 2011.07.07 14:20:03 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57041
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Northern Illinois University, Dekalb, IL, USA
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Iterative methods; Number theory
rawauthor: R. Hashemian
rawtitle: Square Rooting Algorithms for Integer and Floating-Point Numbers
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

abstract:
An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple two-step procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bit-shift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.

keywords:
Bit-shift operation; Close estimate; Division by 2; Fast converging iteration; Floating-point numbers; Initial value modification; Integer numbers; Precise root; Real numbers; Square rooting algorithms

rawabstract:
An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple two-step procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bit-shift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.

entry:
@Article{Hashemian:1990:SRA,
  author =       "R. Hashemian",
  title =        "Square Rooting Algorithms for Integer and
                 Floating-Point Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1025--1029",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57041",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57041",
  abstract =     "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise root is evaluated.
                 The major effort in this development has been
                 concentrated on two objectives: high speed and no
                 division operation other than division by 2. The first
                 objective is achieved through a simple two-step
                 procedure for getting the first estimate, and then
                 modifying it by employing a fast converging iteration
                 technique. The second objective is also fulfilled
                 through applying bit-shift operation rather than
                 division operation. The algorithm is simulated for both
                 integer and real numbers, and the results are compared
                 to two methods being widely used. The results
                 (tabulated) show considerable improvement in speed
                 compared to these other two methods.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Department of Electr. Eng., Northern Illinois
                 University, Dekalb, IL, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Bit-shift operation; Close estimate; Division by 2;
                 Fast converging iteration; Floating-point numbers;
                 Initial value modification; Integer numbers; Precise
                 root; Real numbers; Square rooting algorithms",
  summary =      "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise \ldots{}",
  thesaurus =    "Digital arithmetic; Iterative methods; Number theory",
}


bibtype: article
filename: fparith.bib
label: Hokenek:1990:LZA
author: E. Hokenek and R. K. Montoye
title: Leading-zero anticipator (LZA) in the IBM RISC System / 6000 floating-point execution unit
journal: j-IBM-JRD
volume: 34
number: 1
pages: 71--77
month: jan
monthnumber: 1
year: 1990
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
affiliation: IBM Res. Div., Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
thesaurus: Digital arithmetic; IBM computers; Reduced instruction set computing
rawauthor: E. Hokenek and R. K. Montoye
rawtitle: Leading-zero anticipator ({LZA}) in the {IBM RISC System\slash 6000} floating-point execution unit
abstract:
Presents a novel technique used in the multiply-add-fused (MAF) unit of the IBM RISC System/6000 (RS/6000) processor for normalizing the floating-point results. Unlike the conventional procedures applied thus far, the so-called leading-zero anticipator (LZA) of the RS/6000 carries out processing of the leading zeros and ones in parallel with floating-point addition. Therefore, the new circuitry reduces the total latency of the MAF unit by enabling the normalization and addition to take place in a single cycle.

keywords:
Circuitry; Floating-point addition; IBM RISC System/6000 floating-point execution unit; Latency; Leading-zero anticipator; Multiply-add-fused; Normalization; Parallel

rawabstract:
Presents a novel technique used in the multiply-add-fused (MAF) unit of the IBM RISC System/6000 (RS/6000) processor for normalizing the floating-point results. Unlike the conventional procedures applied thus far, the so-called leading-zero anticipator (LZA) of the RS/6000 carries out processing of the leading zeros and ones in parallel with floating-point addition. Therefore, the new circuitry reduces the total latency of the MAF unit by enabling the normalization and addition to take place in a single cycle.

entry:
@Article{Hokenek:1990:LZA,
  author =       "E. Hokenek and R. K. Montoye",
  title =        "Leading-zero anticipator ({LZA}) in the {IBM RISC
                 System\slash 6000} floating-point execution unit",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "71--77",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents a novel technique used in the
                 multiply-add-fused (MAF) unit of the IBM RISC
                 System/6000 (RS/6000) processor for normalizing the
                 floating-point results. Unlike the conventional
                 procedures applied thus far, the so-called leading-zero
                 anticipator (LZA) of the RS/6000 carries out processing
                 of the leading zeros and ones in parallel with
                 floating-point addition. Therefore, the new circuitry
                 reduces the total latency of the MAF unit by enabling
                 the normalization and addition to take place in a
                 single cycle.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classification = "B1265B (Logic circuits); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "Circuitry; Floating-point addition; IBM RISC
                 System/6000 floating-point execution unit; Latency;
                 Leading-zero anticipator; Multiply-add-fused;
                 Normalization; Parallel",
  thesaurus =    "Digital arithmetic; IBM computers; Reduced instruction
                 set computing",
}


bibtype: article
filename: fparith.bib
label: Hokenek:1990:SGR
author: E. Hokenek and R. K. Montoye and P. W. Cook
title: Second-Generation RISC Floating Point with Multiply-Add Fused
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 25
number: 5
pages: 1207--1213
month: oct
monthnumber: 10
year: 1990
CODEN: IJSCBC
DOI: https://doi.org/10.1109/4.62143
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: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; 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
affiliation: IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
rawauthor: E. Hokenek and R. K. Montoye and P. W. Cook
rawtitle: Second-Generation {RISC} Floating Point with Multiply-Add Fused
abstract:
A 440000-transistor second-generation RISC (reduced instruction set computer) floating-point chip is described. The pipeline latency is only two cycles, and a double-precision result is produced every cycle. System throughput and accuracy are increased by using a floating-point multiply-add-fused unit, which carries out a double-precision accumulate as a two-cycle pipelined execution with only one rounding error. While the cycle time (40 ns) is competitive with other CMOS RISC systems, the floating-point performance stretches to the range of bipolar RISC systems (7.4-13 MFLOPS LINPACK). Leading zero anticipation makes the two-cycle pipeline possible by nearly eliminating the additional postnormalization time, and it allows for reduced overall system latency. Partial decode shifters allow complete time sharing for the multiply and data alignment. Improved design techniques for logarithmic addition and higher order counters for multiplication complete this second-generation RISC floating-point unit design.

keywords:
40 Ns; 7.4 To 13 MFLOPS; Double-precision accumulate; Double-precision result; Floating-point chip; Higher order counters; Logarithmic addition; Multiplication; Multiply-add-fused unit; Partial decode shifters; Pipeline latency; Reduced instruction set computer; RISC; Two-cycle pipelined execution

thesaurus:
CMOS integrated circuits; Microprocessor chips; Pipeline processing; Reduced instruction set computing

rawabstract:
A 440000-transistor second-generation RISC (reduced instruction set computer) floating-point chip is described. The pipeline latency is only two cycles, and a double-precision result is produced every cycle. System throughput and accuracy are increased by using a floating-point multiply-add-fused unit, which carries out a double-precision accumulate as a two-cycle pipelined execution with only one rounding error. While the cycle time (40 ns) is competitive with other CMOS RISC systems, the floating-point performance stretches to the range of bipolar RISC systems (7.4-13 MFLOPS LINPACK). Leading zero anticipation makes the two-cycle pipeline possible by nearly eliminating the additional postnormalization time, and it allows for reduced overall system latency. Partial decode shifters allow complete time sharing for the multiply and data alignment. Improved design techniques for logarithmic addition and higher order counters for multiplication complete this second-generation RISC floating-point unit design.

entry:
@Article{Hokenek:1990:SGR,
  author =       "E. Hokenek and R. K. Montoye and P. W. Cook",
  title =        "Second-Generation {RISC} Floating Point with
                 Multiply-Add Fused",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "25",
  number =       "5",
  pages =        "1207--1213",
  month =        oct,
  year =         "1990",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.62143",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 440000-transistor second-generation RISC (reduced
                 instruction set computer) floating-point chip is
                 described. The pipeline latency is only two cycles, and
                 a double-precision result is produced every cycle.
                 System throughput and accuracy are increased by using a
                 floating-point multiply-add-fused unit, which carries
                 out a double-precision accumulate as a two-cycle
                 pipelined execution with only one rounding error. While
                 the cycle time (40 ns) is competitive with other CMOS
                 RISC systems, the floating-point performance stretches
                 to the range of bipolar RISC systems (7.4-13 MFLOPS
                 LINPACK). Leading zero anticipation makes the two-cycle
                 pipeline possible by nearly eliminating the additional
                 postnormalization time, and it allows for reduced
                 overall system latency. Partial decode shifters allow
                 complete time sharing for the multiply and data
                 alignment. Improved design techniques for logarithmic
                 addition and higher order counters for multiplication
                 complete this second-generation RISC floating-point
                 unit design.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "40 Ns; 7.4 To 13 MFLOPS; Double-precision accumulate;
                 Double-precision result; Floating-point chip; Higher
                 order counters; Logarithmic addition; Multiplication;
                 Multiply-add-fused unit; Partial decode shifters;
                 Pipeline latency; Reduced instruction set computer;
                 RISC; Two-cycle pipelined execution",
  numericalindex = "Time 4.0E-08 s; Computer speed 7.4E+06 to 1.3E+07
                 FLOPS",
  summary =      "A 440000-transistor second-generation RISC (reduced
                 instruction set computer) floating-point chip is
                 described. The pipeline latency is only two cycles, and
                 a double-precision result is produced every cycle.
                 System throughput and accuracy are increased \ldots{}",
  thesaurus =    "CMOS integrated circuits; Microprocessor chips;
                 Pipeline processing; Reduced instruction set
                 computing",
}


bibtype: article
filename: fparith.bib
label: Hong:1990:DTP
author: S. J. Hong
title: The design of a testable parallel multiplier
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 3
pages: 411--416
month: mar
monthnumber: 3
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.48874
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:00 MDT 2011
bibtimestamp: 2011.07.07 14:20:00 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48874
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. J. Hong
rawtitle: The design of a testable parallel multiplier
entry:
@Article{Hong:1990:DTP,
  author =       "S. J. Hong",
  title =        "The design of a testable parallel multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "3",
  pages =        "411--416",
  month =        mar,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.48874",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48874",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Horiguchi:1990:FNR
author: Hiroshi Horiguchi
title: Floating-Point Numbers and Real Numbers
journal: j-ADV-SOFT-SCI-TECH
volume: 1
pages: 157--??
year: 1990
ISSN: 1044-7997 OR 10447997
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Advances in software science and technology
acknowledgement: ack-nhfb
rawauthor: Hiroshi Horiguchi
rawtitle: Floating-Point Numbers and Real Numbers
entry:
@Article{Horiguchi:1990:FNR,
  author =       "Hiroshi Horiguchi",
  title =        "Floating-Point Numbers and Real Numbers",
  journal =      j-ADV-SOFT-SCI-TECH,
  volume =       "1",
  number =       "??",
  pages =        "157--??",
  year =         "1990",
  ISSN =         "1044-7997",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in software science and technology",
}


bibtype: techreport
filename: fparith.bib
label: IBM:1990:AXI
author: IBM Corporation
title: ACRITH-XSC: IBM High Accuracy Arithmetic --- Extended Scientific Computation
type: Technical Report
number: GC33-6461-01, SC33-6462-00, SC33-6463-00, SC33-6464-00, SC33-6466-00.
institution: pub-IBM
address: pub-IBM:adr
pages: 157--??
year: 1990
bibdate: Thu Jan 21 17:27:09 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2016.01.21 17:27:09 ???
TOC: 1. General Information 2. Reference 3. Sample Programs 4. How To Use 5. Syntax Diagrams
acknowledgement: ack-nhfb
rawauthor: {IBM Corporation}
rawtitle: {ACRITH-XSC}: {IBM} High Accuracy Arithmetic --- Extended Scientific Computation
rawTOC: 1. General Information \\ 2. Reference \\ 3. Sample Programs \\ 4. How To Use \\ 5. Syntax Diagrams
entry:
@TechReport{IBM:1990:AXI,
  author =       "{IBM Corporation}",
  title =        "{ACRITH-XSC}: {IBM} High Accuracy Arithmetic ---
                 Extended Scientific Computation",
  type =         "Technical Report",
  number =       "GC33-6461-01, SC33-6462-00, SC33-6463-00,
                 SC33-6464-00, SC33-6466-00.",
  institution =  pub-IBM,
  address =      pub-IBM:adr,
  year =         "1990",
  bibdate =      "Thu Jan 21 17:27:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. General Information \\
                 2. Reference \\
                 3. Sample Programs \\
                 4. How To Use \\
                 5. Syntax Diagrams",
}


bibtype: book
filename: fparith.bib
label: IBM:1990:IRS
editor: Mamata Misra
title: IBM RISC System / 6000 Technology, publication SA23-2619-00
publisher: pub-IBM
address: pub-IBM:adr
pages: 157--??
year: 1990
bibdate: Wed Sep 14 23:02:26 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 23:02:26 ???
acknowledgement: ack-nhfb
raweditor: Mamata Misra
rawtitle: {IBM RISC System\slash 6000 Technology, publication SA23-2619-00}
entry:
@Book{IBM:1990:IRS,
  editor =       "Mamata Misra",
  title =        "{IBM RISC System\slash 6000 Technology, publication
                 SA23-2619-00}",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1990",
  bibdate =      "Wed Sep 14 23:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Jarvis:1990:ICA
author: P. Jarvis
title: Implementing Cordic Algorithms
journal: j-DDJ
volume: 15
number: 10
pages: 152--158
month: oct
monthnumber: 10
year: 1990
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Sep 1 10:15:40 1994
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: P. Jarvis
rawtitle: Implementing {Cordic} Algorithms
entry:
@Article{Jarvis:1990:ICA,
  author =       "P. Jarvis",
  title =        "Implementing {Cordic} Algorithms",
  journal =      j-DDJ,
  volume =       "15",
  number =       "10",
  pages =        "152--158",
  month =        oct,
  year =         "1990",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: inproceedings
filename: fparith.bib
label: Kahan:1990:HCA
author: W. Kahan
title: How Cray's arithmetic hurts scientific computation (and what might be done about it)
crossref: CUG:1990:PSC
pages: 42
day: 14
month: jun
monthnumber: 6
year: 1990
bibdate: Tue Jan 03 18:17:16 2006
bibtimestamp: 2006.01.03 18:17:16 ???
note: Manuscript prepared for the Cray User Group meeting in Toronto, Canada, April 10, 1990.
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Manuscript prepared for the Cray User Group meeting in Toronto, Canada, April 10, 1990.
rawtitle: How {Cray}'s arithmetic hurts scientific computation (and what might be done about it)
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://754r.ucbtest.org/issues/cray-hurts-uk.pdf; http://754r.ucbtest.org/issues/cray-hurts-ut.pdf; http://754r.ucbtest.org/issues/cray-hurts.pdf

entry:
@InProceedings{Kahan:1990:HCA,
  author =       "W. Kahan",
  title =        "How {Cray}'s arithmetic hurts scientific computation
                 (and what might be done about it)",
  crossref =     "CUG:1990:PSC",
  pages =        "42",
  day =          "14",
  month =        jun,
  year =         "1990",
  bibdate =      "Tue Jan 03 18:17:16 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript prepared for the Cray User Group meeting in
                 Toronto, Canada, April 10, 1990.",
  URL =          "http://754r.ucbtest.org/issues/cray-hurts-uk.pdf;
                 http://754r.ucbtest.org/issues/cray-hurts-ut.pdf;
                 http://754r.ucbtest.org/issues/cray-hurts.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Kahan:1990:PCA
author: William Kahan
title: Paradoxes in concepts of accuracy
publisher: Carnegie Mellon University
address: Pittsburgh, PA, USA
pages: 42
year: 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: 1 videocassette (60 min.)
series: Distinguished lecture series
keywords: Computer arithmetic.; Floating-point arithmetic --- Data processing.
acknowledgement: ack-nhfb
rawauthor: William Kahan
rawnote: 1 videocassette (60 min.)
rawtitle: Paradoxes in concepts of accuracy
remark:
Lecture given February 15, 1990. VHS format. Lecturer, William Kahan. Paradoxes expose errors in conventional wisdom about floating-point arithmetic.

entry:
@Misc{Kahan:1990:PCA,
  author =       "William Kahan",
  title =        "Paradoxes in concepts of accuracy",
  publisher =    "Carnegie Mellon University",
  address =      "Pittsburgh, PA, USA",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "1 videocassette (60 min.)",
  series =       "Distinguished lecture series",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Floating-point arithmetic ---
                 Data processing.",
  remark =       "Lecture given February 15, 1990. VHS format. Lecturer,
                 William Kahan. Paradoxes expose errors in conventional
                 wisdom about floating-point arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Kalbasi:1990:CYT
author: K. Kalbasi
title: Can you trust your computer?
journal: j-IEEE-POT
volume: 9
number: 2
pages: 15--18
month: apr
monthnumber: 4
year: 1990
CODEN: IEPTDF
ISSN: 0278-6648 (print), 1558-1772 (electronic) OR 02786648 (print), 15581772 (electronic)
ISSNL: 0278-6648 OR 02786648
bibdate: Wed Sep 14 19:14:21 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 19:14:21 ???
fjournal: IEEE Potentials
acknowledgement: ack-nj
rawauthor: K. Kalbasi
rawtitle: Can you trust your computer?
entry:
@Article{Kalbasi:1990:CYT,
  author =       "K. Kalbasi",
  title =        "Can you trust your computer?",
  journal =      j-IEEE-POT,
  volume =       "9",
  number =       "2",
  pages =        "15--18",
  month =        apr,
  year =         "1990",
  CODEN =        "IEPTDF",
  ISSN =         "0278-6648 (print), 1558-1772 (electronic)",
  ISSN-L =       "0278-6648",
  bibdate =      "Wed Sep 14 19:14:21 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Potentials",
}


bibtype: article
filename: fparith.bib
label: Katsuno:1990:BFP
author: A. Katsuno and H. Takahashi and H. Kubosawa and T. Sato and A. Suga and G. Goto
title: A 64-bit Floating-Point Processing Unit with a Horizontal Instruction Code for Parallel Operations
crossref: IEEE:1990:PII
pages: 347--350
year: 1990
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
acknowledgement: ack-nj
rawauthor: A. Katsuno and H. Takahashi and H. Kubosawa and T. Sato and A. Suga and G. Goto
rawtitle: A 64-bit Floating-Point Processing Unit with a Horizontal Instruction Code for Parallel Operations
entry:
@Article{Katsuno:1990:BFP,
  author =       "A. Katsuno and H. Takahashi and H. Kubosawa and T.
                 Sato and A. Suga and G. Goto",
  title =        "A 64-bit Floating-Point Processing Unit with a
                 Horizontal Instruction Code for Parallel Operations",
  crossref =     "IEEE:1990:PII",
  pages =        "347--350",
  year =         "1990",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Khan:1990:FPA
author: A. Khan
title: Floating point architecture and implementation
crossref: Wescon:1990:WCR
pages: 205--213
year: 1990
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
acknowledgement: ack-nhfb
thesaurus: Computer architecture; Digital arithmetic
rawauthor: A. Khan
rawtitle: Floating point architecture and implementation
abstract:
Analyzes various requirements of efficient floating point architecture and implementation. The basic elements of architecture such as latency, repeat rate and issue rate are defined. Handling various exceptions in a precise manner is described. Finally, a description of one example (MIPS R3010) is provided. (0 Refs.)

keywords:
Elements of architecture; Floating point architecture; Issue rate; Latency; MIPS R3010; Repeat rate; Requirements

rawabstract:
Analyzes various requirements of efficient floating point architecture and implementation. The basic elements of architecture such as latency, repeat rate and issue rate are defined. Handling various exceptions in a precise manner is described. Finally, a description of one example (MIPS R3010) is provided. (0 Refs.)

entry:
@InProceedings{Khan:1990:FPA,
  author =       "A. Khan",
  title =        "Floating point architecture and implementation",
  crossref =     "Wescon:1990:WCR",
  pages =        "205--213",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Analyzes various requirements of efficient floating
                 point architecture and implementation. The basic
                 elements of architecture such as latency, repeat rate
                 and issue rate are defined. Handling various exceptions
                 in a precise manner is described. Finally, a
                 description of one example (MIPS R3010) is provided. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  availability = "Western Periodicals Co., 13000 Rayner Street, North
                 Hollywood, CA 91605, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods)",
  keywords =     "Elements of architecture; Floating point architecture;
                 Issue rate; Latency; MIPS R3010; Repeat rate;
                 Requirements",
  thesaurus =    "Computer architecture; Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Kiernan:1990:FAE
author: J. M. Kiernan and T. B. Blachowiak
title: Fast, Accurate Elementary Functions For the Cray Y-MP Computer
crossref: CUG:1990:PSC
pages: 243--252
year: 1990
bibdate: Thu Sep 1 10:15:30 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:30 ???
acknowledgement: ack-nj
rawauthor: J. M. Kiernan and T. B. Blachowiak
rawtitle: Fast, Accurate Elementary Functions For the {Cray Y-MP} Computer
entry:
@InProceedings{Kiernan:1990:FAE,
  author =       "J. M. Kiernan and T. B. Blachowiak",
  title =        "Fast, Accurate Elementary Functions For the {Cray
                 Y-MP} Computer",
  crossref =     "CUG:1990:PSC",
  pages =        "243--252",
  year =         "1990",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: incollection
filename: fparith.bib
label: Knuth:1990:SPW
author: Donald E. Knuth
title: A Simple Program Whose Proof Isn't
crossref: Feijen:1990:BOB
chapter: 27
pages: 233--242
year: 1990
bibdate: Mon Feb 03 07:07:55 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.02.03 07:07:55 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawtitle: A Simple Program Whose Proof Isn't
note:
Reprinted in cite [Chapter 11]Knuth:2010:SPD. This paper discusses the algorithm used in TeX for converting between decimal and scaled fixed-point binary values, and for guaranteeing a minimum number of digits in the decimal representation. See also cite Clinger:1990:HRF,Clinger:2004:RHR for decimal to binary conversion, cite Steele:1990:HPF,Steele:2004:RHP for binary to decimal conversion, and cite Gries:1990:BDO for an alternate proof of Knuth's algorithm.

rawnote:
Reprinted in \cite[Chapter 11]{Knuth:2010:SPD}. This paper discusses the algorithm used in {\TeX} for converting between decimal and scaled fixed-point binary values, and for guaranteeing a minimum number of digits in the decimal representation. See also \cite{Clinger:1990:HRF,Clinger:2004:RHR} for decimal to binary conversion, \cite{Steele:1990:HPF,Steele:2004:RHP} for binary to decimal conversion, and \cite{Gries:1990:BDO} for an alternate proof of Knuth's algorithm.

entry:
@InCollection{Knuth:1990:SPW,
  author =       "Donald E. Knuth",
  title =        "A Simple Program Whose Proof Isn't",
  crossref =     "Feijen:1990:BOB",
  chapter =      "27",
  pages =        "233--242",
  year =         "1990",
  bibdate =      "Mon Feb 03 07:07:55 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[Chapter 11]{Knuth:2010:SPD}. This
                 paper discusses the algorithm used in {\TeX} for
                 converting between decimal and scaled fixed-point
                 binary values, and for guaranteeing a minimum number of
                 digits in the decimal representation. See also
                 \cite{Clinger:1990:HRF,Clinger:2004:RHR} for decimal to
                 binary conversion,
                 \cite{Steele:1990:HPF,Steele:2004:RHP} for binary to
                 decimal conversion, and \cite{Gries:1990:BDO} for an
                 alternate proof of Knuth's algorithm.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Koren:1990:EEF
author: I. Koren and O. Zinaty
title: Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
journal: j-IEEE-TRANS-COMPUT
volume: C-39
number: 8
pages: 1030--1037
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57042
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:30 1994
bibtimestamp: 1994.09.01 10:15:30 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: I. Koren and O. Zinaty
rawtitle: Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Koren:1990:EEF,
  author =       "I. Koren and O. Zinaty",
  title =        "Evaluating Elementary Functions in a Numerical
                 Coprocessor Based on Rational Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1030--1037",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57042",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Kornerup:1990:ARB
author: Peter Kornerup and David W. Matula
title: An algorithm for redundant binary bit-pipelined rational arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1106--1115
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57048
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:04 MDT 2011
bibtimestamp: 2011.07.07 14:20:04 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57048
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Peter Kornerup and David W. Matula
rawtitle: An algorithm for redundant binary bit-pipelined rational arithmetic
abstract:
The authors introduce a redundant binary representation of the rationals and an associated algorithm for computing the sum, difference, product, quotient, and other useful functions of two rational operands, using this representation. The algorithm extends R. W. Gosper's (1972) partial quotient arithmetic algorithm and allows the design of an online arithmetic unit with computations granularized at the signed bit level. Each input or output port can be independently set to receive/produce operands/result in either binary radix or the binary rational representation. The authors investigate by simulation the interconnection of several such units for the parallel computation of more complicated expressions in a tree-pipelined manner, with particular regard to measuring individual and compounded online delays

rawabstract:
The authors introduce a redundant binary representation of the rationals and an associated algorithm for computing the sum, difference, product, quotient, and other useful functions of two rational operands, using this representation. The algorithm extends R. W. Gosper's (1972) partial quotient arithmetic algorithm and allows the design of an online arithmetic unit with computations granularized at the signed bit level. Each input or output port can be independently set to receive/produce operands/result in either binary radix or the binary rational representation. The authors investigate by simulation the interconnection of several such units for the parallel computation of more complicated expressions in a tree-pipelined manner, with particular regard to measuring individual and compounded online delays

entry:
@Article{Kornerup:1990:ARB,
  author =       "Peter Kornerup and David W. Matula",
  title =        "An algorithm for redundant binary bit-pipelined
                 rational arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1106--1115",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57048",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57048",
  abstract =     "The authors introduce a redundant binary
                 representation of the rationals and an associated
                 algorithm for computing the sum, difference, product,
                 quotient, and other useful functions of two rational
                 operands, using this representation. The algorithm
                 extends R. W. Gosper's (1972) partial quotient
                 arithmetic algorithm and allows the design of an online
                 arithmetic unit with computations granularized at the
                 signed bit level. Each input or output port can be
                 independently set to receive/produce operands/result in
                 either binary radix or the binary rational
                 representation. The authors investigate by simulation
                 the interconnection of several such units for the
                 parallel computation of more complicated expressions in
                 a tree-pipelined manner, with particular regard to
                 measuring individual and compounded online delays",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Laakso:1990:RFP
author: T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo
booktitle: IEEE International Conference on Systems Engineering, 1990
title: Reduction of floating-point roundoff noise in recursive digital filters with error feedback
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 244--247
year: 1990
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo
rawbooktitle: {IEEE} International Conference on Systems Engineering, 1990
rawtitle: Reduction of floating-point roundoff noise in recursive digital filters with error feedback
entry:
@InProceedings{Laakso:1990:RFP,
  author =       "T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo",
  booktitle =    "{IEEE} International Conference on Systems
                 Engineering, 1990",
  title =        "Reduction of floating-point roundoff noise in
                 recursive digital filters with error feedback",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "244--247",
  year =         "1990",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The reduction of roundoff noise in floating-point
                 recursive digital filters by means of error feedback is
                 discussed. Optimal (minimum-noise) error feedback is
                 formulated, and it is shown to be different from the
                 optimal solution in the fixed-point \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Lee:1990:OPC
author: Vernon A. Lee, Jr. and Hans-J. Boehm
title: Optimizing programs over the constructive reals
journal: j-SIGPLAN
volume: 25
number: 6
pages: 102--111
month: jun
monthnumber: 6
year: 1990
CODEN: SINODQ
DOI: https://doi.org/10.1145/93542.93558
ISBN: 0-89791-364-7 OR 0897913647
ISBN13: 978-0-89791-364-5 OR 9780897913645
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:15:53 MST 2003
bibtimestamp: 2003.12.14 09:15:53 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p102-lee/
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Rice University
affiliationaddress: Houston, TX, USA
annote: Published as part of the Proceedings of PLDI'90.
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
journalabr: SIGPLAN Not
thesaurus: Data structures; Mathematics computing; Programming
rawauthor: Vernon A. {Lee, Jr.} and Hans-J. Boehm
rawtitle: Optimizing programs over the constructive reals
bibsource:
Compendex database; http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/93542/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The constructive reals provide programmers with a useful mechanism for prototyping numerical programs, and for experimenting with numerical algorithms. Unfortunately, the performance of current implementations is inadequate for some potential applications. In particular, these implementations tend to be space inefficient, in that they essentially require a complete computation history to be maintained. Some numerical analysts propose that the programmer instead be provided with variable precision interval arithmetic, and then be required to write code to restart a computation when the intervals become too inaccurate. Though this model is no doubt appropriate at times, it is not an adequate replacement for exact arithmetic. The correct transformation from a program operating on the constructive reals to a reasonable program using iterated interval arithmetic can be nontrivial and error prone. Here we present a technique based on program slicing to both automate this process and reduce the amount of reexecution. Thus the programmer is still free to use the simpler abstraction of exact real arithmetic, but we can provide a more efficient interval arithmetic based implementation. Some preliminary empirical results are presented.

keywords:
algorithms; Computer Operating Systems; Computer Programming Languages --- Design; Constructive reals; Efficient interval arithmetic based implementation; Empirical results; Exact real arithmetic; Numerical algorithms; Numerical analysts; Numerical programs; Optimizing Compilers; performance; Performance; Program Compilers; Program slicing; Reexecution; Variable precision interval arithmetic

subject:
bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Optimization. bf F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf F.2.2 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.

rawabstract:
The constructive reals provide programmers with a useful mechanism for prototyping numerical programs, and for experimenting with numerical algorithms. Unfortunately, the performance of current implementations is inadequate for some potential applications. In particular, these implementations tend to be space inefficient, in that they essentially require a complete computation history to be maintained. Some numerical analysts propose that the programmer instead be provided with variable precision interval arithmetic, and then be required to write code to restart a computation when the intervals become too inaccurate. Though this model is no doubt appropriate at times, it is not an adequate replacement for exact arithmetic. The correct transformation from a program operating on the constructive reals to a reasonable program using iterated interval arithmetic can be nontrivial and error prone. Here we present a technique based on program slicing to both automate this process and reduce the amount of reexecution. Thus the programmer is still free to use the simpler abstraction of exact real arithmetic, but we can provide a more efficient interval arithmetic based implementation. Some preliminary empirical results are presented.

entry:
@Article{Lee:1990:OPC,
  author =       "Vernon A. {Lee, Jr.} and Hans-J. Boehm",
  title =        "Optimizing programs over the constructive reals",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "6",
  pages =        "102--111",
  month =        jun,
  year =         "1990",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/93542.93558",
  ISBN =         "0-89791-364-7",
  ISBN-13 =      "978-0-89791-364-5",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:53 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/93542/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p102-lee/",
  abstract =     "The constructive reals provide programmers with a
                 useful mechanism for prototyping numerical programs,
                 and for experimenting with numerical algorithms.
                 Unfortunately, the performance of current
                 implementations is inadequate for some potential
                 applications. In particular, these implementations tend
                 to be space inefficient, in that they essentially
                 require a complete computation history to be
                 maintained. Some numerical analysts propose that the
                 programmer instead be provided with variable precision
                 interval arithmetic, and then be required to write code
                 to restart a computation when the intervals become too
                 inaccurate. Though this model is no doubt appropriate
                 at times, it is not an adequate replacement for exact
                 arithmetic. The correct transformation from a program
                 operating on the constructive reals to a reasonable
                 program using iterated interval arithmetic can be
                 nontrivial and error prone. Here we present a technique
                 based on program slicing to both automate this process
                 and reduce the amount of reexecution. Thus the
                 programmer is still free to use the simpler abstraction
                 of exact real arithmetic, but we can provide a more
                 efficient interval arithmetic based implementation.
                 Some preliminary empirical results are presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Rice University",
  affiliationaddress = "Houston, TX, USA",
  annote =       "Published as part of the Proceedings of PLDI'90.",
  classification = "722; 723; C6110 (Systems analysis and programming);
                 C6120 (File organisation); C7310 (Mathematics)",
  confdate =     "20-22 June 1990",
  conference =   "Proceedings of the ACM SIGPLAN '90 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1990",
  conflocation = "White Plains, NY, USA",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "algorithms; Computer Operating Systems; Computer
                 Programming Languages --- Design; Constructive reals;
                 Efficient interval arithmetic based implementation;
                 Empirical results; Exact real arithmetic; Numerical
                 algorithms; Numerical analysts; Numerical programs;
                 Optimizing Compilers; performance; Performance; Program
                 Compilers; Program slicing; Reexecution; Variable
                 precision interval arithmetic",
  meetingaddress = "White Plains, NY, USA",
  meetingdate =  "Jun 20--22 1990",
  meetingdate2 = "06/20--22/90",
  sponsor =      "Assoc for Computing Machinery, Special Interest Group
                 on Programming Languages",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Optimization. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures.",
  thesaurus =    "Data structures; Mathematics computing; Programming",
}


bibtype: article
filename: fparith.bib
label: Ling:1990:AIM
author: H. Ling
title: An approach to implementing multiplication with small tables
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 5
pages: 717--718
month: may
monthnumber: 5
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.53588
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:02 MDT 2011
bibtimestamp: 2011.07.07 14:20:02 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53588
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. Ling
rawtitle: An approach to implementing multiplication with small tables
entry:
@Article{Ling:1990:AIM,
  author =       "H. Ling",
  title =        "An approach to implementing multiplication with small
                 tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "5",
  pages =        "717--718",
  month =        may,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.53588",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53588",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Lozier:1990:CPL
author: D. W. Lozier and F. W. J. Olver
title: Closure and Precision in Level-Index Arithmetic
journal: j-SIAM-J-NUMER-ANAL
volume: 27
number: 5
pages: 1295--1304
month: oct
monthnumber: 10
year: 1990
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65-04 (65G05)
MRnumber: 91f:65002
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: D. W. Lozier and F. W. J. Olver
rawtitle: Closure and Precision in Level-Index Arithmetic
entry:
@Article{Lozier:1990:CPL,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Closure and Precision in Level-Index Arithmetic",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "5",
  pages =        "1295--1304",
  month =        oct,
  year =         "1990",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65-04 (65G05)",
  MRnumber =     "91f:65002",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: article
filename: fparith.bib
label: MacDonald:1990:IFP
author: Tom MacDonald
title: IEEE Floating-Point Arithmetic and C
journal: j-JCLT
volume: 2
number: 2
pages: 102--112
month: sep
monthnumber: 9
year: 1990
ISSN: 1042-5721 OR 10425721
bibdate: Thu Nov 8 14:50:33 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:33 ???
fjournal: The Journal of C Language Translation
acknowledgement: ack-nj
rawauthor: Tom MacDonald
rawtitle: {IEEE} Floating-Point Arithmetic and {C}
entry:
@Article{MacDonald:1990:IFP,
  author =       "Tom MacDonald",
  title =        "{IEEE} Floating-Point Arithmetic and {C}",
  journal =      j-JCLT,
  volume =       "2",
  number =       "2",
  pages =        "102--112",
  month =        sep,
  year =         "1990",
  ISSN =         "1042-5721",
  bibdate =      "Thu Nov 8 14:50:33 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Journal of {C} Language Translation",
}


bibtype: article
filename: fparith.bib
label: Mandelbaum:1990:SMD
author: D. M. Mandelbaum
title: A systematic method for division with high average bit skipping
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 1
pages: 127--130
month: jan
monthnumber: 1
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.46287
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:19:59 MDT 2011
bibtimestamp: 2011.07.07 14:19:59 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=46287
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. M. Mandelbaum
rawtitle: A systematic method for division with high average bit skipping
entry:
@Article{Mandelbaum:1990:SMD,
  author =       "D. M. Mandelbaum",
  title =        "A systematic method for division with high average bit
                 skipping",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "1",
  pages =        "127--130",
  month =        jan,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.46287",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:19:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=46287",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: phdthesis
filename: fparith.bib
label: MangaEbongue:1990:PBV
author: Charles Manga Ebongue
type: These Doctoral
school: Sciences Appliquees, Universite Paris 6
address: Paris, France
pages: 127--130
year: 1990
bibdate: Thu May 09 10:03:41 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 10:03:41 ???
note: Sous la direction de Alain Greiner.
language: French
acknowledgement: ack-nhfb
rawauthor: Charles {Manga Ebongue}
rawnote: Sous la direction de Alain Greiner.
title:
Processeur 32 Bits en Virgule Flottante: Techniques de Validation Fonctionnelle, Electrique et Test a la Conception. (French) [32-bit Floating-Point Processor: Techniques of Functional and Electrical Validation and Test in the Design]

abstract:
Cette these developpe deux aspects de la conception des circuits integres: (1) le premier aspect correspond a la methodologie d'implantation du processeur de calcul en virgule flottante developpe au laboratoire MASI par l'equipe de Cao & VLSI de l'Universite Pierre et Marie Curie, (2) le deuxieme aspect presente les travaux concernant une methodologie de test a la conception conduisant aussi bien a la validation fonctionnelle et electrique au cours de la conception qu'a la testabilite apres fabrication. Le premier aspect a des implications a differents niveaux: (1) au niveau assemblage par l'introduction d'une methodologie de conception specifique au circuit, (2) au niveau electrique pour le choix et la conception d'une bibliotheque de cellules standards qui tient compte des caracteristiques dynamiques des signaux sur chaque nud du circuit. Le deuxieme aspect a pour resultat l'introduction d'une technique originale de recherche de vecteurs de test. De meme, la validation fonctionnelle de ce circuit sera invoquee en resolvant les principaux problemes de coherence entre les masques dessines et la liste des interconnexions.

rawabstract:
Cette th{\`e}se d{\'e}veloppe deux aspects de la conception des circuits integr{\'e}s: (1) le premier aspect correspond {\`a} la m{\'e}thodologie d'implantation du processeur de calcul en virgule flottante d{\'e}velopp{\'e} au laboratoire MASI par l'{\'e}quipe de Cao \& VLSI de l'Universit{\'e} Pierre et Marie Curie, (2) le deuxi{\'e}me aspect pr{\'e}sente les travaux concernant une m{\'e}thodologie de test {\`a} la conception conduisant aussi bien {\`a} la validation fonctionnelle et {\'e}lectrique au cours de la conception qu'{\`a} la testabilit{\'e} apr{\`e}s fabrication. Le premier aspect a des implications {\`a} diff{\'e}rents niveaux: (1) au niveau assemblage par l'introduction d'une m{\'e}thodologie de conception sp{\'e}cifique au circuit, (2) au niveau {\'e}lectrique pour le choix et la conception d'une biblioth{\`e}que de cellules standards qui tient compte des caract{\'e}ristiques dynamiques des signaux sur chaque nud du circuit. Le deuxi{\`e}me aspect a pour r{\'e}sultat l'introduction d'une technique originale de recherche de vecteurs de test. De m{\^e}me, la validation fonctionnelle de ce circuit sera invoqu{\^e}e en r{\^e}solvant les principaux probl{\`e}mes de coh{\'e}rence entre les masques d{\'e}ssin{\'e}s et la liste des interconnexions.

rawtitle:
Processeur 32 Bits en Virgule Flottante: Techniques de Validation Fonctionnelle, {{\'E}}lectrique et Test {\`a} la Conception. ({French}) [32-bit Floating-Point Processor: Techniques of Functional and Electrical Validation and Test in the Design]

entry:
@PhdThesis{MangaEbongue:1990:PBV,
  author =       "Charles {Manga Ebongue}",
  title =        "Processeur 32 Bits en Virgule Flottante: Techniques de
                 Validation Fonctionnelle, {{\'E}}lectrique et Test
                 {\`a} la Conception. ({French}) [32-bit Floating-Point
                 Processor: Techniques of Functional and Electrical
                 Validation and Test in the Design]",
  type =         "Th{\`e}se Doctoral",
  school =       "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
  address =      "Paris, France",
  year =         "1990",
  bibdate =      "Thu May 09 10:03:41 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Sous la direction de Alain Greiner.",
  abstract =     "Cette th{\`e}se d{\'e}veloppe deux aspects de la
                 conception des circuits integr{\'e}s: (1) le premier
                 aspect correspond {\`a} la m{\'e}thodologie
                 d'implantation du processeur de calcul en virgule
                 flottante d{\'e}velopp{\'e} au laboratoire MASI par
                 l'{\'e}quipe de Cao \& VLSI de l'Universit{\'e} Pierre
                 et Marie Curie, (2) le deuxi{\'e}me aspect pr{\'e}sente
                 les travaux concernant une m{\'e}thodologie de test
                 {\`a} la conception conduisant aussi bien {\`a} la
                 validation fonctionnelle et {\'e}lectrique au cours de
                 la conception qu'{\`a} la testabilit{\'e} apr{\`e}s
                 fabrication. Le premier aspect a des implications {\`a}
                 diff{\'e}rents niveaux: (1) au niveau assemblage par
                 l'introduction d'une m{\'e}thodologie de conception
                 sp{\'e}cifique au circuit, (2) au niveau {\'e}lectrique
                 pour le choix et la conception d'une biblioth{\`e}que
                 de cellules standards qui tient compte des
                 caract{\'e}ristiques dynamiques des signaux sur chaque
                 nud du circuit. Le deuxi{\`e}me aspect a pour
                 r{\'e}sultat l'introduction d'une technique originale
                 de recherche de vecteurs de test. De m{\^e}me, la
                 validation fonctionnelle de ce circuit sera
                 invoqu{\^e}e en r{\^e}solvant les principaux
                 probl{\`e}mes de coh{\'e}rence entre les masques
                 d{\'e}ssin{\'e}s et la liste des interconnexions.",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: book
filename: fparith.bib
label: Mar:1990:DSP
editor: Amy Mar
title: Digital signal processing applications using the ADSP-2100 family
publisher: pub-PH
address: pub-PH:adr
pages: xvi + 611
year: 1990
ISBN: 0-13-212978-7 OR 0132129787
ISBN13: 978-0-13-212978-7 OR 9780132129787
LCCN: TK5102.5 .D44824 1990
bibdate: Sat Jan 15 05:58:58 MST 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2005.01.15 05:58:58 MST
remark: System requirements for computer disks: IBM PC; PC-DOS 3.0.
subject: Signal processing; Digital techniques; Microprocessors
acknowledgement: ack-nhfb
raweditor: Amy Mar
rawtitle: Digital signal processing applications using the {ADSP-2100} family
entry:
@Book{Mar:1990:DSP,
  editor =       "Amy Mar",
  title =        "Digital signal processing applications using the
                 {ADSP-2100} family",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xvi + 611",
  year =         "1990",
  ISBN =         "0-13-212978-7",
  ISBN-13 =      "978-0-13-212978-7",
  LCCN =         "TK5102.5 .D44824 1990",
  bibdate =      "Sat Jan 15 05:58:58 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "System requirements for computer disks: IBM PC; PC-DOS
                 3.0.",
  subject =      "Signal processing; Digital techniques;
                 Microprocessors",
}


bibtype: article
filename: fparith.bib
label: Margulis:1990:IMI
author: N. Margulis
title: i860 microprocessor internal architecture
journal: j-MICROPROC-MICROSYS
volume: 14
number: 2
pages: 89--96
month: mar
monthnumber: 3
year: 1990
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: N. Margulis
rawtitle: i860 microprocessor internal architecture
entry:
@Article{Margulis:1990:IMI,
  author =       "N. Margulis",
  title =        "i860 microprocessor internal architecture",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "14",
  number =       "2",
  pages =        "89--96",
  month =        mar,
  year =         "1990",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: article
filename: fparith.bib
label: Markstein:1990:CEF
author: P. W. Markstein
title: Computation of elementary functions on the IBM RISC System / 6000 processor
journal: j-IBM-JRD
volume: 34
number: 1
pages: 111--119
month: jan
monthnumber: 1
year: 1990
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65-04 (65D20)
MRnumber: 1 057 659
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
affiliation: IBM Res. Div., Austin, TX, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
thesaurus: Digital arithmetic; IBM computers; Reduced instruction set computing
rawauthor: P. W. Markstein
rawtitle: Computation of elementary functions on the {IBM RISC System\slash 6000} processor
abstract:
The additional speed and precision of the IBM RISC System / 6000 floating-point unit have motivated reexamination of algorithms to perform division, square root, and the elementary functions. New results are obtained which avoid the necessity of doing special testing to get the last bit rounded correctly in accordance with all of the IEEE rounding modes in the case of division and square root. For the elementary function library, a technique is described for always getting the last bit rounded correctly in the selected IEEE rounding mode.

keywords:
correct rounding; Division; Elementary functions; Floating-point unit; IBM RISC System / 6000 processor; IEEE rounding modes; IEEE rounding modes, IBM RISC System/6000 processor; Square root

rawabstract:
The additional speed and precision of the IBM RISC System\slash 6000 floating-point unit have motivated reexamination of algorithms to perform division, square root, and the elementary functions. New results are obtained which avoid the necessity of doing special testing to get the last bit rounded correctly in accordance with all of the IEEE rounding modes in the case of division and square root. For the elementary function library, a technique is described for always getting the last bit rounded correctly in the selected IEEE rounding mode.

entry:
@Article{Markstein:1990:CEF,
  author =       "P. W. Markstein",
  title =        "Computation of elementary functions on the {IBM RISC
                 System\slash 6000} processor",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "111--119",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65-04 (65D20)",
  MRnumber =     "1 057 659",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The additional speed and precision of the IBM RISC
                 System\slash 6000 floating-point unit have motivated
                 reexamination of algorithms to perform division, square
                 root, and the elementary functions. New results are
                 obtained which avoid the necessity of doing special
                 testing to get the last bit rounded correctly in
                 accordance with all of the IEEE rounding modes in the
                 case of division and square root. For the elementary
                 function library, a technique is described for always
                 getting the last bit rounded correctly in the selected
                 IEEE rounding mode.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "correct rounding; Division; Elementary functions;
                 Floating-point unit; IBM RISC System\slash 6000
                 processor; IEEE rounding modes; IEEE rounding modes,
                 IBM RISC System/6000 processor; Square root",
  thesaurus =    "Digital arithmetic; IBM computers; Reduced instruction
                 set computing",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1990:HPD
author: D. Matula
title: Highly parallel divide and square root algorithms for a new generation floating point processor
crossref: Ullrich:1990:CCA
pages: ??--??
year: 1990
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: D. Matula
rawtitle: Highly parallel divide and square root algorithms for a new generation floating point processor
entry:
@InProceedings{Matula:1990:HPD,
  author =       "D. Matula",
  title =        "Highly parallel divide and square root algorithms for
                 a new generation floating point processor",
  crossref =     "Ullrich:1990:CCA",
  pages =        "??--??",
  year =         "1990",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: McCloud:1990:FPU
author: S. McCloud and D. Anderson and C. DeWitt and C. Hinds and Y. W. Ho and D. Marquette and E. Quintana
title: A Floating Point Unit for the 68040
crossref: IEEE:1990:PII
pages: 187--190
year: 1990
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
acknowledgement: ack-nj
rawauthor: S. McCloud and D. Anderson and C. DeWitt and C. Hinds and Y. W. Ho and D. Marquette and E. Quintana
rawtitle: A Floating Point Unit for the 68040
entry:
@InProceedings{McCloud:1990:FPU,
  author =       "S. McCloud and D. Anderson and C. DeWitt and C. Hinds
                 and Y. W. Ho and D. Marquette and E. Quintana",
  title =        "A Floating Point Unit for the 68040",
  crossref =     "IEEE:1990:PII",
  pages =        "187--190",
  year =         "1990",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Metafas:1990:DPP
author: Dimitris E. Metafas and Costas E. Goutis
journal: j-MICROPROC-MICROPROG
volume: 30
number: 1
pages: 51--57
year: 1990
CODEN: MMICDT
DOI: https://doi.org/10.1016/0165-6074(90)90217-W
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
bibdate: Wed Oct 29 14:21:46 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.29 14:21:46 ???
note: Proceedings Euromicro 90: Hardware and Software in System Engineering
URL: https://www.sciencedirect.com/science/article/pii/016560749090217W
fjournal: Microprocessing and Microprogramming
acknowledgement: ack-nhfb
journalURL: https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues
rawauthor: Dimitris E. Metafas and Costas E. Goutis
rawnote: Proceedings Euromicro 90: Hardware and Software in System Engineering
title:
A DSP processor with a powerful set of elementary arithmetic operations based on CORDIC and CCM algorithms

rawtitle:
A {DSP} processor with a powerful set of elementary arithmetic operations based on {CORDIC} and {CCM} algorithms

entry:
@Article{Metafas:1990:DPP,
  author =       "Dimitris E. Metafas and Costas E. Goutis",
  title =        "A {DSP} processor with a powerful set of elementary
                 arithmetic operations based on {CORDIC} and {CCM}
                 algorithms",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "30",
  number =       "1",
  pages =        "51--57",
  year =         "1990",
  CODEN =        "MMICDT",
  DOI =          "https://doi.org/10.1016/0165-6074(90)90217-W",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Wed Oct 29 14:21:46 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Proceedings Euromicro 90: Hardware and Software in
                 System Engineering",
  URL =          "https://www.sciencedirect.com/science/article/pii/016560749090217W",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}


bibtype: mastersthesis
filename: fparith.bib
label: Mills:1990:DIH
author: Karl Scott Mills
type: Thesis (M.S.E.E.)
school: University of Washington
address: Seattle, WA, USA
pages: v + 60 + 3
year: 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer graphics.; Image processing --- Digital techniques.
acknowledgement: ack-nhfb
rawauthor: Karl Scott Mills
title:
The design and implementation of a high performance floating-point image processing and graphics subsystem for the NeXT computer

rawtitle:
The design and implementation of a high performance floating-point image processing and graphics subsystem for the {NeXT} computer

entry:
@MastersThesis{Mills:1990:DIH,
  author =       "Karl Scott Mills",
  title =        "The design and implementation of a high performance
                 floating-point image processing and graphics subsystem
                 for the {NeXT} computer",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Washington",
  address =      "Seattle, WA, USA",
  pages =        "v + 60 + 3",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer graphics.; Image processing --- Digital
                 techniques.",
}


bibtype: article
filename: fparith.bib
label: Montoye:1990:DIR
author: R. K. Montoye and E. Hokenek and S. L. Runyon
title: Design of the IBM RISC System / 6000 floating-point execution unit
journal: j-IBM-JRD
volume: 34
number: 1
pages: 59--70
month: jan
monthnumber: 1
year: 1990
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.341.0059
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Tue Mar 25 14:26:59 MST 1997
bibtimestamp: 1997.03.25 14:26:59 MST
URL: http://www.research.ibm.com/journal/rd/341/ibmrd3401G.pdf
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
affiliation: IBM Res. Div., Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
corpsource: IBM Res. Div., Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
thesaurus: Circuit layout CAD; Digital arithmetic; IBM computers; Logic CAD; Reduced instruction set computing
treatment: P Practical
rawauthor: R. K. Montoye and E. Hokenek and S. L. Runyon
rawtitle: Design of the {IBM RISC System\slash 6000} floating-point execution unit
abstract:
The IBM RISC System / 6000 (RS / 6000) floating-point unit (FPU) exemplifies a second-generation RISC CPU architecture and an implementation which greatly increases floating-point performance and accuracy. The key feature of the FPU is a unified floating-point multiply-add-fused unit (MAF) which performs the accumulate operation (A*B)+C as an indivisible operation. The paper first discusses the motivation for MAF, explaining in some detail why it is an appropriate addition to the floating-point architecture in VLSI. A summary of floating-point operations is then given, with a discussion to demonstrate the parallelism that is possible when the multiply and add are fused. This is followed by a description of the two-stage pipeline used for the version of IEEE double-precision floating-point arithmetic used in the RS / 6000 processor, with delays consistent with its over-all superscalar second-generation RISC architecture. Then the paper describes the interaction of logical and physical design required to incorporate several advances in VLSI arithmetic while accommodating required delay and technological (physical) constraints. The results are then summarized.

keywords:
Accumulate operation; accumulate operation; arithmetic; CAD; circuit layout CAD; digital arithmetic; floating-point architecture; Floating-point architecture; generation RISC CPU architecture; IBM computers; IBM RISC System/6000 floating-point execution unit; IBM RISC System / 6000 floating-point execution unit; IEEE double-precision floating-point; IEEE double-precision floating-point arithmetic; indivisible; Indivisible operation; logic; multiply-add-fused unit; operation; Parallelism; parallelism; reduced instruction set computing; second-; Second-generation RISC CPU architecture; stage pipeline; Superscalar second-generation RISC architecture; superscalar second-generation RISC architecture; two-; Two-stage pipeline; unified floating-point; Unified floating-point multiply-add-fused unit; VLSI arithmetic; VLSI arithmetic, IBM RISC System/6000 floating-point execution unit

classcodes:
B1265B (Logic circuits); B1130B (Computer-aided circuit analysis and design); B1265F (Microprocessors and microcomputers); C5230 (Digital arithmetic methods); C5220 (Computer architecture); C5210B (Computer-aided logic design)C7410D (Electronic engineering)

rawabstract:
The IBM RISC System\slash 6000 (RS\slash 6000) floating-point unit (FPU) exemplifies a second-generation RISC CPU architecture and an implementation which greatly increases floating-point performance and accuracy. The key feature of the FPU is a unified floating-point multiply-add-fused unit (MAF) which performs the accumulate operation (A*B)+C as an indivisible operation. The paper first discusses the motivation for MAF, explaining in some detail why it is an appropriate addition to the floating-point architecture in VLSI. A summary of floating-point operations is then given, with a discussion to demonstrate the parallelism that is possible when the multiply and add are fused. This is followed by a description of the two-stage pipeline used for the version of IEEE double-precision floating-point arithmetic used in the RS\slash 6000 processor, with delays consistent with its over-all superscalar second-generation RISC architecture. Then the paper describes the interaction of logical and physical design required to incorporate several advances in VLSI arithmetic while accommodating required delay and technological (physical) constraints. The results are then summarized.

entry:
@Article{Montoye:1990:DIR,
  author =       "R. K. Montoye and E. Hokenek and S. L. Runyon",
  title =        "Design of the {IBM RISC System\slash 6000}
                 floating-point execution unit",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "59--70",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.341.0059",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://www.research.ibm.com/journal/rd/341/ibmrd3401G.pdf",
  abstract =     "The IBM RISC System\slash 6000 (RS\slash 6000)
                 floating-point unit (FPU) exemplifies a
                 second-generation RISC CPU architecture and an
                 implementation which greatly increases floating-point
                 performance and accuracy. The key feature of the FPU is
                 a unified floating-point multiply-add-fused unit (MAF)
                 which performs the accumulate operation (A*B)+C as an
                 indivisible operation. The paper first discusses the
                 motivation for MAF, explaining in some detail why it is
                 an appropriate addition to the floating-point
                 architecture in VLSI. A summary of floating-point
                 operations is then given, with a discussion to
                 demonstrate the parallelism that is possible when the
                 multiply and add are fused. This is followed by a
                 description of the two-stage pipeline used for the
                 version of IEEE double-precision floating-point
                 arithmetic used in the RS\slash 6000 processor, with
                 delays consistent with its over-all superscalar
                 second-generation RISC architecture. Then the paper
                 describes the interaction of logical and physical
                 design required to incorporate several advances in VLSI
                 arithmetic while accommodating required delay and
                 technological (physical) constraints. The results are
                 then summarized.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classcodes =   "B1265B (Logic circuits); B1130B (Computer-aided
                 circuit analysis and design); B1265F (Microprocessors
                 and microcomputers); C5230 (Digital arithmetic
                 methods); C5220 (Computer architecture); C5210B
                 (Computer-aided logic design)C7410D (Electronic
                 engineering)",
  classification = "B1130B (Computer-aided circuit analysis and design);
                 B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); C5210B (Computer-aided logic design);
                 C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods); C7410D (Electronic engineering)",
  corpsource =   "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "Accumulate operation; accumulate operation;
                 arithmetic; CAD; circuit layout CAD; digital
                 arithmetic; floating-point architecture; Floating-point
                 architecture; generation RISC CPU architecture; IBM
                 computers; IBM RISC System/6000 floating-point
                 execution unit; IBM RISC System\slash 6000
                 floating-point execution unit; IEEE double-precision
                 floating-point; IEEE double-precision floating-point
                 arithmetic; indivisible; Indivisible operation; logic;
                 multiply-add-fused unit; operation; Parallelism;
                 parallelism; reduced instruction set computing;
                 second-; Second-generation RISC CPU architecture; stage
                 pipeline; Superscalar second-generation RISC
                 architecture; superscalar second-generation RISC
                 architecture; two-; Two-stage pipeline; unified
                 floating-point; Unified floating-point
                 multiply-add-fused unit; VLSI arithmetic; VLSI
                 arithmetic, IBM RISC System/6000 floating-point
                 execution unit",
  thesaurus =    "Circuit layout CAD; Digital arithmetic; IBM computers;
                 Logic CAD; Reduced instruction set computing",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Montuschi:1990:SSR
author: P. Montuschi and P. M. Mezzalama
title: Survey of square rooting algorithms
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 137
number: 1
pages: 31--40
month: jan
monthnumber: 1
year: 1990
CODEN: ICDTEA
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEE Proceedings. Computers and Digital Techniques
acknowledgement: ack-nhfb
rawauthor: P. Montuschi and P. M. Mezzalama
rawtitle: Survey of square rooting algorithms
entry:
@Article{Montuschi:1990:SSR,
  author =       "P. Montuschi and P. M. Mezzalama",
  title =        "Survey of square rooting algorithms",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "137",
  number =       "1",
  pages =        "31--40",
  month =        jan,
  year =         "1990",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "The paper reviews the algorithms for the computation
                 of square roots for binary machines. After an initial
                 classification, the algorithms are analysed in detail
                 by considering their specific peculiarities and
                 properties. Finally, some comments are \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Morita:1990:FMM
author: Hikaru Morita
title: A Fast Modular-Multiplication Algorithm Based on a Higher Radix
journal: j-LECT-NOTES-COMP-SCI
volume: 435
pages: 387--??
year: 1990
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Mon Feb 4 12:01:59 MST 2002
bibtimestamp: 2002.02.04 12:01:59 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Hikaru Morita
rawtitle: A Fast Modular-Multiplication Algorithm Based on a Higher Radix
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t0435.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/0435/04350387.htm; http://link.springer-ny.com/link/service/series/0558/papers/0435/04350387.pdf

entry:
@Article{Morita:1990:FMM,
  author =       "Hikaru Morita",
  title =        "A Fast Modular-Multiplication Algorithm Based on a
                 Higher Radix",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "435",
  pages =        "387--??",
  year =         "1990",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Feb 4 12:01:59 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0435.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0435/04350387.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0435/04350387.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: mastersthesis
filename: fparith.bib
label: Muller:1990:HCA
author: Volker Muller
type: Diplomarbeit
school: Institut fur angewandte Mathematik, Universitat Karlsruhe
address: Karlsruhe, Germany
month: dec
monthnumber: 12
year: 1990
bibdate: Fri Sep 16 16:30:40 1994
bibtimestamp: 1994.09.16 16:30:40 ???
language: German
acknowledgement: ack-nj
rawauthor: Volker M{\"u}ller
title:
Hochgenaue CORDIC-Algorithmen fur reelle Standardfunktionen mittels dynamischer Defektberechnung. (German) [High-accuracy CORDIC Algorithms for Real Elementary Functions by Means of Dynamic Error Computation]

bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle Standardfunktionen mittels dynamischer Defektberechnung}. ({German}) [{High}-accuracy {CORDIC} Algorithms for Real Elementary Functions by Means of Dynamic Error Computation]

entry:
@MastersThesis{Muller:1990:HCA,
  author =       "Volker M{\"u}ller",
  title =        "{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle
                 Standardfunktionen mittels dynamischer
                 Defektberechnung}. ({German}) [{High}-accuracy {CORDIC}
                 Algorithms for Real Elementary Functions by Means of
                 Dynamic Error Computation]",
  type =         "{Diplomarbeit}",
  school =       "Institut f{\"u}r angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  month =        dec,
  year =         "1990",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Murthy:1990:MPA
author: Narayan Murthy and Allen Stix
title: Multiple precision arithmetic: a programming assignment in CS2 applying linked lists
journal: j-SIGCSE
volume: 22
number: 1
pages: 129--133
month: feb
monthnumber: 2
year: 1990
CODEN: SIGSD3
DOI: https://doi.org/10.1145/319059.323431
ISSN: 0097-8418 (print), 2331-3927 (electronic) OR 00978418 (print), 23313927 (electronic)
ISSNL: 0097-8418 OR 00978418
bibdate: Sat Nov 17 18:57:12 MST 2012
bibtimestamp: 2012.11.17 18:57:12 MST
fjournal: SIGCSE Bulletin (ACM Special Interest Group on Computer Science Education)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J688
rawauthor: Narayan Murthy and Allen Stix
rawtitle: Multiple precision arithmetic: a programming assignment in {CS2} applying linked lists
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib

entry:
@Article{Murthy:1990:MPA,
  author =       "Narayan Murthy and Allen Stix",
  title =        "Multiple precision arithmetic: a programming
                 assignment in {CS2} applying linked lists",
  journal =      j-SIGCSE,
  volume =       "22",
  number =       "1",
  pages =        "129--133",
  month =        feb,
  year =         "1990",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/319059.323431",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 18:57:12 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}


bibtype: article
filename: fparith.bib
label: Ohtomo:1990:FPD
author: Hiroyasu Ohtomo and Hisao Ishizuka and Masahiko Kashimura and Akio Nakajima and Tetsuhiro Hira
title: A 32-bit Floating Point Digital Signal Processor for Graphics Application
journal: j-NEC-RES-DEV
number: 99
pages: 47--??
month: oct
monthnumber: 10
year: 1990
CODEN: NECRAU
ISSN: 0048-0436 OR 00480436
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Nippon Electric Company research and development
acknowledgement: ack-nhfb
rawauthor: Hiroyasu Ohtomo and Hisao Ishizuka and Masahiko Kashimura and Akio Nakajima and Tetsuhiro Hira
rawtitle: A 32-bit Floating Point Digital Signal Processor for Graphics Application
entry:
@Article{Ohtomo:1990:FPD,
  author =       "Hiroyasu Ohtomo and Hisao Ishizuka and Masahiko
                 Kashimura and Akio Nakajima and Tetsuhiro Hira",
  title =        "A 32-bit Floating Point Digital Signal Processor for
                 Graphics Application",
  journal =      j-NEC-RES-DEV,
  volume =       "??",
  number =       "99",
  pages =        "47--??",
  month =        oct,
  year =         "1990",
  CODEN =        "NECRAU",
  ISSN =         "0048-0436",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nippon Electric Company research and development",
}


bibtype: inproceedings
filename: fparith.bib
label: Olson:1990:FAA
author: T. Olson and B. Stewart
title: Floating-point architecture of the Am29050
crossref: Wescon:1990:WCR
pages: 214--217
year: 1990
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
acknowledgement: ack-nhfb
affiliation: Adv. Micro Devices, Austin, TX, USA
thesaurus: Computer architecture; Digital arithmetic; Microprocessor chips; Reduced instruction set computing
rawauthor: T. Olson and B. Stewart
rawtitle: Floating-point architecture of the Am29050
abstract:
The Am29050 is the newest member of Advanced Micro Devices' 29K family of RISC microprocessors. It is both binary and pin compatible with the Am29000, and also incorporates a high-performance floating-point unit (FPU) on chip. The FPU, which complies with the IEEE 754 standard, consists of parallel add, multiply, and divide/square-root units, operating on single-precision and double-precision values. In addition to the standard operations, the FPU implements two types of multiply-add functions, which take three operands and produce one result. A single register file, which is shared between the integer and floating-point units, can supply two 64-bit operands and write back both a 32-bit integer result and a 64-bit floating-point result in a single cycle.

keywords:
29K family; 64 Bit; Advanced Micro Devices; Am29050; Double-precision; Floating point architecture; Floating point arithmetic; Floating-point unit; FPU; IEEE 754 standard; Multiply-add functions; Parallel add; RISC microprocessors; Single-precision

rawabstract:
The Am29050 is the newest member of Advanced Micro Devices' 29K family of RISC microprocessors. It is both binary and pin compatible with the Am29000, and also incorporates a high-performance floating-point unit (FPU) on chip. The FPU, which complies with the IEEE 754 standard, consists of parallel add, multiply, and divide/square-root units, operating on single-precision and double-precision values. In addition to the standard operations, the FPU implements two types of multiply-add functions, which take three operands and produce one result. A single register file, which is shared between the integer and floating-point units, can supply two 64-bit operands and write back both a 32-bit integer result and a 64-bit floating-point result in a single cycle.

entry:
@InProceedings{Olson:1990:FAA,
  author =       "T. Olson and B. Stewart",
  title =        "Floating-point architecture of the Am29050",
  crossref =     "Wescon:1990:WCR",
  pages =        "214--217",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Am29050 is the newest member of Advanced Micro
                 Devices' 29K family of RISC microprocessors. It is both
                 binary and pin compatible with the Am29000, and also
                 incorporates a high-performance floating-point unit
                 (FPU) on chip. The FPU, which complies with the IEEE
                 754 standard, consists of parallel add, multiply, and
                 divide/square-root units, operating on single-precision
                 and double-precision values. In addition to the
                 standard operations, the FPU implements two types of
                 multiply-add functions, which take three operands and
                 produce one result. A single register file, which is
                 shared between the integer and floating-point units,
                 can supply two 64-bit operands and write back both a
                 32-bit integer result and a 64-bit floating-point
                 result in a single cycle.",
  acknowledgement = ack-nhfb,
  affiliation =  "Adv. Micro Devices, Austin, TX, USA",
  availability = "Western Periodicals Co., 13000 Rayner Street, North
                 Hollywood, CA 91605, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220 (Computer architecture);
                 C5230 (Digital arithmetic methods)",
  keywords =     "29K family; 64 Bit; Advanced Micro Devices; Am29050;
                 Double-precision; Floating point architecture; Floating
                 point arithmetic; Floating-point unit; FPU; IEEE 754
                 standard; Multiply-add functions; Parallel add; RISC
                 microprocessors; Single-precision",
  numericalindex = "Word length 6.4E+01 bit",
  thesaurus =    "Computer architecture; Digital arithmetic;
                 Microprocessor chips; Reduced instruction set
                 computing",
}


bibtype: article
filename: fparith.bib
label: Owens:1990:BSM
author: R. M. Owens and M. J. Irwin
title: Being stingy with multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 6
pages: 809--818
month: jun
monthnumber: 6
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.53602
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:02 MDT 2011
bibtimestamp: 2011.07.07 14:20:02 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53602
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. M. Owens and M. J. Irwin
rawtitle: Being stingy with multipliers
entry:
@Article{Owens:1990:BSM,
  author =       "R. M. Owens and M. J. Irwin",
  title =        "Being stingy with multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "6",
  pages =        "809--818",
  month =        jun,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.53602",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53602",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Palmore:1990:CAC
author: J. Palmore and C. Herring
title: Computer arithmetic, chaos and fractals
journal: j-PHYSICA-D
volume: 42
number: 1-3
pages: 99--110
month: jun
monthnumber: 6
year: 1990
CODEN: PDNPDT
ISSN: 0167-2789 (print), 1872-8022 (electronic) OR 01672789 (print), 18728022 (electronic)
ISSNL: 0167-2789 OR 01672789
bibdate: Tue Dec 12 09:17:24 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:17:24 MST
fjournal: Physica. D, Nonlinear phenomena
acknowledgement: ack-nhfb
affiliation: Department of Math., Illinois University, Urbana, IL, USA
journalURL: http://www.sciencedirect.com/science/journal/01672789
thesaurus: Chaos; Digital arithmetic; Fractals; Random number generation; Roundoff errors
rawauthor: J. Palmore and C. Herring
rawtitle: Computer arithmetic, chaos and fractals
note:
Ninth Annual International Conference of the Center for Nonlinear Studies on Self-Organizing, Collective and Cooperative Phenomena in Natural and Artificial Networks

abstract:
The authors explore aspects of computer arithmetic from the viewpoint of dynamical systems. They demonstrate the effects of finite precision arithmetic in three uniformly hyperbolic chaotic dynamical systems: Bernoulli shifts, cat maps, and pseudorandom number generators. They show that elementary floating-point operations in binary computer arithmetic possess an inherently fractal structure. Each of these dynamical systems allows us to compare the exact results in integer arithmetic with those obtained by using floating-point arithmetic.

keywords:
Bernoulli shifts; Binary computer arithmetic; Cat maps; Chaos; Computer arithmetic; Dynamical systems; Elementary floating-point operations; Finite precision arithmetic; Floating-point arithmetic; Fractal structure; Integer arithmetic; Pseudorandom number generators; Self-similar structure; Uniformly hyperbolic chaotic dynamical systems

rawabstract:
The authors explore aspects of computer arithmetic from the viewpoint of dynamical systems. They demonstrate the effects of finite precision arithmetic in three uniformly hyperbolic chaotic dynamical systems: Bernoulli shifts, cat maps, and pseudorandom number generators. They show that elementary floating-point operations in binary computer arithmetic possess an inherently fractal structure. Each of these dynamical systems allows us to compare the exact results in integer arithmetic with those obtained by using floating-point arithmetic.

rawnote:
Ninth Annual International Conference of the Center for Nonlinear Studies on Self-Organizing, Collective and Cooperative Phenomena in Natural and Artificial Networks

entry:
@Article{Palmore:1990:CAC,
  author =       "J. Palmore and C. Herring",
  title =        "Computer arithmetic, chaos and fractals",
  journal =      j-PHYSICA-D,
  volume =       "42",
  number =       "1-3",
  pages =        "99--110",
  month =        jun,
  year =         "1990",
  CODEN =        "PDNPDT",
  ISSN =         "0167-2789 (print), 1872-8022 (electronic)",
  ISSN-L =       "0167-2789",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Ninth Annual International Conference of the Center
                 for Nonlinear Studies on Self-Organizing, Collective
                 and Cooperative Phenomena in Natural and Artificial
                 Networks",
  abstract =     "The authors explore aspects of computer arithmetic
                 from the viewpoint of dynamical systems. They
                 demonstrate the effects of finite precision arithmetic
                 in three uniformly hyperbolic chaotic dynamical
                 systems: Bernoulli shifts, cat maps, and pseudorandom
                 number generators. They show that elementary
                 floating-point operations in binary computer arithmetic
                 possess an inherently fractal structure. Each of these
                 dynamical systems allows us to compare the exact
                 results in integer arithmetic with those obtained by
                 using floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Math., Illinois University, Urbana, IL,
                 USA",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  confdate =     "22-26 May 1989",
  conflocation = "Los Alamos, NM, USA",
  fjournal =     "Physica. D, Nonlinear phenomena",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01672789",
  keywords =     "Bernoulli shifts; Binary computer arithmetic; Cat
                 maps; Chaos; Computer arithmetic; Dynamical systems;
                 Elementary floating-point operations; Finite precision
                 arithmetic; Floating-point arithmetic; Fractal
                 structure; Integer arithmetic; Pseudorandom number
                 generators; Self-similar structure; Uniformly
                 hyperbolic chaotic dynamical systems",
  pubcountry =   "Netherlands",
  thesaurus =    "Chaos; Digital arithmetic; Fractals; Random number
                 generation; Roundoff errors",
}


bibtype: inproceedings
filename: fparith.bib
label: Pan:1990:FSI
author: J. Pan and K. N. Levitz
crossref: Chen:1990:CRT
pages: 505--510
year: 1990
bibdate: Wed Dec 13 18:41:54 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:41:54 ???
acknowledgement: ack-nhfb
affiliation: Div. of Computer Science, California University, Berkeley, CA, USA
thesaurus: Digital arithmetic; Formal specification; Microprocessor chips; Satellite computers; Standards
rawauthor: J. Pan and K. N. Levitz
title:
A Formal Specification of the IEEE Floating-Point Standard with Application to the Verification of Floating-Point Coprocessors

abstract:
A description is given of work in progress on verifying a floating-point coprocessor based on the MC68881/82, with respect to the IEEE standard floating-point arithmetic (ANSI-IEEE Std 754-1985). A complete formalization of the IEEE floating-point standard using the HOL (high-order-logic) specification and verification system is presented. The specification of floating-point numbers, floating-point arithmetic functions, rounding schemes and post-normalization is described. In order for the specification to be adaptable to different implementation, several model parameters are used in specifying all the functions. The floating-point coprocessor is specified as a hierarchy of interpreters. The communication with the CPU is modeled as standard interprocessor communication. A technique for verifying hierarchies of communicating hardware interpreters is described. (11 Refs.)

keywords:
ANSI-IEEE Std 754-1985; Communicating hardware interpreters; CPU communication; Floating-point coprocessors; Higher order logic specification; HOL; IEEE standard floating-point arithmetic; Interpreter hierarchy; Interprocessor communication; MC68881/82; Post-normalization; Rounding schemes; Standard formalization; Verification system

rawabstract:
A description is given of work in progress on verifying a floating-point coprocessor based on the MC68881/82, with respect to the IEEE standard floating-point arithmetic (ANSI-IEEE Std 754-1985). A complete formalization of the IEEE floating-point standard using the HOL (high-order-logic) specification and verification system is presented. The specification of floating-point numbers, floating-point arithmetic functions, rounding schemes and post-normalization is described. In order for the specification to be adaptable to different implementation, several model parameters are used in specifying all the functions. The floating-point coprocessor is specified as a hierarchy of interpreters. The communication with the CPU is modeled as standard interprocessor communication. A technique for verifying hierarchies of communicating hardware interpreters is described. (11 Refs.)

rawtitle:
A Formal Specification of the {IEEE Floating-Point Standard} with Application to the Verification of Floating-Point Coprocessors

entry:
@InProceedings{Pan:1990:FSI,
  author =       "J. Pan and K. N. Levitz",
  title =        "A Formal Specification of the {IEEE Floating-Point
                 Standard} with Application to the Verification of
                 Floating-Point Coprocessors",
  crossref =     "Chen:1990:CRT",
  pages =        "505--510",
  year =         "1990",
  bibdate =      "Wed Dec 13 18:41:54 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A description is given of work in progress on
                 verifying a floating-point coprocessor based on the
                 MC68881/82, with respect to the IEEE standard
                 floating-point arithmetic (ANSI-IEEE Std 754-1985). A
                 complete formalization of the IEEE floating-point
                 standard using the HOL (high-order-logic) specification
                 and verification system is presented. The specification
                 of floating-point numbers, floating-point arithmetic
                 functions, rounding schemes and post-normalization is
                 described. In order for the specification to be
                 adaptable to different implementation, several model
                 parameters are used in specifying all the functions.
                 The floating-point coprocessor is specified as a
                 hierarchy of interpreters. The communication with the
                 CPU is modeled as standard interprocessor
                 communication. A technique for verifying hierarchies of
                 communicating hardware interpreters is described. (11
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Div. of Computer Science, California University,
                 Berkeley, CA, USA",
  availability = "IEEE Computer Society Press, Los Alamitos, CA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  keywords =     "ANSI-IEEE Std 754-1985; Communicating hardware
                 interpreters; CPU communication; Floating-point
                 coprocessors; Higher order logic specification; HOL;
                 IEEE standard floating-point arithmetic; Interpreter
                 hierarchy; Interprocessor communication; MC68881/82;
                 Post-normalization; Rounding schemes; Standard
                 formalization; Verification system",
  thesaurus =    "Digital arithmetic; Formal specification;
                 Microprocessor chips; Satellite computers; Standards",
}


bibtype: article
filename: fparith.bib
label: Parhami:1990:GSD
author: Behrooz Parhami
title: Generalized Signed-Digit Number Systems: a Unifying Framework for Redundant Number Representations
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 1
pages: 89--98
month: jan
monthnumber: 1
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.46283
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Feb 15 15:47:08 2007
bibtimestamp: 2007.02.15 15:47:08 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Behrooz Parhami
rawtitle: Generalized Signed-Digit Number Systems: a Unifying Framework for Redundant Number Representations
abstract:
Signed-digit (SD) number representation systems have been defined for any radix r ?? 3 with digit values ranging over the set $ ( - alpha , ldots , - 1, 0, 1, ldots , alpha ) $, where $ alpha $ is an arbitrary integer in the range $ 1 / 2 r > alpha > r $. Such number representation systems possess sufficient redundancy to allow for the annihilation of carry or borrow chains and hence result in fast propagation-free addition and subtraction. The author refers to the above as ordinary SD number systems and defines generalized SD number systems which contain them as a special symmetric subclass. It is shown that the generalization not only provides a unified view of all redundant number systems which have proven useful in practice (including stored-carry and stored-borrowed systems), but also leads to new number systems not examined before. Examples of such new number systems are stored-carry-or-borrow systems, stored-double-carry systems, and certain redundant decimal representations.

rawabstract:
Signed-digit (SD) number representation systems have been defined for any radix r ?? 3 with digit values ranging over the set $ ( - \alpha, \ldots {}, - 1, 0, 1, \ldots {}, \alpha) $, where $ \alpha $ is an arbitrary integer in the range $ 1 / 2 r > \alpha > r $. Such number representation systems possess sufficient redundancy to allow for the annihilation of carry or borrow chains and hence result in fast propagation-free addition and subtraction. The author refers to the above as ordinary SD number systems and defines generalized SD number systems which contain them as a special symmetric subclass. It is shown that the generalization not only provides a unified view of all redundant number systems which have proven useful in practice (including stored-carry and stored-borrowed systems), but also leads to new number systems not examined before. Examples of such new number systems are stored-carry-or-borrow systems, stored-double-carry systems, and certain redundant decimal representations.

entry:
@Article{Parhami:1990:GSD,
  author =       "Behrooz Parhami",
  title =        "Generalized Signed-Digit Number Systems: a Unifying
                 Framework for Redundant Number Representations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "1",
  pages =        "89--98",
  month =        jan,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.46283",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Feb 15 15:47:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  abstract =     "Signed-digit (SD) number representation systems have
                 been defined for any radix r ?? 3 with digit values
                 ranging over the set $ ( - \alpha, \ldots {}, - 1, 0,
                 1, \ldots {}, \alpha) $, where $ \alpha $ is an
                 arbitrary integer in the range $ 1 / 2 r > \alpha > r
                 $. Such number representation systems possess
                 sufficient redundancy to allow for the annihilation of
                 carry or borrow chains and hence result in fast
                 propagation-free addition and subtraction. The author
                 refers to the above as ordinary SD number systems and
                 defines generalized SD number systems which contain
                 them as a special symmetric subclass. It is shown that
                 the generalization not only provides a unified view of
                 all redundant number systems which have proven useful
                 in practice (including stored-carry and stored-borrowed
                 systems), but also leads to new number systems not
                 examined before. Examples of such new number systems
                 are stored-carry-or-borrow systems, stored-double-carry
                 systems, and certain redundant decimal
                 representations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Payne:1990:PLCa
author: M. Payne and C. Schaffert and B. Wichmann
title: Proposal for a language compatible arithmetic standard
journal: j-SIGNUM
volume: 25
number: 1
pages: 2--43
month: jan
monthnumber: 1
year: 1990
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Dec 12 09:17:24 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:17:24 MST
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
affiliation: Digital Equipment Corp, Maynard, MA, USA
journalURL: https://dl.acm.org/loi/signum
thesaurus: Digital arithmetic; Mathematics computing; Standards
rawauthor: M. Payne and C. Schaffert and B. Wichmann
rawtitle: Proposal for a language compatible arithmetic standard
abstract:
Describes the proposal for an arithmetic standard which has been submitted to the American National Standards Institute and the International Organization for Standardization. It is being processed by the ANSI X3T2 committee and the ISO/IEC JTC1/SC22/WG11 working group. The specifications cover both integer and floating point arithmetic.

keywords:
American National Standards Institute; ANSI X3T2 committee; Floating point arithmetic; Integer arithmetic; International Organization for Standardization; Language compatible arithmetic standard

rawabstract:
Describes the proposal for an arithmetic standard which has been submitted to the American National Standards Institute and the International Organization for Standardization. It is being processed by the ANSI X3T2 committee and the ISO/IEC JTC1/SC22/WG11 working group. The specifications cover both integer and floating point arithmetic.

entry:
@Article{Payne:1990:PLCa,
  author =       "M. Payne and C. Schaffert and B. Wichmann",
  title =        "Proposal for a language compatible arithmetic
                 standard",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "1",
  pages =        "2--43",
  month =        jan,
  year =         "1990",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes the proposal for an arithmetic standard
                 which has been submitted to the American National
                 Standards Institute and the International Organization
                 for Standardization. It is being processed by the ANSI
                 X3T2 committee and the ISO/IEC JTC1/SC22/WG11 working
                 group. The specifications cover both integer and
                 floating point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Digital Equipment Corp, Maynard, MA, USA",
  classification = "C7310 (Mathematics)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "American National Standards Institute; ANSI X3T2
                 committee; Floating point arithmetic; Integer
                 arithmetic; International Organization for
                 Standardization; Language compatible arithmetic
                 standard",
  thesaurus =    "Digital arithmetic; Mathematics computing; Standards",
}


bibtype: article
filename: fparith.bib
label: Payne:1990:PLCb
author: M. Payne and C. Schaffert and B. Wichmann
title: Proposal for a language compatible arithmetic standard
journal: j-SIGPLAN
volume: 25
number: 1
pages: 59--86
month: jan
monthnumber: 1
year: 1990
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:15:49 MST 2003
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.12.14 09:15:49 MST
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: Digital Equipment Corp., Maynard, MA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
thesaurus: Digital arithmetic; High level languages; Standards
rawauthor: M. Payne and C. Schaffert and B. Wichmann
rawtitle: Proposal for a language compatible arithmetic standard
abstract:
The proposal for an arithmetic standard has been submitted to the American National Standard Institute and the International Organization for Standardization. The proposal covers both integer and floating point arithmetic. The underlying goal is to expedite the production of robust numerical software which is portable among the diverse arithmetic implementations currently in wide-spread use. The proposal requires that a complying system provide error detection capabilities beyond those currently required by many language standards. The proposal requires that a conforming system makes the values of certain parameters known to users, although the method for doing so is not specified. It also required a number of useful operations, beyond those usually implemented. It is acceptable to implement them by subroutine calls.

keywords:
American National Standard Institute; Error detection capabilities; Floating point arithmetic; International Organization for Standardization; Language compatible arithmetic standard; Robust numerical software; Subroutine calls

rawabstract:
The proposal for an arithmetic standard has been submitted to the American National Standard Institute and the International Organization for Standardization. The proposal covers both integer and floating point arithmetic. The underlying goal is to expedite the production of robust numerical software which is portable among the diverse arithmetic implementations currently in wide-spread use. The proposal requires that a complying system provide error detection capabilities beyond those currently required by many language standards. The proposal requires that a conforming system makes the values of certain parameters known to users, although the method for doing so is not specified. It also required a number of useful operations, beyond those usually implemented. It is acceptable to implement them by subroutine calls.

entry:
@Article{Payne:1990:PLCb,
  author =       "M. Payne and C. Schaffert and B. Wichmann",
  title =        "Proposal for a language compatible arithmetic
                 standard",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "1",
  pages =        "59--86",
  month =        jan,
  year =         "1990",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:49 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The proposal for an arithmetic standard has been
                 submitted to the American National Standard Institute
                 and the International Organization for Standardization.
                 The proposal covers both integer and floating point
                 arithmetic. The underlying goal is to expedite the
                 production of robust numerical software which is
                 portable among the diverse arithmetic implementations
                 currently in wide-spread use. The proposal requires
                 that a complying system provide error detection
                 capabilities beyond those currently required by many
                 language standards. The proposal requires that a
                 conforming system makes the values of certain
                 parameters known to users, although the method for
                 doing so is not specified. It also required a number of
                 useful operations, beyond those usually implemented. It
                 is acceptable to implement them by subroutine calls.",
  acknowledgement = ack-nhfb,
  affiliation =  "Digital Equipment Corp., Maynard, MA, USA",
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages)",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "American National Standard Institute; Error detection
                 capabilities; Floating point arithmetic; International
                 Organization for Standardization; Language compatible
                 arithmetic standard; Robust numerical software;
                 Subroutine calls",
  thesaurus =    "Digital arithmetic; High level languages; Standards",
}


bibtype: article
filename: fparith.bib
label: Peter:1990:PZW
author: O. Peter
title: Prozessor zieht Wurzeln toenglish Processor Extracts Roots endtoenglish
journal: j-CT
volume: 1
pages: 300--306
year: 1990
ISSN: 0724-8679 OR 07248679
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: C T: Magazin fur Computer Technik (Hannover)
acknowledgement: ack-nj
rawauthor: O. Peter
rawtitle: {Prozessor zieht Wurzeln} \toenglish {Processor Extracts Roots} \endtoenglish
entry:
@Article{Peter:1990:PZW,
  author =       "O. Peter",
  title =        "{Prozessor zieht Wurzeln} \toenglish {Processor
                 Extracts Roots} \endtoenglish",
  journal =      j-CT,
  volume =       "1",
  pages =        "300--306",
  year =         "1990",
  ISSN =         "0724-8679",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}


bibtype: article
filename: fparith.bib
label: Piestrak:1990:DHS
author: S. J. Piestrak
title: Design of high-speed and cost-effective self-testing checkers for low-cost arithmetic codes
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 3
pages: 360--374
month: mar
monthnumber: 3
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.48866
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:00 MDT 2011
bibtimestamp: 2011.07.07 14:20:00 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48866
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. J. Piestrak
rawtitle: Design of high-speed and cost-effective self-testing checkers for low-cost arithmetic codes
entry:
@Article{Piestrak:1990:DHS,
  author =       "S. J. Piestrak",
  title =        "Design of high-speed and cost-effective self-testing
                 checkers for low-cost arithmetic codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "3",
  pages =        "360--374",
  month =        mar,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.48866",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48866",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Popov:1990:AFA
author: Wladimir Popov
journal: IMACS Ann. Comput. Appl. Math.
volume: 7
publisher: pub-BALTZER
address: pub-BALTZER:adr
pages: 55--66
year: 1990
MRclass: 03B70 (65G05)
MRnumber: 93g:03024
bibdate: Fri Dec 08 12:21:25 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 12:21:25 ???
acknowledgement: ack-nhfb
rawauthor: Wladimir Popov
title:
On the axiomatizations of floating-point arithmetics. Contributions to computer arithmetic and self-validating numerical methods (Basel, 1989)

rawtitle:
On the axiomatizations of floating-point arithmetics. Contributions to computer arithmetic and self-validating numerical methods ({Basel, 1989})

entry:
@Article{Popov:1990:AFA,
  author =       "Wladimir Popov",
  title =        "On the axiomatizations of floating-point arithmetics.
                 Contributions to computer arithmetic and
                 self-validating numerical methods ({Basel, 1989})",
  journal =      "IMACS Ann. Comput. Appl. Math.",
  volume =       "7",
  publisher =    pub-BALTZER,
  address =      pub-BALTZER:adr,
  pages =        "55--66",
  year =         "1990",
  MRclass =      "03B70 (65G05)",
  MRnumber =     "93g:03024",
  bibdate =      "Fri Dec 08 12:21:25 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Preparata:1990:PCD
author: F. P. Preparata and Jean E. Vuillemin
title: Practical cellular dividers
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 5
pages: 605--614
month: may
monthnumber: 5
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.53574
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:01 MDT 2011
bibtimestamp: 2011.07.07 14:20:01 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53574
fjournal: IEEE Transactions on Computers
language: English
acknowledgement: ack-nhfb
affiliation: Ecole Normale Superieure, Paris, France
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Dividing circuits; Parallel algorithms
rawauthor: F. P. Preparata and Jean E. Vuillemin
rawtitle: Practical cellular dividers
abstract:
A discussion is presented of parallel division algorithms that can be classified among modified higher radix nonrestoring online division methods, where redundant representations are extensively utilized to speed up the operation. The network realizations of these algorithms are cellular, or even systolic with exclusively local control; they have both size (area) and time of $ O(n) $, where $n$ is the length of the dividend representation. The same structures can also be used as a signed, digit-serial multiplier. When suitably equipped with some control and a few registers, the divider / multiplier brings remarkable performance to large modular arithmetic, RSA cryptography, and greatest common divisor computations. They are also of interest for the design of floating-point units and signal processing applications.

keywords:
Digit-serial multiplier; Divider/multiplier; Floating-point units; Greatest common divisor computations; Modular arithmetic; Nonrestoring online division methods; Parallel division algorithms; Redundant representations; RSA cryptography; Signal processing; Signed; Systolic

rawabstract:
A discussion is presented of parallel division algorithms that can be classified among modified higher radix nonrestoring online division methods, where redundant representations are extensively utilized to speed up the operation. The network realizations of these algorithms are cellular, or even systolic with exclusively local control; they have both size (area) and time of $ O(n) $, where $n$ is the length of the dividend representation. The same structures can also be used as a signed, digit-serial multiplier. When suitably equipped with some control and a few registers, the divider\slash multiplier brings remarkable performance to large modular arithmetic, RSA cryptography, and greatest common divisor computations. They are also of interest for the design of floating-point units and signal processing applications.

entry:
@Article{Preparata:1990:PCD,
  author =       "F. P. Preparata and Jean E. Vuillemin",
  title =        "Practical cellular dividers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "5",
  pages =        "605--614",
  month =        may,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.53574",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53574",
  abstract =     "A discussion is presented of parallel division
                 algorithms that can be classified among modified higher
                 radix nonrestoring online division methods, where
                 redundant representations are extensively utilized to
                 speed up the operation. The network realizations of
                 these algorithms are cellular, or even systolic with
                 exclusively local control; they have both size (area)
                 and time of $ O(n) $, where $n$ is the length of the
                 dividend representation. The same structures can also
                 be used as a signed, digit-serial multiplier. When
                 suitably equipped with some control and a few
                 registers, the divider\slash multiplier brings
                 remarkable performance to large modular arithmetic, RSA
                 cryptography, and greatest common divisor computations.
                 They are also of interest for the design of
                 floating-point units and signal processing
                 applications.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure, Paris, France",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Digit-serial multiplier; Divider/multiplier;
                 Floating-point units; Greatest common divisor
                 computations; Modular arithmetic; Nonrestoring online
                 division methods; Parallel division algorithms;
                 Redundant representations; RSA cryptography; Signal
                 processing; Signed; Systolic",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Dividing circuits; Parallel
                 algorithms",
}


bibtype: article
filename: fparith.bib
label: Prince:1990:GST
author: Timothy Prince
title: Generating Source For tt <float.h>
journal: j-CUJ
volume: 8
number: 6
pages: 119--??
month: jun
monthnumber: 6
year: 1990
ISSN: 0898-9788 OR 08989788
bibdate: Fri Aug 30 16:52:23 MDT 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.30 16:52:23 MDT
fjournal: C Users Journal
acknowledgement: ack-nhfb
rawauthor: Timothy Prince
rawtitle: Generating Source For {{\tt <float.h>}}
entry:
@Article{Prince:1990:GST,
  author =       "Timothy Prince",
  title =        "Generating Source For {{\tt <float.h>}}",
  journal =      j-CUJ,
  volume =       "8",
  number =       "6",
  pages =        "119--??",
  month =        jun,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}


bibtype: article
filename: fparith.bib
label: Pugh:1990:CBF
author: Kenneth Pugh
title: Converting BASIC Floating Point Files to C
journal: j-CUJ
volume: 8
type: Questions and Answers
number: 5
pages: 69--??
month: may
monthnumber: 5
year: 1990
ISSN: 0898-9788 OR 08989788
bibdate: Fri Aug 30 16:52:23 MDT 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.30 16:52:23 MDT
fjournal: C Users Journal
acknowledgement: ack-nhfb
rawauthor: Kenneth Pugh
rawtitle: Converting {BASIC} Floating Point Files to {C}
entry:
@Article{Pugh:1990:CBF,
  author =       "Kenneth Pugh",
  title =        "Converting {BASIC} Floating Point Files to {C}",
  journal =      j-CUJ,
  volume =       "8",
  type =         "Questions and Answers",
  number =       "5",
  pages =        "69--??",
  month =        may,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}


bibtype: techreport
filename: fparith.bib
label: Quach:1990:IAH
author: N. T. Quach and M. J. Flynn
title: An improved algorithm for high-speed floating-point addition
type: Technical Report
number: CSL-TR-90-442
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 69--??
month: aug
monthnumber: 8
year: 1990
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: N. T. Quach and M. J. Flynn
rawtitle: An improved algorithm for high-speed floating-point addition
entry:
@TechReport{Quach:1990:IAH,
  author =       "N. T. Quach and M. J. Flynn",
  title =        "An improved algorithm for high-speed floating-point
                 addition",
  type =         "Technical Report",
  number =       "CSL-TR-90-442",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        aug,
  year =         "1990",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Quinn:1990:REL
author: T. Quinn and S. Tremaine
title: Roundoff error in long-term planetary orbit integrations
journal: j-ASTRON-J
volume: 99
number: 3
pages: 1016--1023
month: mar
monthnumber: 3
year: 1990
CODEN: ANJOAA
ISSN: 0004-6256 (print), 1538-3881 (electronic) OR 00046256 (print), 15383881 (electronic)
ISSNL: 0004-6256 OR 00046256
bibdate: Tue Dec 12 09:17:24 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:17:24 MST
fjournal: Astronomical Journal
acknowledgement: ack-nhfb
affiliation: Canadian Inst. for Theor. Astrophys., Toronto University, Ont., Canada
journalURL: http://iopscience.iop.org/1538-3881
rawauthor: T. Quinn and S. Tremaine
rawtitle: Roundoff error in long-term planetary orbit integrations
abstract:
The dominant source of error in most long-term integrations of the solar system is roundoff, which leads to a fractional energy error of order $ n i_n $ where $n$ is the number of steps and $ i_n $ is the precision of the floating-point arithmetic. The most accurate computers are those with optimal floating-point arithmetic, that is, arithmetic in which the result of evaluating in arithmetic expression is the representable number closest to the true value of that expression. The authors argue that when floating-point arithmetic is optimal, most of the roundoff error arises from two sources: the approximate representation of the numerical coefficients used in multistep integration formulas, and the additions required to evaluate these formulas. The authors present an algorithm that removes these two sources of error in computers with optimal arithmetic, and appears to reduce the fractional energy error to of order $ n^0.5i_n $ (at least for $ n < $ or approximately $ = 10^7 $), at the cost of less than a factor of $2$ increase in computing time.

keywords:
Addition error; Approximate representation; Arithmetic expression; Celestial mechanics; Computing time; Floating-point arithmetic precision; Fractional energy error; Integration steps number; Long-term planetary orbit integrations; Multistep integration formulas; Numerical coefficients; Optimal floating-point arithmetic; Representable number; Roundoff error; Solar system long-term stability; True value

thesaurus:
Astronomical techniques; Astronomy computing; Celestial mechanics; Error correction; Planets; Solar system; Stability

rawabstract:
The dominant source of error in most long-term integrations of the solar system is roundoff, which leads to a fractional energy error of order $ n i_n $ where $n$ is the number of steps and $ i_n $ is the precision of the floating-point arithmetic. The most accurate computers are those with optimal floating-point arithmetic, that is, arithmetic in which the result of evaluating in arithmetic expression is the representable number closest to the true value of that expression. The authors argue that when floating-point arithmetic is optimal, most of the roundoff error arises from two sources: the approximate representation of the numerical coefficients used in multistep integration formulas, and the additions required to evaluate these formulas. The authors present an algorithm that removes these two sources of error in computers with optimal arithmetic, and appears to reduce the fractional energy error to of order $ n^{0.5i}_n $ (at least for $ n < $ or approximately $ = 10^7 $), at the cost of less than a factor of $2$ increase in computing time.

entry:
@Article{Quinn:1990:REL,
  author =       "T. Quinn and S. Tremaine",
  title =        "Roundoff error in long-term planetary orbit
                 integrations",
  journal =      j-ASTRON-J,
  volume =       "99",
  number =       "3",
  pages =        "1016--1023",
  month =        mar,
  year =         "1990",
  CODEN =        "ANJOAA",
  ISSN =         "0004-6256 (print), 1538-3881 (electronic)",
  ISSN-L =       "0004-6256",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The dominant source of error in most long-term
                 integrations of the solar system is roundoff, which
                 leads to a fractional energy error of order $ n i_n $
                 where $n$ is the number of steps and $ i_n $ is the
                 precision of the floating-point arithmetic. The most
                 accurate computers are those with optimal
                 floating-point arithmetic, that is, arithmetic in which
                 the result of evaluating in arithmetic expression is
                 the representable number closest to the true value of
                 that expression. The authors argue that when
                 floating-point arithmetic is optimal, most of the
                 roundoff error arises from two sources: the approximate
                 representation of the numerical coefficients used in
                 multistep integration formulas, and the additions
                 required to evaluate these formulas. The authors
                 present an algorithm that removes these two sources of
                 error in computers with optimal arithmetic, and appears
                 to reduce the fractional energy error to of order $
                 n^{0.5i}_n $ (at least for $ n < $ or approximately $ =
                 10^7 $), at the cost of less than a factor of $2$
                 increase in computing time.",
  acknowledgement = ack-nhfb,
  affiliation =  "Canadian Inst. for Theor. Astrophys., Toronto
                 University, Ont., Canada",
  classification = "A9510C (Celestial mechanics); A9575P (Mathematical
                 and computer techniques); A9630 (Planets and
                 satellites); C7350 (Astronomy and astrophysics)",
  fjournal =     "Astronomical Journal",
  journal-URL =  "http://iopscience.iop.org/1538-3881",
  keywords =     "Addition error; Approximate representation; Arithmetic
                 expression; Celestial mechanics; Computing time;
                 Floating-point arithmetic precision; Fractional energy
                 error; Integration steps number; Long-term planetary
                 orbit integrations; Multistep integration formulas;
                 Numerical coefficients; Optimal floating-point
                 arithmetic; Representable number; Roundoff error; Solar
                 system long-term stability; True value",
  thesaurus =    "Astronomical techniques; Astronomy computing;
                 Celestial mechanics; Error correction; Planets; Solar
                 system; Stability",
}


bibtype: inproceedings
filename: fparith.bib
label: Ramamoorthy:1990:MRN
author: P. A. Ramamoorthy and P. E. Pace and D. Styer
booktitle: Proceedings of the 33rd Midwest Symposium on Circuits and Systems, 1990
title: A modified residue number system with applications to signal processing
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1018--1021
year: 1990
DOI: https://doi.org/10.1109/MWSCAS.1990.140897
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: P. A. Ramamoorthy and P. E. Pace and D. Styer
rawbooktitle: Proceedings of the 33rd Midwest Symposium on Circuits and Systems, 1990
rawtitle: A modified residue number system with applications to signal processing
entry:
@InProceedings{Ramamoorthy:1990:MRN,
  author =       "P. A. Ramamoorthy and P. E. Pace and D. Styer",
  booktitle =    "Proceedings of the 33rd Midwest Symposium on Circuits
                 and Systems, 1990",
  title =        "A modified residue number system with applications to
                 signal processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1018--1021",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1990.140897",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors have developed a number system, the
                 modified residue number system (MRNS), which is a
                 direct consequence of considering the need for a more
                 convenient folding waveform that can be implemented
                 easily. Through various arrangements of the \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Rao:1990:SAA
author: B. D. Rao
title: A systematic approach for the analysis of roundoff noise in floating point digital filters
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 495
year: 1990
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: B. D. Rao
rawtitle: A systematic approach for the analysis of roundoff noise in floating point digital filters
booktitle:
Signals, Systems and Computers, 1990. 1990 Conference Record Twenty-Fourth Asilomar Conference on. 5--7 Nov 1990

rawbooktitle:
Signals, Systems and Computers, 1990. 1990 Conference Record Twenty-Fourth Asilomar Conference on. 5--7 Nov 1990

entry:
@InProceedings{Rao:1990:SAA,
  author =       "B. D. Rao",
  booktitle =    "Signals, Systems and Computers, 1990. 1990 Conference
                 Record Twenty-Fourth Asilomar Conference on. 5--7 Nov
                 1990",
  title =        "A systematic approach for the analysis of roundoff
                 noise in floating point digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "495",
  year =         "1990",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Rauchwerger:1990:MFPa
author: Lawrence Rauchwerger and Michael P. Farmwald
title: A multiple floating point coprocessor architecture
journal: j-COMP-ARCH-NEWS
volume: 18
number: 2
pages: 15--24
month: jun
monthnumber: 6
year: 1990
CODEN: CANED2
ISSN: 0163-5964 (print), 1943-5851 (electronic) OR 01635964 (print), 19435851 (electronic)
ISSNL: 0163-5964 OR 01635964
bibdate: Fri May 12 09:40:46 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.05.12 09:40:46 MDT
fjournal: ACM SIGARCH Computer Architecture News
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/sigarch
rawauthor: Lawrence Rauchwerger and Michael P. Farmwald
rawtitle: A multiple floating point coprocessor architecture
entry:
@Article{Rauchwerger:1990:MFPa,
  author =       "Lawrence Rauchwerger and Michael P. Farmwald",
  title =        "A multiple floating point coprocessor architecture",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "18",
  number =       "2",
  pages =        "15--24",
  month =        jun,
  year =         "1990",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:46 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}


bibtype: inproceedings
filename: fparith.bib
label: Rauchwerger:1990:MFPb
author: L. Rauchwerger and P. M. Farmwald
title: A multiple floating point coprocessor architecture
crossref: IEEE:1990:MMM
pages: 216--222
year: 1990
bibdate: Tue Dec 12 09:26:54 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:26:54 MST
acknowledgement: ack-nhfb
affiliation: Center for Supercomput. Res. and Dev., Illinois University, Urbana-Champaign, IL, USA
thesaurus: Computer architecture; Digital arithmetic; Satellite computers
rawauthor: L. Rauchwerger and P. M. Farmwald
rawtitle: A multiple floating point coprocessor architecture
abstract:
General purpose microprocessor based computers usually speed their arithmetic processing performance by using a floating point co-processor. Because adding more co-processors represents neither a technological nor a cost problem, the authors investigated a system based on a MIPS R2000 and 4 floating point units. They show a block diagram of such an implementation and how two important scientific operations can be accelerated using a single unmodified data bus. A large percentage of the engineering applications are solved with the help of linear algebra methods like BLAS3 algorithms; it is precisely for these primitives that the proposed architecture brings significant performance gains. The first operation described is a matrix multiplication algorithm, its timing diagram and some results. Next a polynomial evaluation technique is examined. Finally they show how to use the same ideas with various other microprocessors.

keywords:
Arithmetic processing performance; BLAS3; Engineering applications; Matrix multiplication algorithm; Microprocessors; MIPS R2000; Multiple floating point coprocessor architecture; Polynomial evaluation; RISC

rawabstract:
General purpose microprocessor based computers usually speed their arithmetic processing performance by using a floating point co-processor. Because adding more co-processors represents neither a technological nor a cost problem, the authors investigated a system based on a MIPS R2000 and 4 floating point units. They show a block diagram of such an implementation and how two important scientific operations can be accelerated using a single unmodified data bus. A large percentage of the engineering applications are solved with the help of linear algebra methods like BLAS3 algorithms; it is precisely for these primitives that the proposed architecture brings significant performance gains. The first operation described is a matrix multiplication algorithm, its timing diagram and some results. Next a polynomial evaluation technique is examined. Finally they show how to use the same ideas with various other microprocessors.

entry:
@InProceedings{Rauchwerger:1990:MFPb,
  author =       "L. Rauchwerger and P. M. Farmwald",
  title =        "A multiple floating point coprocessor architecture",
  crossref =     "IEEE:1990:MMM",
  pages =        "216--222",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "General purpose microprocessor based computers usually
                 speed their arithmetic processing performance by using
                 a floating point co-processor. Because adding more
                 co-processors represents neither a technological nor a
                 cost problem, the authors investigated a system based
                 on a MIPS R2000 and 4 floating point units. They show a
                 block diagram of such an implementation and how two
                 important scientific operations can be accelerated
                 using a single unmodified data bus. A large percentage
                 of the engineering applications are solved with the
                 help of linear algebra methods like BLAS3 algorithms;
                 it is precisely for these primitives that the proposed
                 architecture brings significant performance gains. The
                 first operation described is a matrix multiplication
                 algorithm, its timing diagram and some results. Next a
                 polynomial evaluation technique is examined. Finally
                 they show how to use the same ideas with various other
                 microprocessors.",
  acknowledgement = ack-nhfb,
  affiliation =  "Center for Supercomput. Res. and Dev., Illinois
                 University, Urbana-Champaign, IL, USA",
  classification = "C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Arithmetic processing performance; BLAS3; Engineering
                 applications; Matrix multiplication algorithm;
                 Microprocessors; MIPS R2000; Multiple floating point
                 coprocessor architecture; Polynomial evaluation; RISC",
  thesaurus =    "Computer architecture; Digital arithmetic; Satellite
                 computers",
}


bibtype: article
filename: fparith.bib
label: Reemtsen:1990:MFR
author: Rembert Reemtsen
title: Modifications of the First Remez Algorithm
journal: j-SIAM-J-NUMER-ANAL
volume: 27
number: 2
pages: 507--518
month: apr
monthnumber: 4
year: 1990
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0727031
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65D15
MRnumber: 91a:65039
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: Rembert Reemtsen
rawtitle: Modifications of the First {Remez} Algorithm
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database

entry:
@Article{Reemtsen:1990:MFR,
  author =       "Rembert Reemtsen",
  title =        "Modifications of the First {Remez} Algorithm",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "2",
  pages =        "507--518",
  month =        apr,
  year =         "1990",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0727031",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65D15",
  MRnumber =     "91a:65039",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: article
filename: fparith.bib
label: Reif:1990:OSI
author: John H. Reif and Stephen R. Tate
title: Optimal Size Integer Division Circuits
journal: j-SIAM-J-COMPUT
volume: 19
number: 5
pages: 912--924
month: oct
monthnumber: 10
year: 1990
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
MRclass: 68Q40 (68Q15 68Q25)
MRnumber: 91h:68092
MRreviewer: Helmut Alt
bibdate: Mon Nov 29 11:01:37 MST 2010
bibtimestamp: 2010.11.29 11:01:37 MST
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: John H. Reif and Stephen R. Tate
rawtitle: Optimal Size Integer Division Circuits
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/19/5; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Reif:1990:OSI,
  author =       "John H. Reif and Stephen R. Tate",
  title =        "Optimal Size Integer Division Circuits",
  journal =      j-SIAM-J-COMPUT,
  volume =       "19",
  number =       "5",
  pages =        "912--924",
  month =        oct,
  year =         "1990",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68Q40 (68Q15 68Q25)",
  MRnumber =     "91h:68092",
  MRreviewer =   "Helmut Alt",
  bibdate =      "Mon Nov 29 11:01:37 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/19/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}


bibtype: phdthesis
filename: fparith.bib
label: Rowan:1990:FSA
author: Thomas Harvey Rowan
title: Functional stability analysis of numerical algorithms
type: Ph.D. thesis
school: University of Texas at Austin
address: Austin, TX, USA
pages: xii + 206
month: may
monthnumber: 5
year: 1990
bibdate: Mon Oct 21 18:08:52 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.10.21 18:08:52 ???
URL: https://search.proquest.com/pqdtglobal/docview/303865032
acknowledgement: ack-nhfb
advisor: Alan K. Cline
rawauthor: Thomas Harvey Rowan
rawtitle: Functional stability analysis of numerical algorithms
abstract:
The standard technique for detecting instability in numerical algorithms is backward error analysis. The analysis is difficult and tedious when performed by hand, while attempts to automate it have always placed severe restrictions on the tested numerical algorithms. A new approach for detecting instability, functional stability analysis, removes these restrictions by treating numerical algorithms as black boxes. The approach consists of two parts. The first part uses the relationship between the forward error, the backward error, and a problem's condition to define a function that estimates a lower bound on the backward error. In the second part, a new optimization method maximizes the function. A numerical algorithm is unstable if the maximization shows that the backward error can become large. Since numerical algorithms are treated as black boxes, functional stability analysis normally requires little more than an executable version of a numerical algorithm to determine if it is unstable.

rawabstract:
The standard technique for detecting instability in numerical algorithms is backward error analysis. The analysis is difficult and tedious when performed by hand, while attempts to automate it have always placed severe restrictions on the tested numerical algorithms. A new approach for detecting instability, functional stability analysis, removes these restrictions by treating numerical algorithms as black boxes. The approach consists of two parts. The first part uses the relationship between the forward error, the backward error, and a problem's condition to define a function that estimates a lower bound on the backward error. In the second part, a new optimization method maximizes the function. A numerical algorithm is unstable if the maximization shows that the backward error can become large. Since numerical algorithms are treated as black boxes, functional stability analysis normally requires little more than an executable version of a numerical algorithm to determine if it is unstable.

entry:
@PhdThesis{Rowan:1990:FSA,
  author =       "Thomas Harvey Rowan",
  title =        "Functional stability analysis of numerical
                 algorithms",
  type =         "{Ph.D.} thesis",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "xii + 206",
  month =        may,
  year =         "1990",
  bibdate =      "Mon Oct 21 18:08:52 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/303865032",
  abstract =     "The standard technique for detecting instability in
                 numerical algorithms is backward error analysis. The
                 analysis is difficult and tedious when performed by
                 hand, while attempts to automate it have always placed
                 severe restrictions on the tested numerical algorithms.
                 A new approach for detecting instability, functional
                 stability analysis, removes these restrictions by
                 treating numerical algorithms as black boxes. The
                 approach consists of two parts. The first part uses the
                 relationship between the forward error, the backward
                 error, and a problem's condition to define a function
                 that estimates a lower bound on the backward error. In
                 the second part, a new optimization method maximizes
                 the function. A numerical algorithm is unstable if the
                 maximization shows that the backward error can become
                 large. Since numerical algorithms are treated as black
                 boxes, functional stability analysis normally requires
                 little more than an executable version of a numerical
                 algorithm to determine if it is unstable.",
  acknowledgement = ack-nhfb,
  advisor =      "Alan K. Cline",
}


bibtype: article
filename: fparith.bib
label: Sam:1990:GMR
author: H. Sam and A. Gupta
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1006--1015
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57039
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:03 MDT 2011
bibtimestamp: 2011.07.07 14:20:03 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57039
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. Sam and A. Gupta
title:
A generalized multibit recoding of two's complement binary numbers and its proof with application in multiplier implementations

rawtitle:
A generalized multibit recoding of two's complement binary numbers and its proof with application in multiplier implementations

entry:
@Article{Sam:1990:GMR,
  author =       "H. Sam and A. Gupta",
  title =        "A generalized multibit recoding of two's complement
                 binary numbers and its proof with application in
                 multiplier implementations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1006--1015",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57039",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Schatte:1990:SBF
author: Peter Schatte
title: On the stochastic behaviour of the floating point mantissas of sums
journal: J. Inform. Process. Cybernet.
volume: 26
number: 4
pages: 249--254
year: 1990
MRclass: 60F99 (11K99)
MRnumber: 91m:60065
bibdate: Fri Dec 8 08:24:13 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:13 ???
acknowledgement: ack-nhfb
reviewer: Eugenijus Manstavicius
rawauthor: Peter Schatte
rawtitle: On the stochastic behaviour of the floating point mantissas of sums
entry:
@Article{Schatte:1990:SBF,
  author =       "Peter Schatte",
  title =        "On the stochastic behaviour of the floating point
                 mantissas of sums",
  journal =      "J. Inform. Process. Cybernet.",
  volume =       "26",
  number =       "4",
  pages =        "249--254",
  year =         "1990",
  MRclass =      "60F99 (11K99)",
  MRnumber =     "91m:60065",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Eugenijus Manstavi{\v{c}}ius",
}


bibtype: article
filename: fparith.bib
label: Schimandle:1990:MBC
author: James Schimandle
title: Microsoft BASIC's and C's Floating Point Formats
journal: j-CUJ
volume: 8
type: Letter
number: 7
pages: 139--??
month: jul
monthnumber: 7
year: 1990
ISSN: 0898-9788 OR 08989788
bibdate: Fri Aug 30 16:52:23 MDT 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.30 16:52:23 MDT
fjournal: C Users Journal
acknowledgement: ack-nhfb
rawauthor: James Schimandle
rawtitle: {Microsoft BASIC}'s and {C}'s Floating Point Formats
entry:
@Article{Schimandle:1990:MBC,
  author =       "James Schimandle",
  title =        "{Microsoft BASIC}'s and {C}'s Floating Point Formats",
  journal =      j-CUJ,
  volume =       "8",
  type =         "Letter",
  number =       "7",
  pages =        "139--??",
  month =        jul,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}


bibtype: article
filename: fparith.bib
label: Sheppard:1990:EYF
author: Gene Sheppard
title: Evaluating Your Floating Point Library
journal: j-CUJ
volume: 8
number: 8
pages: 121--??
month: aug
monthnumber: 8
year: 1990
ISSN: 0898-9788 OR 08989788
bibdate: Fri Aug 30 16:52:23 MDT 1996
bibsource: http://www.cuj.com/cbklist.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.08.30 16:52:23 MDT
fjournal: C Users Journal
acknowledgement: ack-nhfb
rawauthor: Gene Sheppard
rawtitle: Evaluating Your Floating Point Library
entry:
@Article{Sheppard:1990:EYF,
  author =       "Gene Sheppard",
  title =        "Evaluating Your Floating Point Library",
  journal =      j-CUJ,
  volume =       "8",
  number =       "8",
  pages =        "121--??",
  month =        aug,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}


bibtype: article
filename: fparith.bib
label: Silverman:1990:PPA
author: Robert D. Silverman
title: Parallel polynomial arithmetic over finite rings
journal: j-J-PAR-DIST-COMP
volume: 10
number: 3
pages: 265--270
month: nov
monthnumber: 11
year: 1990
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: MITRE Corp
affiliationaddress: Bedford, Ma, USA
corpsource: Mitre Corp., Bedford, MA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Robert D. Silverman
rawtitle: Parallel polynomial arithmetic over finite rings
keywords:
Alliant FX/8; Chinese remainder; Chinese Remainder Theorem; Computer Systems, Digital--Parallel Processing; Computers, Digital--Computational Methods; Convolution Algorithms; digital arithmetic; Finite Rings; finite rings; Mathematical Techniques; message passing; message passing parallel computer; multiplication; parallel algorithms; parallel computers; parallel polynomial arithmetic; performance; polynomial; Polynomial Arithmetic; Polynomials; polynomials; residue number systems; shared memory; Symult S2010; theorem

entry:
@Article{Silverman:1990:PPA,
  author =       "Robert D. Silverman",
  title =        "Parallel polynomial arithmetic over finite rings",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "10",
  number =       "3",
  pages =        "265--270",
  month =        nov,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "MITRE Corp",
  affiliationaddress = "Bedford, Ma, USA",
  classification = "723; 921; C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory); C5230 (Digital arithmetic methods)",
  corpsource =   "Mitre Corp., Bedford, MA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Alliant FX/8; Chinese remainder; Chinese Remainder
                 Theorem; Computer Systems, Digital--Parallel
                 Processing; Computers, Digital--Computational Methods;
                 Convolution Algorithms; digital arithmetic; Finite
                 Rings; finite rings; Mathematical Techniques; message
                 passing; message passing parallel computer;
                 multiplication; parallel algorithms; parallel
                 computers; parallel polynomial arithmetic; performance;
                 polynomial; Polynomial Arithmetic; Polynomials;
                 polynomials; residue number systems; shared memory;
                 Symult S2010; theorem",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: fparith.bib
label: Silverstein:1990:USM
author: Joel D. Silverstein and Steven E. Sommars and Yio-Chian Tao
title: The UNIX System Math Library, a Status Report
crossref: USENIX:1990:PWU
pages: 117--131
year: 1990
bibdate: Thu Sep 01 11:51:21 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 11:51:21 ???
acknowledgement: ack-nj
rawauthor: Joel D. Silverstein and Steven E. Sommars and Yio-Chian Tao
rawtitle: The {UNIX} System Math Library, a Status Report
entry:
@InProceedings{Silverstein:1990:USM,
  author =       "Joel D. Silverstein and Steven E. Sommars and
                 Yio-Chian Tao",
  title =        "The {UNIX} System Math Library, a Status Report",
  crossref =     "USENIX:1990:PWU",
  pages =        "117--131",
  year =         "1990",
  bibdate =      "Thu Sep 01 11:51:21 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Sips:1990:NML
author: Henk J. Sips and Hai Xiang Lin
title: A new model for on-line arithmetic with an application to the reciprocal calculation
journal: j-J-PAR-DIST-COMP
volume: 8
number: 3
pages: 218--230
month: mar
monthnumber: 3
year: 1990
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: Delft Univ of Technology
affiliationaddress: Delft, Neth
corpsource: Delft University of Technol., Netherlands
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: T Theoretical or Mathematical
rawauthor: Henk J. Sips and Hai Xiang Lin
rawtitle: A new model for on-line arithmetic with an application to the reciprocal calculation
keywords:
adapted Newton--Raphson; approximation method; Approximation Theory; arithmetic; attainable on-; computation pipelining; Computational Models; Computer Systems, Digital--On Line Operation; conditional on-line; cycle times; delay; delays; Digital Arithmetic; digital arithmetic; exact function value; functions; iteration; iteration method; iterative; Iterative Methods; iterative methods; line delay; Mathematical Techniques; on-line arithmetic; on-line computation; on-line digits; online arithmetic; overlapping computation; pipeline; processing; reciprocal calculation; seed table; step; table look-up

entry:
@Article{Sips:1990:NML,
  author =       "Henk J. Sips and Hai Xiang Lin",
  title =        "A new model for on-line arithmetic with an application
                 to the reciprocal calculation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "8",
  number =       "3",
  pages =        "218--230",
  month =        mar,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Delft Univ of Technology",
  affiliationaddress = "Delft, Neth",
  classification = "722; 723; 921; C4130 (Interpolation and function
                 approximation); C5230 (Digital arithmetic methods)",
  corpsource =   "Delft University of Technol., Netherlands",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "adapted Newton--Raphson; approximation method;
                 Approximation Theory; arithmetic; attainable on-;
                 computation pipelining; Computational Models; Computer
                 Systems, Digital--On Line Operation; conditional
                 on-line; cycle times; delay; delays; Digital
                 Arithmetic; digital arithmetic; exact function value;
                 functions; iteration; iteration method; iterative;
                 Iterative Methods; iterative methods; line delay;
                 Mathematical Techniques; on-line arithmetic; on-line
                 computation; on-line digits; online arithmetic;
                 overlapping computation; pipeline; processing;
                 reciprocal calculation; seed table; step; table
                 look-up",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: fparith.bib
label: Skelton:1990:GSE
author: R. E. Skelton and D. Williamson
booktitle: Proceedings of the 29th IEEE Conference on Decision and Control, 1990
title: Guaranteed state estimation accuracies with roundoff error
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 297--298
year: 1990
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: R. E. Skelton and D. Williamson
rawbooktitle: Proceedings of the 29th {IEEE} Conference on Decision and Control, 1990
rawtitle: Guaranteed state estimation accuracies with roundoff error
entry:
@InProceedings{Skelton:1990:GSE,
  author =       "R. E. Skelton and D. Williamson",
  booktitle =    "Proceedings of the 29th {IEEE} Conference on Decision
                 and Control, 1990",
  title =        "Guaranteed state estimation accuracies with roundoff
                 error",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "297--298",
  year =         "1990",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Kalman filter theory is modified to accommodate
                 roundoff errors in state computation. Two problems are
                 solved: (i) choosing the wordlength required for each
                 state computation to guarantee specified estimation
                 accuracies of multiple output variables \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Slishman:1990:FPR
author: G. Slishman
title: Fast and Perfectly Rounding Decimal / Hexadecimal Conversions
type: Research Report
number: RC-15683
institution: pub-IBM-WATSON
address: pub-IBM-WATSON:adr
pages: 297--298
year: 1990
bibdate: Fri Apr 21 07:04:09 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.04.21 07:04:09 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: G. Slishman
rawtitle: Fast and Perfectly Rounding Decimal\slash Hexadecimal Conversions
entry:
@TechReport{Slishman:1990:FPR,
  author =       "G. Slishman",
  title =        "Fast and Perfectly Rounding Decimal\slash Hexadecimal
                 Conversions",
  type =         "Research Report",
  number =       "RC-15683",
  institution =  pub-IBM-WATSON,
  address =      pub-IBM-WATSON:adr,
  year =         "1990",
  bibdate =      "Fri Apr 21 07:04:09 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Steele:1990:HPF
author: Guy L. Steele Jr. and Jon L. White
title: How to Print Floating-Point Numbers Accurately
journal: j-SIGPLAN
volume: 25
number: 6
pages: 112--126
month: jun
monthnumber: 6
year: 1990
CODEN: SINODQ
DOI: https://doi.org/10.1145/93548.93559
ISBN: 0-89791-364-7 OR 0897913647
ISBN13: 978-0-89791-364-5 OR 9780897913645
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Sun Dec 14 09:15:53 MST 2003
bibtimestamp: 2003.12.14 09:15:53 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p112-steele/
fjournal: ACM SIGPLAN Notices
remark: Published as part of the Proceedings of PLDI'90.
acknowledgement: ack-nhfb
affiliation: Thinking Machines Corp
affiliationaddress: Cambridge, MA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
journalabr: SIGPLAN Not
thesaurus: Digital arithmetic; Mathematics computing
rawauthor: Guy L. {Steele Jr.} and Jon L. White
rawtitle: How to Print Floating-Point Numbers Accurately
bibsource:
Compendex database; http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/93542/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib

note:
See also input algorithm in cite Clinger:1990:HRF,Clinger:2004:RHR, and a faster output algorithm in cite Burger:1996:PFP and cite Knuth:1990:SPW, IBM S/360 algorithms in cite Abbott:1999:ASS for both IEEE 754 and S/360 formats, and a twenty-year retrospective in cite Steele:2004:RHP. In electronic mail dated Wed, 27 Jun 1990 11:55:36 EDT, Guy Steele reported that an intrepid pre-SIGPLAN 90 conference implementation of what is stated in the paper revealed 3 mistakes: begin itemize item [1.] Table~5 (page 124):par noindent insert tt k <-- 0 after assertion, and also delete tt k <-- 0 from Table~6. item [2.] Table~9 (page 125):par noindent begin tabular ll for & tt -1:USER!(""); substitute & tt -1:USER!("0"); end tabularpar noindent and delete the comment. item [3.] Table~10 (page 125):par noindent begin tabularll for & tt fill(-k, "0") substitute & tt fill(-k-1, "0") end tabular end itemize def EatBibTeXPeriod #1ifx #1.else #1fi EatBibTeXPeriod 

abstract:
Algorithms are presented for accurately converting floating-point numbers to decimal representation. The key idea is to carry along with the computation an explicit representation of the required rounding accuracy. The authors begin with the simpler problem of converting fixed-point fractions. A modification of the well-known algorithm for radix-conversion of fixed-point fractions by multiplication explicitly determines when to terminate the conversion process; a variable number of digits are produced. They derive two algorithms for free-format output of floating-point numbers. Finally, they modify the free-format conversion algorithm for use in fixed-format applications. Information may be lost if the fixed format provides too few digit positions, but the output is always correctly rounded. On the other hand, no `garbage digits' are ever produced, even if the fixed format specifies too many digit positions (intuitively, the `4/3 prints as 1.333333328366279602' problem does not occur).

keywords:
algorithms; computer programming languages; computers, digital --- computational methods; conversion process; correct rounding; decimal decimal representation; design; digit positions; explicit representation; fixed-format applications; fixed-point fractions; floating point numbers; floating-point arithmetic; floating-point numbers; free-format conversion algorithm; free-format output; garbage digits; performance; radix-conversion; rounding accuracy; verification

subject:
bf F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.

rawabstract:
Algorithms are presented for accurately converting floating-point numbers to decimal representation. The key idea is to carry along with the computation an explicit representation of the required rounding accuracy. The authors begin with the simpler problem of converting fixed-point fractions. A modification of the well-known algorithm for radix-conversion of fixed-point fractions by multiplication explicitly determines when to terminate the conversion process; a variable number of digits are produced. They derive two algorithms for free-format output of floating-point numbers. Finally, they modify the free-format conversion algorithm for use in fixed-format applications. Information may be lost if the fixed format provides too few digit positions, but the output is always correctly rounded. On the other hand, no `garbage digits' are ever produced, even if the fixed format specifies too many digit positions (intuitively, the `4/3 prints as 1.333333328366279602' problem does not occur).

rawnote:
See also input algorithm in \cite{Clinger:1990:HRF,Clinger:2004:RHR}, and a faster output algorithm in \cite{Burger:1996:PFP} and \cite{Knuth:1990:SPW}, IBM S/360 algorithms in \cite{Abbott:1999:ASS} for both IEEE 754 and S/360 formats, and a twenty-year retrospective in \cite{Steele:2004:RHP}. In electronic mail dated Wed, 27 Jun 1990 11:55:36 EDT, Guy Steele reported that an intrepid pre-SIGPLAN 90 conference implementation of what is stated in the paper revealed 3 mistakes: \begin{itemize} \item[1.] Table~5 (page 124):\par \noindent insert {\tt k <-- 0} after assertion, and also delete {\tt k <-- 0} from Table~6. \item[2.] Table~9 (page 125):\par \noindent \begin{tabular} {ll} for & {\tt -1:USER!({"}{"});} \\ substitute & {\tt -1:USER!({"}0{"});} \end{tabular}\par \noindent and delete the comment. \item[3.] Table~10 (page 125):\par \noindent \begin{tabular}{ll} for & {\tt fill(-k, "0")}\\ substitute & {\tt fill(-k-1, "0")} \end{tabular} \end{itemize} \def\EatBibTeXPeriod#1{\ifx#1.\else#1\fi}\EatBibTeXPeriod

entry:
@Article{Steele:1990:HPF,
  author =       "Guy L. {Steele Jr.} and Jon L. White",
  title =        "How to Print Floating-Point Numbers Accurately",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "6",
  pages =        "112--126",
  month =        jun,
  year =         "1990",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/93548.93559",
  ISBN =         "0-89791-364-7",
  ISBN-13 =      "978-0-89791-364-5",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:53 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/93542/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib",
  note =         "See also input algorithm in
                 \cite{Clinger:1990:HRF,Clinger:2004:RHR}, and a faster
                 output algorithm in \cite{Burger:1996:PFP} and
                 \cite{Knuth:1990:SPW}, IBM S/360 algorithms in
                 \cite{Abbott:1999:ASS} for both IEEE 754 and S/360
                 formats, and a twenty-year retrospective in
                 \cite{Steele:2004:RHP}. In electronic mail dated Wed,
                 27 Jun 1990 11:55:36 EDT, Guy Steele reported that an
                 intrepid pre-SIGPLAN 90 conference implementation of
                 what is stated in the paper revealed 3 mistakes:
                 \begin{itemize} \item[1.] Table~5 (page 124):\par
                 \noindent insert {\tt k <-- 0} after assertion, and
                 also delete {\tt k <-- 0} from Table~6. \item[2.]
                 Table~9 (page 125):\par \noindent \begin{tabular} {ll}
                 for & {\tt -1:USER!({"}{"});} \\
                 substitute & {\tt -1:USER!({"}0{"});} \end{tabular}\par
                 \noindent and delete the comment. \item[3.] Table~10
                 (page 125):\par \noindent \begin{tabular}{ll} for &
                 {\tt fill(-k, "0")}\\
                 substitute & {\tt fill(-k-1, "0")} \end{tabular}
                 \end{itemize}
                 \def\EatBibTeXPeriod#1{\ifx#1.\else#1\fi}\EatBibTeXPeriod",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p112-steele/",
  abstract =     "Algorithms are presented for accurately converting
                 floating-point numbers to decimal representation. The
                 key idea is to carry along with the computation an
                 explicit representation of the required rounding
                 accuracy. The authors begin with the simpler problem of
                 converting fixed-point fractions. A modification of the
                 well-known algorithm for radix-conversion of
                 fixed-point fractions by multiplication explicitly
                 determines when to terminate the conversion process; a
                 variable number of digits are produced. They derive two
                 algorithms for free-format output of floating-point
                 numbers. Finally, they modify the free-format
                 conversion algorithm for use in fixed-format
                 applications. Information may be lost if the fixed
                 format provides too few digit positions, but the output
                 is always correctly rounded. On the other hand, no
                 `garbage digits' are ever produced, even if the fixed
                 format specifies too many digit positions (intuitively,
                 the `4/3 prints as 1.333333328366279602' problem does
                 not occur).",
  acknowledgement = ack-nhfb,
  affiliation =  "Thinking Machines Corp",
  affiliationaddress = "Cambridge, MA, USA",
  classification = "722; 723; C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  confdate =     "20-22 June 1990",
  conference =   "Proceedings of the ACM SIGPLAN '90 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1990",
  conflocation = "White Plains, NY, USA",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "algorithms; computer programming languages; computers,
                 digital --- computational methods; conversion process;
                 correct rounding; decimal decimal representation;
                 design; digit positions; explicit representation;
                 fixed-format applications; fixed-point fractions;
                 floating point numbers; floating-point arithmetic;
                 floating-point numbers; free-format conversion
                 algorithm; free-format output; garbage digits;
                 performance; radix-conversion; rounding accuracy;
                 verification",
  remark =       "Published as part of the Proceedings of PLDI'90.",
  sponsor =      "Assoc for Computing Machinery, Special Interest Group
                 on Programming Languages",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic.",
  thesaurus =    "Digital arithmetic; Mathematics computing",
  xxabstract =   "We present algorithms for accurately converting
                 floating-point numbers to decimal representation. The
                 key idea is to carry along with the computation an
                 explicit representation of the required rounding
                 accuracy. We begin with the simpler problem of
                 converting fixed-point fractions. A modification of the
                 well-known algorithm for radix-conversion of
                 fixed-point fractions by multiplication explicitly
                 determines when to terminate the conversion process; a
                 variable number of digits are produced. We then derive
                 two algorithms for free-format output of floating-point
                 numbers. Finally, we modify the free-format conversion
                 algorithm for use in fixed-format applications.",
}


bibtype: article
filename: fparith.bib
label: Su:1990:ASS
author: C.-C. Su and H.-Y. Lo
title: An algorithm for scaling and single residue error correction in residue number systems
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1053--1064
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57044
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:03 MDT 2011
bibtimestamp: 2011.07.07 14:20:03 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C.-C. Su and H.-Y. Lo
rawtitle: An algorithm for scaling and single residue error correction in residue number systems
URL:
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2065; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57044

entry:
@Article{Su:1990:ASS,
  author =       "C.-C. Su and H.-Y. Lo",
  title =        "An algorithm for scaling and single residue error
                 correction in residue number systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1053--1064",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57044",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2065;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57044",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "An algorithm for scaling and single residue digit
                 error correction is proposed. This algorithm is fully
                 based on mixed radix conversion (MRC). The redundant
                 digits of MRC can be used to establish a lookup table
                 to correct single residue digit \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Sun:1990:FAM
author: Jenn-Dong Sun and H. Krishna
title: Fast Algorithms for Multiple Errors Detection and Correction in Redundant Residue Number Systems
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 831
year: 1990
DOI: https://doi.org/10.1109/MWSCAS.1990.140897
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Jenn-Dong Sun and H. Krishna
rawtitle: Fast Algorithms for Multiple Errors Detection and Correction in Redundant Residue Number Systems
booktitle:
Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 5--7 Nov 1990

rawbooktitle:
Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 5--7 Nov 1990

entry:
@InProceedings{Sun:1990:FAM,
  author =       "Jenn-Dong Sun and H. Krishna",
  booktitle =    "Conference Record Twenty-Fourth Asilomar Conference on
                 Signals, Systems and Computers, 5--7 Nov 1990",
  title =        "Fast Algorithms for Multiple Errors Detection and
                 Correction in Redundant Residue Number Systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "831",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1990.140897",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}


bibtype: book
filename: fparith.bib
label: Tabak:1990:RS
author: Daniel Tabak
title: RISC Systems
publisher: pub-JW
address: pub-JW:adr
pages: xii + 300
year: 1990
ISBN: 0-471-92694-9 OR 0471926949
ISBN13: 978-0-471-92694-8 OR 9780471926948
LCCN: QA76.9.A73.T294 1990
bibdate: Wed Aug 10 11:51:06 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.10 11:51:06 ???
acknowledgement: ack-nhfb
rawauthor: Daniel Tabak
rawtitle: {RISC} Systems
entry:
@Book{Tabak:1990:RS,
  author =       "Daniel Tabak",
  title =        "{RISC} Systems",
  publisher =    pub-JW,
  address =      pub-JW:adr,
  pages =        "xii + 300",
  year =         "1990",
  ISBN =         "0-471-92694-9",
  ISBN-13 =      "978-0-471-92694-8",
  LCCN =         "QA76.9.A73.T294 1990",
  bibdate =      "Wed Aug 10 11:51:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$49.95",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
}


bibtype: article
filename: fparith.bib
label: Tang:1990:AET
author: Ping Tak Peter Tang
title: Accurate and Efficient Testing of the Exponential and Logarithm Functions
journal: j-TOMS
volume: 16
number: 3
pages: 185--200
month: sep
monthnumber: 9
year: 1990
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65-04 (65G99)
MRnumber: 1 070 797
bibdate: Sun Sep 04 23:14:59 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 23:14:59 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; languages; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawtitle: Accurate and Efficient Testing of the Exponential and Logarithm Functions
URL:
http://doi.acm.org/10.1145/79505.79506; http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/

abstract:
Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests' reliability are discussed. Results of applying the tests to our own as well as to a number of other implementations of EXP and LOG are presented.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.

rawabstract:
Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests' reliability are discussed. Results of applying the tests to our own as well as to a number of other implementations of EXP and LOG are presented.

entry:
@Article{Tang:1990:AET,
  author =       "Ping Tak Peter Tang",
  title =        "Accurate and Efficient Testing of the Exponential and
                 Logarithm Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "185--200",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G99)",
  MRnumber =     "1 070 797",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/79505.79506;
                 http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
  abstract =     "Table-driven techniques can be used to test highly
                 accurate implementation of EXP LOG. The largest error
                 observed in EXP and LOG accurately to within 1/500 unit
                 in the last place are reported in our tests. Methods to
                 verify the tests' reliability are discussed. Results of
                 applying the tests to our own as well as to a number of
                 other implementations of EXP and LOG are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability.",
}


bibtype: techreport
filename: fparith.bib
label: Tang:1990:SSI
author: P. T. P. Tang
title: Some Software Implementations of the Functions Sine and Cosine
number: Report ANL-90/3
institution: Argonne National Laboratory
address: Argonne, IL, USA
pages: 27
month: apr
monthnumber: 4
year: 1990
bibdate: Mon Sep 12 23:55:17 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 23:55:17 ???
acknowledgement: ack-nj
rawauthor: P. T. P. Tang
rawtitle: Some Software Implementations of the Functions Sine and Cosine
entry:
@TechReport{Tang:1990:SSI,
  author =       "P. T. P. Tang",
  title =        "Some Software Implementations of the Functions Sine
                 and Cosine",
  number =       "Report ANL-90/3",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "27",
  month =        apr,
  year =         "1990",
  bibdate =      "Mon Sep 12 23:55:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Tang:1990:TDIa
author: Ping Tak Peter Tang
title: Table-Driven Implementation of the Logarithm Function in IEEE Floating-Point Arithmetic
journal: j-TOMS
volume: 16
number: 4
pages: 378--400
month: dec
monthnumber: 12
year: 1990
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 23:26:09 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 23:26:09 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; design; performance; reliability; standardization; theory; verification
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawtitle: Table-Driven Implementation of the Logarithm Function in {IEEE} Floating-Point Arithmetic
abstract:
Algorithms and implementation details for the logarithm functions in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementation need only working- precision arithmetic and are provably accurate to within 0.57 ulp.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
Algorithms and implementation details for the logarithm functions in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementation need only working- precision arithmetic and are provably accurate to within 0.57 ulp.

entry:
@Article{Tang:1990:TDIa,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "378--400",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:26:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
  abstract =     "Algorithms and implementation details for the
                 logarithm functions in both single and double precision
                 of IEEE 754 arithmetic are presented here. With a table
                 of moderate size, the implementation need only working-
                 precision arithmetic and are provably accurate to
                 within 0.57 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; reliability;
                 standardization; theory; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}


bibtype: techreport
filename: fparith.bib
label: Tang:1990:TDIb
author: P. T. P. Tang
title: Table-driven Implementation of the Expm1 Function in IEEE Floating-Point Arithmetic
number: Preprint MCS-P144-0390
institution: Argonne National Laboratory
address: Argonne, IL, USA
month: mar
monthnumber: 3
year: 1990
bibdate: Mon Sep 12 23:55:14 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 23:55:14 ???
acknowledgement: ack-nj
rawauthor: P. T. P. Tang
rawtitle: Table-driven Implementation of the Expm1 Function in {IEEE} Floating-Point Arithmetic
entry:
@TechReport{Tang:1990:TDIb,
  author =       "P. T. P. Tang",
  title =        "Table-driven Implementation of the Expm1 Function in
                 {IEEE} Floating-Point Arithmetic",
  number =       "Preprint MCS-P144-0390",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "??",
  month =        mar,
  year =         "1990",
  bibdate =      "Mon Sep 12 23:55:14 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: fparith.bib
label: Teetz:1990:SNS
author: Ingo Teetz and Thomas Fischer and Walter Issel
type: Report
number: R-Math-01/90 0233-2876
institution: Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut fur Mathematik
address: Berlin, Germany
pages: vii + 79
year: 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
remark: Summary in English and German.
acknowledgement: ack-nhfb
rawauthor: Ingo Teetz and Thomas Fischer and Walter Issel
title:
Die Sprache NBSF fur die strukturelle Beschreibung von Schaltkreisen.: Eine Darstellung am Beispiel eines Gleitkomma-Prozessors

keywords:
Computer hardware description languages.; Floating-point arithmetic.; NBSF (Computer hardware description language)

rawtitle:
{Die Sprache NBSF fur die strukturelle Beschreibung von Schaltkreisen.: Eine Darstellung am Beispiel eines Gleitkomma-Prozessors}

entry:
@TechReport{Teetz:1990:SNS,
  author =       "Ingo Teetz and Thomas Fischer and Walter Issel",
  title =        "{Die Sprache NBSF fur die strukturelle Beschreibung
                 von Schaltkreisen.: Eine Darstellung am Beispiel eines
                 Gleitkomma-Prozessors}",
  type =         "Report",
  number =       "R-Math-01/90 0233-2876",
  institution =  "Akademie der Wissenschaften der DDR,
                 Karl-Weierstrass-Institut fur Mathematik",
  address =      "Berlin, Germany",
  pages =        "vii + 79",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer hardware description languages.;
                 Floating-point arithmetic.; NBSF (Computer hardware
                 description language)",
  remark =       "Summary in English and German.",
}


bibtype: incollection
filename: fparith.bib
label: Trefethen:1990:PSP
author: L. N. Trefethen and M. H. Gutknecht
title: Pade, Stable Pade, and Chebyshev--Pade Approximation
crossref: Mason:1990:AAI
pages: ??--??
year: 1990
bibdate: Thu Sep 01 12:23:25 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 12:23:25 ???
acknowledgement: ack-nj
rawauthor: L. N. Trefethen and M. H. Gutknecht
rawtitle: {Pad{\'e}}, Stable {Pad{\'e}}, and {Chebyshev--Pad{\'e}} Approximation
entry:
@InCollection{Trefethen:1990:PSP,
  author =       "L. N. Trefethen and M. H. Gutknecht",
  title =        "{Pad{\'e}}, Stable {Pad{\'e}}, and
                 {Chebyshev--Pad{\'e}} Approximation",
  crossref =     "Mason:1990:AAI",
  pages =        "??--??",
  year =         "1990",
  bibdate =      "Thu Sep 01 12:23:25 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Tricker:1990:ERP
author: A. R. Tricker
title: The effect of rounding on the power level of certain normal test statistics
journal: j-J-APPL-STAT
volume: 17
number: 2
pages: 219--228
year: 1990
DOI: https://doi.org/10.1080/757582833
ISSN: 0266-4763 (print), 1360-0532 (electronic) OR 02664763 (print), 13600532 (electronic)
ISSNL: 0266-4763 OR 02664763
bibdate: Tue Sep 6 11:16:18 MDT 2011
bibtimestamp: 2011.09.06 11:16:18 MDT
fjournal: Journal of Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/cjas20
onlinedate: 5 Jun 2011
rawauthor: A. R. Tricker
rawtitle: The effect of rounding on the power level of certain normal test statistics
bibsource:
http://www.tandf.co.uk/journals/routledge/02664763.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Tricker:1990:ERP,
  author =       "A. R. Tricker",
  title =        "The effect of rounding on the power level of certain
                 normal test statistics",
  journal =      j-J-APPL-STAT,
  volume =       "17",
  number =       "2",
  pages =        "219--228",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/757582833",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:16:18 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "5 Jun 2011",
}


bibtype: article
filename: fparith.bib
label: Tricker:1990:ERSa
author: A. R. Tricker
title: The effect of rounding on the significance level of certain normal test statistics
journal: j-J-APPL-STAT
volume: 17
number: 1
pages: 31--38
year: 1990
DOI: https://doi.org/10.1080/757582644
ISSN: 0266-4763 (print), 1360-0532 (electronic) OR 02664763 (print), 13600532 (electronic)
ISSNL: 0266-4763 OR 02664763
bibdate: Tue Sep 6 11:16:16 MDT 2011
bibtimestamp: 2011.09.06 11:16:16 MDT
fjournal: Journal of Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/cjas20
onlinedate: 18 Jul 2011
rawauthor: A. R. Tricker
rawtitle: The effect of rounding on the significance level of certain normal test statistics
bibsource:
http://www.tandf.co.uk/journals/routledge/02664763.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Tricker:1990:ERSa,
  author =       "A. R. Tricker",
  title =        "The effect of rounding on the significance level of
                 certain normal test statistics",
  journal =      j-J-APPL-STAT,
  volume =       "17",
  number =       "1",
  pages =        "31--38",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/757582644",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:16:16 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "18 Jul 2011",
}


bibtype: article
filename: fparith.bib
label: Tricker:1990:ERSb
author: A. R. Tricker
journal: j-J-APPL-STAT
volume: 17
number: 3
pages: 329--340
year: 1990
DOI: https://doi.org/10.1080/02664769000000005
ISSN: 0266-4763 (print), 1360-0532 (electronic) OR 02664763 (print), 13600532 (electronic)
ISSNL: 0266-4763 OR 02664763
bibdate: Tue Sep 6 11:16:20 MDT 2011
bibtimestamp: 2011.09.06 11:16:20 MDT
fjournal: Journal of Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/cjas20
onlinedate: 28 Jul 2006
rawauthor: A. R. Tricker
title:
The effect of rounding on the significance level and power of certain test statistics for non-normal data

rawtitle:
The effect of rounding on the significance level and power of certain test statistics for non-normal data

entry:
@Article{Tricker:1990:ERSb,
  author =       "A. R. Tricker",
  title =        "The effect of rounding on the significance level and
                 power of certain test statistics for non-normal data",
  journal =      j-J-APPL-STAT,
  volume =       "17",
  number =       "3",
  pages =        "329--340",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664769000000005",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:16:20 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "28 Jul 2006",
}


bibtype: article
filename: fparith.bib
label: vanderVorst:1990:CBP
author: H. A. van der Vorst
title: The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors
journal: j-LECT-NOTES-MATH
volume: 1457
pages: 126--136
year: 1990
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0090905
ISBN: 3-540-53515-2 (print), 3-540-46746-7 (e-book) OR 3540535152 (print), 3540467467 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
MRclass: 65F35
MRnumber: 1101632 (92a:65141)
MRreviewer: Seymour Bachmuth
bibdate: Fri May 9 19:07:18 MDT 2014
bibtimestamp: 2014.05.09 19:07:18 MDT
URL: http://link.springer.com/chapter/10.1007/BFb0090905/
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0090897
bookURL: http://www.springerlink.com/content/978-3-540-46746-5
journalURL: http://link.springer.com/bookseries/304
rawauthor: H. A. {van der Vorst}
rawtitle: The convergence behaviour of preconditioned {CG} and {CG-S} in the presence of rounding errors
ISBN13:
978-3-540-53515-7 (print), 978-3-540-46746-5 (e-book) OR 9783540535157 (print), 9783540467465 (ebook)

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/lnm1990.bib; MathSciNet database

entry:
@Article{vanderVorst:1990:CBP,
  author =       "H. A. {van der Vorst}",
  title =        "The convergence behaviour of preconditioned {CG} and
                 {CG-S} in the presence of rounding errors",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1457",
  pages =        "126--136",
  year =         "1990",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0090905",
  ISBN =         "3-540-53515-2 (print), 3-540-46746-7 (e-book)",
  ISBN-13 =      "978-3-540-53515-7 (print), 978-3-540-46746-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "65F35",
  MRnumber =     "1101632 (92a:65141)",
  MRreviewer =   "Seymour Bachmuth",
  bibdate =      "Fri May 9 19:07:18 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1990.bib;
                 MathSciNet database",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0090905/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0090897",
  book-URL =     "http://www.springerlink.com/content/978-3-540-46746-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
  MRauthor =     "H. A. {van der Vorst}",
  mynote =       "Not copied. No actual error analysis. Just
                 explanations based on his paper with van der Sluis
                 (don't reference Greenbaum!).",
}


bibtype: mastersthesis
filename: fparith.bib
label: VanElsen:1990:OCL
author: Lucien William Van Elsen
title: An optimizing compiler for low-level floating point operations
type: Thesis (B.S.)
school: Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science
address: Cambridge, MA, USA
pages: v + 56
year: 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: Supervised by William J. Dally.
acknowledgement: ack-nhfb
rawauthor: Lucien William {Van Elsen}
rawnote: Supervised by William J. Dally.
rawtitle: An optimizing compiler for low-level floating point operations
entry:
@MastersThesis{VanElsen:1990:OCL,
  author =       "Lucien William {Van Elsen}",
  title =        "An optimizing compiler for low-level floating point
                 operations",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology, Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "v + 56",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by William J. Dally.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Vuillemin:1990:ERC
author: Jean E. Vuillemin
title: Exact real computer arithmetic with continued fractions
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1087--1105
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57047
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:04 MDT 2011
bibtimestamp: 2011.07.07 14:20:04 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57047
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jean E. Vuillemin
rawtitle: Exact real computer arithmetic with continued fractions
entry:
@Article{Vuillemin:1990:ERC,
  author =       "Jean E. Vuillemin",
  title =        "Exact real computer arithmetic with continued
                 fractions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1087--1105",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57047",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57047",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Wallis:1990:IFP
editor: Peter J. L. Wallis
title: Improving Floating-Point Programming
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xvi + 191
year: 1990
ISBN: 0-471-92437-7 OR 0471924377
ISBN13: 978-0-471-92437-1 OR 9780471924371
LCCN: QA76.6 .I446 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
raweditor: Peter J. L. Wallis
rawtitle: Improving Floating-Point Programming
bibsource:
https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
This contributed work covers, in precise detail, the potential sources of error in floating-point programming and how these trouble spots can be controlled. Explains several methods for improving the accuracy of floating-point programming, concentrating on those methods that are relevant to the exploitation of the Karlsruhe Accurate Arithmetic.

keywords:
Computation by computer systems --- Floating point representation; Electronic digital computers --- Programming; Floating-point arithmetic; Floating-point arithmetic, Compiling (Electronic computers)

TOC:
Fundamentals Basic Concepts Machine Arithmetic Model Arithmetic Error control Sources of Error Different Approaches to Interval Arithmetic / C. Ullrich and J. Wolff von Gudenberg The Karlsruhe Accurate Arithmetic Approach / J. Wolff von Gudenberg Embedding Of Karlsruhe Arithmetic / J. Wolff von Gudenberg The Embedding of Accurate Arithmetic in PASCAL-SC / J. Wolff von Gudenberg The Embedding of Accurate Arithmetic in Ada / J. Kok Improving Accuracy Automatic Identification of Scalar Products / D. Winter Guidelines for Selected Transformations of Existing Programs / L. Bamberger Manipulation of Expressions / J. Davenport and H. Fischer E-Methods for Improving Accuracy / G. Schumacher and J. Wolff von Gudenberg References Index

rawabstract:
This contributed work covers, in precise detail, the potential sources of error in floating-point programming and how these trouble spots can be controlled. Explains several methods for improving the accuracy of floating-point programming, concentrating on those methods that are relevant to the exploitation of the Karlsruhe Accurate Arithmetic.

rawTOC:
Fundamentals \\ Basic Concepts \\ Machine Arithmetic \\ Model Arithmetic \\ \\ Error control \\ Sources of Error \\ Different Approaches to Interval Arithmetic / C. Ullrich and J. Wolff von Gudenberg \\ The Karlsruhe Accurate Arithmetic Approach / J. Wolff von Gudenberg \\ \\ Embedding Of Karlsruhe Arithmetic / J. Wolff von Gudenberg \\ The Embedding of Accurate Arithmetic in PASCAL-SC / J. Wolff von Gudenberg \\ The Embedding of Accurate Arithmetic in Ada / J. Kok \\ \\ Improving Accuracy \\ Automatic Identification of Scalar Products / D. Winter \\ Guidelines for Selected Transformations of Existing Programs / L. Bamberger \\ Manipulation of Expressions / J. Davenport and H. Fischer \\ E-Methods for Improving Accuracy / G. Schumacher and J. Wolff von Gudenberg \\ \\ References \\ Index

entry:
@Book{Wallis:1990:IFP,
  editor =       "Peter J. L. Wallis",
  title =        "Improving Floating-Point Programming",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 191",
  year =         "1990",
  ISBN =         "0-471-92437-7",
  ISBN-13 =      "978-0-471-92437-1",
  LCCN =         "QA76.6 .I446 1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$60.00",
  abstract =     "This contributed work covers, in precise detail, the
                 potential sources of error in floating-point
                 programming and how these trouble spots can be
                 controlled. Explains several methods for improving the
                 accuracy of floating-point programming, concentrating
                 on those methods that are relevant to the exploitation
                 of the Karlsruhe Accurate Arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "Computation by computer systems --- Floating point
                 representation; Electronic digital computers ---
                 Programming; Floating-point arithmetic; Floating-point
                 arithmetic, Compiling (Electronic computers)",
  tableofcontents = "Fundamentals \\
                 Basic Concepts \\
                 Machine Arithmetic \\
                 Model Arithmetic \\
                 \\
                 Error control \\
                 Sources of Error \\
                 Different Approaches to Interval Arithmetic / C.
                 Ullrich and J. Wolff von Gudenberg \\
                 The Karlsruhe Accurate Arithmetic Approach / J. Wolff
                 von Gudenberg \\
                 \\
                 Embedding Of Karlsruhe Arithmetic / J. Wolff von
                 Gudenberg \\
                 The Embedding of Accurate Arithmetic in PASCAL-SC / J.
                 Wolff von Gudenberg \\
                 The Embedding of Accurate Arithmetic in Ada / J. Kok
                 \\
                 \\
                 Improving Accuracy \\
                 Automatic Identification of Scalar Products / D. Winter
                 \\
                 Guidelines for Selected Transformations of Existing
                 Programs / L. Bamberger \\
                 Manipulation of Expressions / J. Davenport and H.
                 Fischer \\
                 E-Methods for Improving Accuracy / G. Schumacher and J.
                 Wolff von Gudenberg \\
                 \\
                 References \\
                 Index",
}


bibtype: article
filename: fparith.bib
label: Weber:1990:EHP
author: Ken Weber
title: An experiment in high-precision arithmetic on shared memory multiprocessors
journal: j-SIGSAM
volume: 24
number: 2
pages: 22--40
month: apr
monthnumber: 4
year: 1990
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Wed Oct 5 08:31:59 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.10.05 08:31:59 MDT
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
rawauthor: Ken Weber
rawtitle: An experiment in high-precision arithmetic on shared memory multiprocessors
entry:
@Article{Weber:1990:EHP,
  author =       "Ken Weber",
  title =        "An experiment in high-precision arithmetic on shared
                 memory multiprocessors",
  journal =      j-SIGSAM,
  volume =       "24",
  number =       "2",
  pages =        "22--40",
  month =        apr,
  year =         "1990",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Oct 5 08:31:59 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "??",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}


bibtype: article
filename: fparith.bib
label: Wigley:1990:MRR
author: N. M. Wigley and G. A. Jullien
title: On modulus replication for residue arithmetic computations of complex inner products
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1065--1076
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57045
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:03 MDT 2011
bibtimestamp: 2011.07.07 14:20:03 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57045
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. M. Wigley and G. A. Jullien
rawtitle: On modulus replication for residue arithmetic computations of complex inner products
entry:
@Article{Wigley:1990:MRR,
  author =       "N. M. Wigley and G. A. Jullien",
  title =        "On modulus replication for residue arithmetic
                 computations of complex inner products",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1065--1076",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57045",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57045",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Wingler:1990:TMI
author: Eric Wingler
title: The Teaching of Mathematics: An Infinite Product Expansion for the Square Root Function
journal: j-AMER-MATH-MONTHLY
volume: 97
number: 9
pages: 836--839
month: nov
monthnumber: 11
year: 1990
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:36:09 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:36:09 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Eric Wingler
rawtitle: The Teaching of Mathematics: An Infinite Product Expansion for the Square Root Function
entry:
@Article{Wingler:1990:TMI,
  author =       "Eric Wingler",
  title =        "The Teaching of Mathematics: An Infinite Product
                 Expansion for the Square Root Function",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "97",
  number =       "9",
  pages =        "836--839",
  month =        nov,
  year =         "1990",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:09 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: mastersthesis
filename: fparith.bib
label: Wong:1990:PFP
author: Kar-pang Wong
title: The precision of floating point computation in digital computer
type: Thesis (M.S. in Computer Science)
school: University of Wisconsin, Milwaukee
address: Milwaukee, WI, USA
pages: vii + 45
year: 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Electronic digital computers --- Programming.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Kar-pang Wong
rawtitle: The precision of floating point computation in digital computer
entry:
@MastersThesis{Wong:1990:PFP,
  author =       "Kar-pang Wong",
  title =        "The precision of floating point computation in digital
                 computer",
  type =         "Thesis ({M.S. in Computer Science})",
  school =       "University of Wisconsin, Milwaukee",
  address =      "Milwaukee, WI, USA",
  pages =        "vii + 45",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Wong:1990:QNF
author: P. W. Wong
title: Quantization noise, fixed-point multiplicative roundoff noise, and dithering
journal: j-IEEE-TRANS-ACOUST-SPEECH
volume: 38
number: 2
pages: 286--300
month: feb
monthnumber: 2
year: 1990
CODEN: IETABA
ISSN: 0096-3518 OR 00963518
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Acoustics, Speech, and Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29
rawauthor: P. W. Wong
rawtitle: Quantization noise, fixed-point multiplicative roundoff noise, and dithering
entry:
@Article{Wong:1990:QNF,
  author =       "P. W. Wong",
  title =        "Quantization noise, fixed-point multiplicative
                 roundoff noise, and dithering",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "38",
  number =       "2",
  pages =        "286--300",
  month =        feb,
  year =         "1990",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "The author considers the characteristics of the error
                 resulting when a continuous amplitude signal $x_n$ is
                 quantized and then multiplied by a constant multiplier
                 a under fixed-point roundoff arithmetic. It is shown
                 that \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Yager:1990:SNM
author: T. Yager
title: Sony NeWS and MIPS Magnum: a double shot of RISC
journal: j-BYTE
volume: 15
number: 13
pages: 172--175
month: dec
monthnumber: 12
year: 1990
CODEN: BYTEDJ
ISSN: 0360-5280 (print), 1082-7838 (electronic) OR 03605280 (print), 10827838 (electronic)
ISSNL: 0360-5280 OR 03605280
bibdate: Thu Sep 12 18:39:30 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.12 18:39:30 MDT
fjournal: BYTE Magazine
acknowledgement: ack-nhfb
thesaurus: Computer evaluation; Microcomputers; Workstations
rawauthor: T. Yager
rawtitle: {Sony NeWS} and {MIPS Magnum}: a double shot of {RISC}
keywords:
20 MHz; 25 MHz; Fast color graphics; Floating-point acceleration; High-density 3/sup 1///sub 2/-inch floppy disk; MIPS Magnum 3000; MIPS R3000 RISC CPU chip set; Quarter-inch cartridge tape drives; RISC/OS; Sony NeWS 3710; System V release 4; Thick-wire Ethernet port; Unix workstations; X Window System

entry:
@Article{Yager:1990:SNM,
  author =       "T. Yager",
  title =        "{Sony NeWS} and {MIPS Magnum}: a double shot of
                 {RISC}",
  journal =      j-BYTE,
  volume =       "15",
  number =       "13",
  pages =        "172--175",
  month =        dec,
  year =         "1990",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 18:39:30 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5430 (Microcomputers)",
  fjournal =     "BYTE Magazine",
  keywords =     "20 MHz; 25 MHz; Fast color graphics; Floating-point
                 acceleration; High-density 3/sup 1///sub 2/-inch floppy
                 disk; MIPS Magnum 3000; MIPS R3000 RISC CPU chip set;
                 Quarter-inch cartridge tape drives; RISC/OS; Sony NeWS
                 3710; System V release 4; Thick-wire Ethernet port;
                 Unix workstations; X Window System",
  numericalindex = "Frequency 2.0E+07 Hz; Frequency 2.5E+07 Hz",
  thesaurus =    "Computer evaluation; Microcomputers; Workstations",
}


bibtype: mastersthesis
filename: fparith.bib
label: Yang:1990:PRN
author: George Chia-Jin Yang
type: Thesis (M.S.)
school: University of Tennessee, Knoxville
address: Knoxville, TN, USA
pages: vii + 67
year: 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Digital filters (Mathematics).; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: George Chia-Jin Yang
title:
A parametric roundoff noise analysis of second-order state-space digital filters with floating-point arithmetic

rawtitle:
A parametric roundoff noise analysis of second-order state-space digital filters with floating-point arithmetic

entry:
@MastersThesis{Yang:1990:PRN,
  author =       "George Chia-Jin Yang",
  title =        "A parametric roundoff noise analysis of second-order
                 state-space digital filters with floating-point
                 arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vii + 67",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital filters (Mathematics).; Floating-point
                 arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Yeh:1990:RTI
author: H.-G. Yeh
title: Real-Time Implementation of a Narrow-Band Kalman Filter with a Floating-Point Processor DSP32
journal: j-IEEE-TRANS-IND-ELECTRON
volume: 37
number: 1
pages: 13--18
month: feb
monthnumber: 2
year: 1990
CODEN: ITIED6
DOI: https://doi.org/10.1109/41.45838
ISSN: 0278-0046 (print), 1557-9948 (electronic) OR 02780046 (print), 15579948 (electronic)
ISSNL: 0278-0046 OR 02780046
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Industrial Electronics
acknowledgement: ack-nhfb
rawauthor: H.-G. Yeh
rawtitle: Real-Time Implementation of a Narrow-Band {Kalman} Filter with a Floating-Point Processor {DSP32}
entry:
@Article{Yeh:1990:RTI,
  author =       "H.-G. Yeh",
  title =        "Real-Time Implementation of a Narrow-Band {Kalman}
                 Filter with a Floating-Point Processor {DSP32}",
  journal =      j-IEEE-TRANS-IND-ELECTRON,
  volume =       "37",
  number =       "1",
  pages =        "13--18",
  month =        feb,
  year =         "1990",
  CODEN =        "ITIED6",
  DOI =          "https://doi.org/10.1109/41.45838",
  ISSN =         "0278-0046 (print), 1557-9948 (electronic)",
  ISSN-L =       "0278-0046",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Industrial Electronics",
  summary =      "The author presents experimental results from two
                 studies. First, a real-time narrowband Kalman filter is
                 implemented with a floating-point digital processor
                 DSP32. The real-time capability of this narrowband
                 filter is investigated by varying parameters \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Yoon:1990:MTP
author: Hyunsoo Yoon and Kyungsook Y. Lee and Amos Bahiri
title: On the modulo $M$ translators for the prime memory system
journal: j-J-PAR-DIST-COMP
volume: 8
number: 1
pages: 72--76
month: jan
monthnumber: 1
year: 1990
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: Ohio State Univ
affiliationaddress: Columbus, OH, USA
corpsource: Department of Comput. and Inf. Sci., Ohio State University, Columbus, OH, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Hyunsoo Yoon and Kyungsook Y. Lee and Amos Bahiri
rawtitle: On the modulo {$M$} translators for the prime memory system
keywords:
array processor; binary number system; Burroughs Scientific Processor; Burroughs Scientific Processor (bsp); casting out nine rule; Computer Operating Systems; Computer Systems Programming--Utility Programs; Computer Systems, Digital--Parallel Processing; conflict-free access; decimal floating-point arithmetic; decimal number system; digital arithmetic; Modulo M Computation; modulo M translators; parallel algorithms; prime memory system; Program Translators; SIMD Architecture; SIMD shared memory parallel processor

entry:
@Article{Yoon:1990:MTP,
  author =       "Hyunsoo Yoon and Kyungsook Y. Lee and Amos Bahiri",
  title =        "On the modulo {$M$} translators for the prime memory
                 system",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "8",
  number =       "1",
  pages =        "72--76",
  month =        jan,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Ohio State Univ",
  affiliationaddress = "Columbus, OH, USA",
  classification = "722; 723; C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Comput. and Inf. Sci., Ohio State
                 University, Columbus, OH, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "array processor; binary number system; Burroughs
                 Scientific Processor; Burroughs Scientific Processor
                 (bsp); casting out nine rule; Computer Operating
                 Systems; Computer Systems Programming--Utility
                 Programs; Computer Systems, Digital--Parallel
                 Processing; conflict-free access; decimal
                 floating-point arithmetic; decimal number system;
                 digital arithmetic; Modulo M Computation; modulo M
                 translators; parallel algorithms; prime memory system;
                 Program Translators; SIMD Architecture; SIMD shared
                 memory parallel processor",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Zarowski:1990:AMH
author: C. J. Zarowski and H. C. Card
title: On addition and multiplication with Hensel codes
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 12
pages: 1417--1423
month: dec
monthnumber: 12
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.61062
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:05 MDT 2011
bibtimestamp: 2011.07.07 14:20:05 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61062
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. J. Zarowski and H. C. Card
rawtitle: On addition and multiplication with {Hensel} codes
entry:
@Article{Zarowski:1990:AMH,
  author =       "C. J. Zarowski and H. C. Card",
  title =        "On addition and multiplication with {Hensel} codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "12",
  pages =        "1417--1423",
  month =        dec,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.61062",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61062",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Zelniker:1990:PBD
author: G. S. Zelniker and F. J. Taylor
title: Prime Blocklength Discrete Fourier Transforms Utilising the Polynomial Residue Number System
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 314
year: 1990
DOI: https://doi.org/10.1109/MWSCAS.1990.140897
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: G. S. Zelniker and F. J. Taylor
rawtitle: Prime Blocklength Discrete {Fourier} Transforms Utilising the Polynomial Residue Number System
booktitle:
Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 5--7 Nov 1990

entry:
@InProceedings{Zelniker:1990:PBD,
  author =       "G. S. Zelniker and F. J. Taylor",
  booktitle =    "Conference Record Twenty-Fourth Asilomar Conference on
                 Signals, Systems and Computers, 5--7 Nov 1990",
  title =        "Prime Blocklength Discrete {Fourier} Transforms
                 Utilising the Polynomial Residue Number System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "314",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1990.140897",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}


bibtype: incollection
filename: fparith.bib
label: Aberth:1991:CHO
author: Oliver Aberth
crossref: Meyer:1991:CAP
pages: 1--4
year: 1991
DOI: https://doi.org/10.1007/978-1-4613-9092-3_1
bibdate: Fri Sep 22 18:54:58 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.22 18:54:58 ???
acknowledgement: ack-nhfb
rawauthor: Oliver Aberth
title:
The Conversion of a High Order Programming Language from Floating-Point Arithmetic to Range Arithmetic

rawtitle:
The Conversion of a High Order Programming Language from Floating-Point Arithmetic to Range Arithmetic

entry:
@InCollection{Aberth:1991:CHO,
  author =       "Oliver Aberth",
  title =        "The Conversion of a High Order Programming Language
                 from Floating-Point Arithmetic to Range Arithmetic",
  crossref =     "Meyer:1991:CAP",
  pages =        "1--4",
  year =         "1991",
  DOI =          "https://doi.org/10.1007/978-1-4613-9092-3_1",
  bibdate =      "Fri Sep 22 18:54:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Adali:1991:FPR
author: T. Adali and S. H. Ardalan
title: Fixed-point roundoff error analysis of the RLS algorithm with time-varying channels
volume: 3
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1865--1868
year: 1991
bibdate: Sat Jul 16 11:25:07 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: T. Adali and S. H. Ardalan
rawtitle: Fixed-point roundoff error analysis of the {RLS} algorithm with time-varying channels
booktitle:
Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference on. 14--17 April 1991

rawbooktitle:
Acoustics, Speech, and Signal Processing, 1991. {ICASSP-91., 1991} International Conference on. 14--17 April 1991

entry:
@InProceedings{Adali:1991:FPR,
  author =       "T. Adali and S. H. Ardalan",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1991.
                 {ICASSP-91., 1991} International Conference on. 14--17
                 April 1991",
  title =        "Fixed-point roundoff error analysis of the {RLS}
                 algorithm with time-varying channels",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1865--1868",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors derive the steady-state mean square
                 prediction error expression for the fixed-point RLS
                 (recursive least squares) algorithm for the case of
                 time-varying channel estimation, which is modeled as a
                 first-order Markov tapped delay line. It \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Alia:1991:VMM
author: G. Alia and E. Martinelli
title: A VLSI modulo $m$ multiplier
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 7
pages: 873--878
month: jul
monthnumber: 7
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.83626
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 12:52:22 MDT 2011
bibtimestamp: 2011.07.07 12:52:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83626
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: G. Alia and E. Martinelli
rawtitle: A {VLSI} modulo $m$ multiplier
entry:
@Article{Alia:1991:VMM,
  author =       "G. Alia and E. Martinelli",
  title =        "A {VLSI} modulo $m$ multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "7",
  pages =        "873--878",
  month =        jul,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83626",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83626",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Alverson:1991:IDU
author: Robert Alverson
title: Integer Division Using Reciprocals
crossref: Kornerup:1991:PIS
pages: 186--190
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Alverson.pdf
keywords: ARITH-10; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Robert Alverson
rawtitle: Integer Division Using Reciprocals
remark:
Demonstrates a correctly-rounded algorithm for integer division that requires six floating-point multiplications and a table lookup. For comparison, cite Markstein:2000:IEF shows an algorithm that needs seven multiply-adds and a reciprocal approximation.

entry:
@InProceedings{Alverson:1991:IDU,
  author =       "Robert Alverson",
  title =        "Integer Division Using Reciprocals",
  crossref =     "Kornerup:1991:PIS",
  pages =        "186--190",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Alverson.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; correct rounding; floating-point
                 arithmetic",
  remark =       "Demonstrates a correctly-rounded algorithm for integer
                 division that requires six floating-point
                 multiplications and a table lookup. For comparison,
                 \cite{Markstein:2000:IEF} shows an algorithm that needs
                 seven multiply-adds and a reciprocal approximation.",
}


bibtype: article
filename: fparith.bib
label: Anido:1991:IDI
author: M. Lois Anido
title: Improving the division instruction of application-specific RISCs
journal: j-MICROPROC-MICROPROG
volume: 32
number: 1-5
pages: 13--21
month: aug
monthnumber: 8
year: 1991
CODEN: MMICDT
ISSN: 0165-6074 (print), 1878-7061 (electronic) OR 01656074 (print), 18787061 (electronic)
ISSNL: 0165-6074 OR 01656074
bibdate: Tue Dec 12 09:26:54 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:26:54 MST
fjournal: Microprocessing and Microprogramming
acknowledgement: ack-nhfb
affiliation: Univ. Federal do Rio de Janeiro, Brazil
journalURL: https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues
thesaurus: Application specific integrated circuits; Digital arithmetic; Reduced instruction set computing
rawauthor: M. Lois Anido
rawtitle: Improving the division instruction of application-specific {RISCs}
note:
17th EUROMICRO Symposium on Microprocessing and Microprogramming. Hardware and Software Design Automation.

abstract:
Presents the development and application of a signed radix-4 division algorithm to a RISC architecture, where the internal ALU Manchester carry adder is used to maintain the partial remainder in irredundant form. There are division algorithms which are faster than the one described in this paper, however they usually make use of a redundant representation of the partial remainder and require carry-save adders which are not normally used in the integer execution unit of RISCs. The method presented in this contribution employs 3x divisor multiples and uses a reduced next divisor multiple estimate table which is implemented by a small and fast logic. Alternative radix-4 schemes with quotient digits (-2,-1,0,1,2) require large and slow PLAs for quotient digit generation. Additionally, there is no need for positive and negative quotient registers because quotient bits are generated on-the-fly by a small-sized logic, concurrently with partial remainder formation. This method also deals directly with signed two's complement numbers, eliminating the need for additional instructions for sign conversion. The application of this radix-4 division algorithm provides a two-bits-at-a-time division instruction, instead of the traditional single bit approach used in some RISCs. The speedup achieved can be very important in many numerically intensive applications, in which the use of floating-point units is not essential.

keywords:
3X divisor multiples; Application-specific RISCs; Binary division; Division instruction; Internal ALU Manchester carry adder; Irredundant form; Logic; Numerically intensive applications; Partial remainder; Quotient bits; Quotient digits; Reduced next divisor multiple estimate table; RISC architecture; Signed radix-4 division algorithm; Signed two's complement numbers; Speedup

rawabstract:
Presents the development and application of a signed radix-4 division algorithm to a RISC architecture, where the internal ALU Manchester carry adder is used to maintain the partial remainder in irredundant form. There are division algorithms which are faster than the one described in this paper, however they usually make use of a redundant representation of the partial remainder and require carry-save adders which are not normally used in the integer execution unit of RISCs. The method presented in this contribution employs 3x divisor multiples and uses a reduced next divisor multiple estimate table which is implemented by a small and fast logic. Alternative radix-4 schemes with quotient digits (-2,-1,0,1,2) require large and slow PLAs for quotient digit generation. Additionally, there is no need for positive and negative quotient registers because quotient bits are generated on-the-fly by a small-sized logic, concurrently with partial remainder formation. This method also deals directly with signed two's complement numbers, eliminating the need for additional instructions for sign conversion. The application of this radix-4 division algorithm provides a two-bits-at-a-time division instruction, instead of the traditional single bit approach used in some RISCs. The speedup achieved can be very important in many numerically intensive applications, in which the use of floating-point units is not essential.

rawnote:
17th EUROMICRO Symposium on Microprocessing and Microprogramming. Hardware and Software Design Automation.

entry:
@Article{Anido:1991:IDI,
  author =       "M. Lois Anido",
  title =        "Improving the division instruction of
                 application-specific {RISCs}",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "32",
  number =       "1-5",
  pages =        "13--21",
  month =        aug,
  year =         "1991",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "17th EUROMICRO Symposium on Microprocessing and
                 Microprogramming. Hardware and Software Design
                 Automation.",
  abstract =     "Presents the development and application of a signed
                 radix-4 division algorithm to a RISC architecture,
                 where the internal ALU Manchester carry adder is used
                 to maintain the partial remainder in irredundant form.
                 There are division algorithms which are faster than the
                 one described in this paper, however they usually make
                 use of a redundant representation of the partial
                 remainder and require carry-save adders which are not
                 normally used in the integer execution unit of RISCs.
                 The method presented in this contribution employs 3x
                 divisor multiples and uses a reduced next divisor
                 multiple estimate table which is implemented by a small
                 and fast logic. Alternative radix-4 schemes with
                 quotient digits (-2,-1,0,1,2) require large and slow
                 PLAs for quotient digit generation. Additionally, there
                 is no need for positive and negative quotient registers
                 because quotient bits are generated on-the-fly by a
                 small-sized logic, concurrently with partial remainder
                 formation. This method also deals directly with signed
                 two's complement numbers, eliminating the need for
                 additional instructions for sign conversion. The
                 application of this radix-4 division algorithm provides
                 a two-bits-at-a-time division instruction, instead of
                 the traditional single bit approach used in some RISCs.
                 The speedup achieved can be very important in many
                 numerically intensive applications, in which the use of
                 floating-point units is not essential.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Federal do Rio de Janeiro, Brazil",
  classification = "C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  confdate =     "2-5 Sept. 1991",
  conflocation = "Vienna, Austria",
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
  keywords =     "3X divisor multiples; Application-specific RISCs;
                 Binary division; Division instruction; Internal ALU
                 Manchester carry adder; Irredundant form; Logic;
                 Numerically intensive applications; Partial remainder;
                 Quotient bits; Quotient digits; Reduced next divisor
                 multiple estimate table; RISC architecture; Signed
                 radix-4 division algorithm; Signed two's complement
                 numbers; Speedup",
  pubcountry =   "Netherlands",
  thesaurus =    "Application specific integrated circuits; Digital
                 arithmetic; Reduced instruction set computing",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1991:FDC
author: Anonymous
title: 60M-flops, floating-point DSP chip
journal: j-EDN
volume: 36
number: 13
pages: 80--??
month: jun
monthnumber: 6
year: 1991
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: EDN
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: {60M-flops}, floating-point {DSP} chip
entry:
@Article{Anonymous:1991:FDC,
  author =       "Anonymous",
  title =        "{60M-flops}, floating-point {DSP} chip",
  journal =      j-EDN,
  volume =       "36",
  number =       "13",
  pages =        "80--??",
  month =        jun,
  year =         "1991",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "EDN",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1991:SIS
author: Anonymous
title: SCAN-1991: International Symposium on Computer Arithmetic and Scientific Computation
journal: j-J-COMPUT-APPL-MATH
volume: 34
number: 2
pages: N13--N14
day: 4
month: apr
monthnumber: 4
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:48 MST 2017
bibtimestamp: 2017.02.25 12:20:48 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704279190071Q
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Anonymous
rawtitle: {SCAN-1991: International Symposium on Computer Arithmetic and Scientific Computation}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib

entry:
@Article{Anonymous:1991:SIS,
  author =       "Anonymous",
  title =        "{SCAN-1991: International Symposium on Computer
                 Arithmetic and Scientific Computation}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "2",
  pages =        "N13--N14",
  day =          "4",
  month =        apr,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704279190071Q",
  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: Arambepola:1991:CVA
author: B. Arambepola
booktitle: IEEE International Symposium on Circuits and Systems, 11--14 June 1991
title: Common VLSI architecture for a practically useful residue number system
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2951--2954
year: 1991
DOI: https://doi.org/10.1109/ISCAS.1991.176164
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: B. Arambepola
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, 11--14 June 1991
rawtitle: Common {VLSI} architecture for a practically useful residue number system
entry:
@InProceedings{Arambepola:1991:CVA,
  author =       "B. Arambepola",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "Common {VLSI} architecture for a practically useful
                 residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2951--2954",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176164",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "An architecture is presented for carrying out modulo
                 arithmetic in a practically useful residue number
                 system. An important feature of this is that it allows
                 a single hardware design to be used for all moduli. An
                 application of this architecture is \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Arvo:1991:GGI
author: James Arvo
title: Graphics gems II
volume: 2
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xxxii + 643
year: 1991
ISBN: 0-12-064480-0 OR 0120644800
ISBN13: 978-0-12-064480-3 OR 9780120644803
LCCN: T385 .G6972 1991
bibdate: Mon Aug 24 17:12:23 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 1998.08.24 17:12:23 ???
series: Graphics Gems
URL: http://www.sciencedirect.com/science/book/9780080507545
ZMnumber: 0774.68010
acknowledgement: ack-nhfb
rawauthor: James Arvo
rawtitle: Graphics gems {II}
abstract:
booktitle Graphics Gems II is a collection of articles shared by a diverse group of people that reflect ideas and approaches in graphics programming which can benefit other computer graphics programmers. This volume presents techniques for doing well-known graphics operations faster or easier. The book contains chapters devoted to topics on two-dimensional and three-dimensional geometry and algorithms, image processing, frame buffer techniques, and ray tracing techniques. The radiosity approach, matrix techniques, and numerical and programming techniques are likewise discussed.

TOC:
Foreword / Andrew Glassner The Area of a Simple Polygon / Jon Rokne Intersection of Line Segments / Mukesh Prasad Distance from a Point to a Line / Jack C. Morrison An Easy Bounding Circle / Jon Rokne The Smallest Circle Containing the Intersection of Two Circles / Jon Rokne Appolonius's 10th Problem / Jon Rokne A Peano Curve Generation Algorithm / Ken Musgrave Space-Filling Curves and a Measure of Coherence / Douglas Voorhies Scanline Coherent Shape Algebra / Jonathan E. Steinhart Image Smoothing and Sharpening by Discrete Convolution / Dale A. Schumacher A Comparison of Digital Halftoning Techniques / Dale A. Schumacher Color Dithering / Spencer W. Thomas and Rod G. Bogart Fast Anamorphic Image Scaling / Dale A. Schumacher Real Pixels / Greg Ward A Fast 90-Degree Bitmap Rotator / Sue-Ken Yap Rotation of Run-Length Encoded Image Data / Jeff Holt Adaptive Run-Length Encoding / Andrew S. Glassner Image File Compression Made Easy / Alan W. Paeth An Optimal Filter for Image Reconstruction / Nelson Max Noise Thresholding in Edge Images / John Schlag Computing the Area, the Circumference, and the Genus of a Binary Digital Image / Hanspeter Bieri and Andreas Kohler Efficient Inverse Color Map Computation / Spencer W. Thomas Efficient Statistical Computations for Optimal Color Quantization / Xiaolin Wu A Random Color Map Animation Algorithm / Ken Musgrave A Fast Approach to PHIGS PLUS Pseudo Color Mapping / James Hall and Terence Lindgren Mapping RGB Triples onto 16 Distinct Values / Alan W. Paeth Television Color Encoding and ``Hot'' Broadcast Colors / David Martindale and Alan W. Paeth An Inexpensive Method of Setting the Monitor White Point / Gary W. Meyer Some Tips for Making Color Hardcopy / Ken Musgrave Area of Planar Polygons and Volume of Polyhedra / Ronald N. Goldman Getting Around on a Sphere / Clifford A. Shaffer Exact Dihedral Metrics for Common Polyhedra / Alan W. Paeth A Simple Viewing Geometry / Andrew S. Glassner View Correlation / Rod G. Bogart Maintaining Winged-Edge Models / Andrew S. Glassner Quadtree / Octree-to-Boundary Conversion / Claudio Montani and Roberto Scopigno Three-Dimensional Homogeneous Clipping of Triangle Strips / Patrick-Gilles Maillot InterPhong Shading / Nadia Magnenat Thalmann, Daniel Thalmann and Hong Tong Minh Fast Ray-Convex Polyhedron Intersection / Eric Haines Intersecting a Ray with an Elliptical Torus / Joseph M. Cychosz Ray-Triangle Intersection Using Binary Recursive Subdivision / Douglas Voorhies and David Kirk Improved Ray Tagging for Voxel-Based Ray Tracing / David Kirk and James Arvo Efficiency Improvements for Hierarchy Traversal in Ray Tracing / Eric Haines A Recursive Shadow Voxel Cache for Ray Tracing / Andrew Pearce Avoiding Incorrect Shadow Intersections for Ray Tracing / Andrew Pearce A Body Color Model: Absorption of Light through Translucent Media / Mark E. Lee and Samuel P. Uselton More Shadow Attenuation for Ray Tracing Transparent or Translucent Objects / Mark E. Lee and Samuel P. Uselton Implementing Progressive Radiosity with User-Provided Polygon Display Routines / Shenchang Eric Chen A Cubic Tetrahedral Adaptation of the Hemi-Cube Algorithm / Jeffrey C. Beran-Koehn and Mark J. Pavicic Fast Vertex Radiosity Update / Filippo Tampieri Radiosity via Ray Tracing / Peter Shirley Detection of Shadow Boundaries for Adaptive Meshing in Radiosity / Francois Sillion Decomposing a Matrix into Simple Transformations / Spencer W. Thomas Recovering the Data from the Transformation Matrix / Ronald N. Goldman Transformations as Exponentials / Ronald N. Goldman More Matrices and Transformations: Shear and Pseudo-Perspective / Ronald N. Goldman Fast Matrix Inversion / Kevin Wu Quaternions and $4 times 4$ Matrices / Ken Shoemake Random Rotation Matrices / James Arvo Classifying Small Sparse Matrices / James Arvo Bit Picking / Ken Shoemake Faster Fourier Transform / Ken Shoemake Of Integers, Fields, and Bit Counting / Alan W. Paeth and David Schilling Using Geometric Constructions to Interpolate Orientation with Quaternions / John Schlag A Half-Angle Identity for Digital Computation: The Joys of the Halved Tangent / Alan W. Paeth An Integer Square Root Algorithm / Christopher J. Musial Fast Approximation to the Arctangent / Ron Capelli Fast Sign of Cross Product Calculation / Jack Ritter Interval Sampling / Ken Shoemake A Recursive Implementation of the Perlin Noise Function / Greg Ward Least-Squares Approximations to Bezier Curves and Surfaces / Doug Moore and Joe Warren Beyond Bezier Curves / Ken Shoemake A Simple Formulation for Curve Interpolation with Variable Control Point Approximation / John Schlag Symmetric Evaluation of Polynomials / Terence Lindgren Menelaus's Theorem / Hans-Peter Seidel Geometrically Continuous Cubic Bezier Curves / Hans-Peter Siedel A Good Straight-Line Approximation of a Circular Arc / Christopher J. Musial Great Circle Plotting / Alan W. Paeth Fast Anti-Aliased Circle Generation / Xiaolin Wu Graphics Gems C Header File 2D and 3D Vector C Library Corrected and Indexed Useful C Macros for Vector Operations / Steve Hollasch

rawabstract:
\booktitle{Graphics Gems II} is a collection of articles shared by a diverse group of people that reflect ideas and approaches in graphics programming which can benefit other computer graphics programmers. This volume presents techniques for doing well-known graphics operations faster or easier. The book contains chapters devoted to topics on two-dimensional and three-dimensional geometry and algorithms, image processing, frame buffer techniques, and ray tracing techniques. The radiosity approach, matrix techniques, and numerical and programming techniques are likewise discussed.

rawTOC:
Foreword / Andrew Glassner \\ The Area of a Simple Polygon / Jon Rokne \\ Intersection of Line Segments / Mukesh Prasad \\ Distance from a Point to a Line / Jack C. Morrison \\ An Easy Bounding Circle / Jon Rokne \\ The Smallest Circle Containing the Intersection of Two Circles / Jon Rokne \\ Appolonius's 10th Problem / Jon Rokne \\ A Peano Curve Generation Algorithm / Ken Musgrave \\ Space-Filling Curves and a Measure of Coherence / Douglas Voorhies \\ Scanline Coherent Shape Algebra / Jonathan E. Steinhart \\ Image Smoothing and Sharpening by Discrete Convolution / Dale A. Schumacher \\ A Comparison of Digital Halftoning Techniques / Dale A. Schumacher \\ Color Dithering / Spencer W. Thomas and Rod G. Bogart \\ Fast Anamorphic Image Scaling / Dale A. Schumacher \\ Real Pixels / Greg Ward \\ A Fast 90-Degree Bitmap Rotator / Sue-Ken Yap \\ Rotation of Run-Length Encoded Image Data / Jeff Holt \\ Adaptive Run-Length Encoding / Andrew S. Glassner \\ Image File Compression Made Easy / Alan W. Paeth \\ An Optimal Filter for Image Reconstruction / Nelson Max \\ Noise Thresholding in Edge Images / John Schlag \\ Computing the Area, the Circumference, and the Genus of a Binary Digital Image / Hanspeter Bieri and Andreas Kohler \\ Efficient Inverse Color Map Computation / Spencer W. Thomas \\ Efficient Statistical Computations for Optimal Color Quantization / Xiaolin Wu \\ A Random Color Map Animation Algorithm / Ken Musgrave \\ A Fast Approach to PHIGS PLUS Pseudo Color Mapping / James Hall and Terence Lindgren \\ Mapping RGB Triples onto 16 Distinct Values / Alan W. Paeth \\ Television Color Encoding and ``Hot'' Broadcast Colors / David Martindale and Alan W. Paeth \\ An Inexpensive Method of Setting the Monitor White Point / Gary W. Meyer \\ Some Tips for Making Color Hardcopy / Ken Musgrave \\ Area of Planar Polygons and Volume of Polyhedra / Ronald N. Goldman \\ Getting Around on a Sphere / Clifford A. Shaffer \\ Exact Dihedral Metrics for Common Polyhedra / Alan W. Paeth \\ A Simple Viewing Geometry / Andrew S. Glassner \\ View Correlation / Rod G. Bogart \\ Maintaining Winged-Edge Models / Andrew S. Glassner \\ Quadtree\slash Octree-to-Boundary Conversion / Claudio Montani and Roberto Scopigno \\ Three-Dimensional Homogeneous Clipping of Triangle Strips / Patrick-Gilles Maillot \\ InterPhong Shading / Nadia Magnenat Thalmann, Daniel Thalmann and Hong Tong Minh \\ Fast Ray-Convex Polyhedron Intersection / Eric Haines \\ Intersecting a Ray with an Elliptical Torus / Joseph M. Cychosz \\ Ray-Triangle Intersection Using Binary Recursive Subdivision / Douglas Voorhies and David Kirk \\ Improved Ray Tagging for Voxel-Based Ray Tracing / David Kirk and James Arvo \\ Efficiency Improvements for Hierarchy Traversal in Ray Tracing / Eric Haines \\ A Recursive Shadow Voxel Cache for Ray Tracing / Andrew Pearce \\ Avoiding Incorrect Shadow Intersections for Ray Tracing / Andrew Pearce \\ A Body Color Model: Absorption of Light through Translucent Media / Mark E. Lee and Samuel P. Uselton \\ More Shadow Attenuation for Ray Tracing Transparent or Translucent Objects / Mark E. Lee and Samuel P. Uselton \\ Implementing Progressive Radiosity with User-Provided Polygon Display Routines / Shenchang Eric Chen \\ A Cubic Tetrahedral Adaptation of the Hemi-Cube Algorithm / Jeffrey C. Beran-Koehn and Mark J. Pavicic \\ Fast Vertex Radiosity Update / Filippo Tampieri \\ Radiosity via Ray Tracing / Peter Shirley \\ Detection of Shadow Boundaries for Adaptive Meshing in Radiosity / Fran{\c{c}}ois Sillion \\ Decomposing a Matrix into Simple Transformations / Spencer W. Thomas \\ Recovering the Data from the Transformation Matrix / Ronald N. Goldman \\ Transformations as Exponentials / Ronald N. Goldman \\ More Matrices and Transformations: Shear and Pseudo-Perspective / Ronald N. Goldman \\ Fast Matrix Inversion / Kevin Wu \\ Quaternions and $4 \times 4$ Matrices / Ken Shoemake \\ Random Rotation Matrices / James Arvo \\ Classifying Small Sparse Matrices / James Arvo \\ Bit Picking / Ken Shoemake \\ Faster Fourier Transform / Ken Shoemake \\ Of Integers, Fields, and Bit Counting / Alan W. Paeth and David Schilling \\ Using Geometric Constructions to Interpolate Orientation with Quaternions / John Schlag \\ A Half-Angle Identity for Digital Computation: The Joys of the Halved Tangent / Alan W. Paeth \\ An Integer Square Root Algorithm / Christopher J. Musial \\ Fast Approximation to the Arctangent / Ron Capelli \\ Fast Sign of Cross Product Calculation / Jack Ritter \\ Interval Sampling / Ken Shoemake \\ A Recursive Implementation of the Perlin Noise Function / Greg Ward \\ Least-Squares Approximations to B{\'e}zier Curves and Surfaces / Doug Moore and Joe Warren \\ Beyond B{\'e}zier Curves / Ken Shoemake \\ A Simple Formulation for Curve Interpolation with Variable Control Point Approximation / John Schlag \\ Symmetric Evaluation of Polynomials / Terence Lindgren \\ Menelaus's Theorem / Hans-Peter Seidel \\ Geometrically Continuous Cubic B{\'e}zier Curves / Hans-Peter Siedel \\ A Good Straight-Line Approximation of a Circular Arc / Christopher J. Musial \\ Great Circle Plotting / Alan W. Paeth \\ Fast Anti-Aliased Circle Generation / Xiaolin Wu \\ Graphics Gems C Header File \\ 2D and 3D Vector C Library \\ Corrected and Indexed \\ Useful C Macros for Vector Operations / Steve Hollasch

entry:
@Book{Arvo:1991:GGI,
  author =       "James Arvo",
  title =        "Graphics gems {II}",
  volume =       "2",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xxxii + 643",
  year =         "1991",
  ISBN =         "0-12-064480-0",
  ISBN-13 =      "978-0-12-064480-3",
  LCCN =         "T385 .G6972 1991",
  bibdate =      "Mon Aug 24 17:12:23 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "Graphics Gems",
  URL =          "http://www.sciencedirect.com/science/book/9780080507545",
  ZMnumber =     "0774.68010",
  abstract =     "\booktitle{Graphics Gems II} is a collection of
                 articles shared by a diverse group of people that
                 reflect ideas and approaches in graphics programming
                 which can benefit other computer graphics programmers.
                 This volume presents techniques for doing well-known
                 graphics operations faster or easier. The book contains
                 chapters devoted to topics on two-dimensional and
                 three-dimensional geometry and algorithms, image
                 processing, frame buffer techniques, and ray tracing
                 techniques. The radiosity approach, matrix techniques,
                 and numerical and programming techniques are likewise
                 discussed.",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  tableofcontents = "Foreword / Andrew Glassner \\
                 The Area of a Simple Polygon / Jon Rokne \\
                 Intersection of Line Segments / Mukesh Prasad \\
                 Distance from a Point to a Line / Jack C. Morrison \\
                 An Easy Bounding Circle / Jon Rokne \\
                 The Smallest Circle Containing the Intersection of Two
                 Circles / Jon Rokne \\
                 Appolonius's 10th Problem / Jon Rokne \\
                 A Peano Curve Generation Algorithm / Ken Musgrave \\
                 Space-Filling Curves and a Measure of Coherence /
                 Douglas Voorhies \\
                 Scanline Coherent Shape Algebra / Jonathan E. Steinhart
                 \\
                 Image Smoothing and Sharpening by Discrete Convolution
                 / Dale A. Schumacher \\
                 A Comparison of Digital Halftoning Techniques / Dale A.
                 Schumacher \\
                 Color Dithering / Spencer W. Thomas and Rod G. Bogart
                 \\
                 Fast Anamorphic Image Scaling / Dale A. Schumacher \\
                 Real Pixels / Greg Ward \\
                 A Fast 90-Degree Bitmap Rotator / Sue-Ken Yap \\
                 Rotation of Run-Length Encoded Image Data / Jeff Holt
                 \\
                 Adaptive Run-Length Encoding / Andrew S. Glassner \\
                 Image File Compression Made Easy / Alan W. Paeth \\
                 An Optimal Filter for Image Reconstruction / Nelson Max
                 \\
                 Noise Thresholding in Edge Images / John Schlag \\
                 Computing the Area, the Circumference, and the Genus of
                 a Binary Digital Image / Hanspeter Bieri and Andreas
                 Kohler \\
                 Efficient Inverse Color Map Computation / Spencer W.
                 Thomas \\
                 Efficient Statistical Computations for Optimal Color
                 Quantization / Xiaolin Wu \\
                 A Random Color Map Animation Algorithm / Ken Musgrave
                 \\
                 A Fast Approach to PHIGS PLUS Pseudo Color Mapping /
                 James Hall and Terence Lindgren \\
                 Mapping RGB Triples onto 16 Distinct Values / Alan W.
                 Paeth \\
                 Television Color Encoding and ``Hot'' Broadcast Colors
                 / David Martindale and Alan W. Paeth \\
                 An Inexpensive Method of Setting the Monitor White
                 Point / Gary W. Meyer \\
                 Some Tips for Making Color Hardcopy / Ken Musgrave \\
                 Area of Planar Polygons and Volume of Polyhedra /
                 Ronald N. Goldman \\
                 Getting Around on a Sphere / Clifford A. Shaffer \\
                 Exact Dihedral Metrics for Common Polyhedra / Alan W.
                 Paeth \\
                 A Simple Viewing Geometry / Andrew S. Glassner \\
                 View Correlation / Rod G. Bogart \\
                 Maintaining Winged-Edge Models / Andrew S. Glassner \\
                 Quadtree\slash Octree-to-Boundary Conversion / Claudio
                 Montani and Roberto Scopigno \\
                 Three-Dimensional Homogeneous Clipping of Triangle
                 Strips / Patrick-Gilles Maillot \\
                 InterPhong Shading / Nadia Magnenat Thalmann, Daniel
                 Thalmann and Hong Tong Minh \\
                 Fast Ray-Convex Polyhedron Intersection / Eric Haines
                 \\
                 Intersecting a Ray with an Elliptical Torus / Joseph M.
                 Cychosz \\
                 Ray-Triangle Intersection Using Binary Recursive
                 Subdivision / Douglas Voorhies and David Kirk \\
                 Improved Ray Tagging for Voxel-Based Ray Tracing /
                 David Kirk and James Arvo \\
                 Efficiency Improvements for Hierarchy Traversal in Ray
                 Tracing / Eric Haines \\
                 A Recursive Shadow Voxel Cache for Ray Tracing / Andrew
                 Pearce \\
                 Avoiding Incorrect Shadow Intersections for Ray Tracing
                 / Andrew Pearce \\
                 A Body Color Model: Absorption of Light through
                 Translucent Media / Mark E. Lee and Samuel P. Uselton
                 \\
                 More Shadow Attenuation for Ray Tracing Transparent or
                 Translucent Objects / Mark E. Lee and Samuel P. Uselton
                 \\
                 Implementing Progressive Radiosity with User-Provided
                 Polygon Display Routines / Shenchang Eric Chen \\
                 A Cubic Tetrahedral Adaptation of the Hemi-Cube
                 Algorithm / Jeffrey C. Beran-Koehn and Mark J. Pavicic
                 \\
                 Fast Vertex Radiosity Update / Filippo Tampieri \\
                 Radiosity via Ray Tracing / Peter Shirley \\
                 Detection of Shadow Boundaries for Adaptive Meshing in
                 Radiosity / Fran{\c{c}}ois Sillion \\
                 Decomposing a Matrix into Simple Transformations /
                 Spencer W. Thomas \\
                 Recovering the Data from the Transformation Matrix /
                 Ronald N. Goldman \\
                 Transformations as Exponentials / Ronald N. Goldman \\
                 More Matrices and Transformations: Shear and
                 Pseudo-Perspective / Ronald N. Goldman \\
                 Fast Matrix Inversion / Kevin Wu \\
                 Quaternions and $4 \times 4$ Matrices / Ken Shoemake
                 \\
                 Random Rotation Matrices / James Arvo \\
                 Classifying Small Sparse Matrices / James Arvo \\
                 Bit Picking / Ken Shoemake \\
                 Faster Fourier Transform / Ken Shoemake \\
                 Of Integers, Fields, and Bit Counting / Alan W. Paeth
                 and David Schilling \\
                 Using Geometric Constructions to Interpolate
                 Orientation with Quaternions / John Schlag \\
                 A Half-Angle Identity for Digital Computation: The Joys
                 of the Halved Tangent / Alan W. Paeth \\
                 An Integer Square Root Algorithm / Christopher J.
                 Musial \\
                 Fast Approximation to the Arctangent / Ron Capelli \\
                 Fast Sign of Cross Product Calculation / Jack Ritter
                 \\
                 Interval Sampling / Ken Shoemake \\
                 A Recursive Implementation of the Perlin Noise Function
                 / Greg Ward \\
                 Least-Squares Approximations to B{\'e}zier Curves and
                 Surfaces / Doug Moore and Joe Warren \\
                 Beyond B{\'e}zier Curves / Ken Shoemake \\
                 A Simple Formulation for Curve Interpolation with
                 Variable Control Point Approximation / John Schlag \\
                 Symmetric Evaluation of Polynomials / Terence Lindgren
                 \\
                 Menelaus's Theorem / Hans-Peter Seidel \\
                 Geometrically Continuous Cubic B{\'e}zier Curves /
                 Hans-Peter Siedel \\
                 A Good Straight-Line Approximation of a Circular Arc /
                 Christopher J. Musial \\
                 Great Circle Plotting / Alan W. Paeth \\
                 Fast Anti-Aliased Circle Generation / Xiaolin Wu \\
                 Graphics Gems C Header File \\
                 2D and 3D Vector C Library \\
                 Corrected and Indexed \\
                 Useful C Macros for Vector Operations / Steve
                 Hollasch",
  xxtableofcontents = "Foreword \\
                 Preface \\
                 Mathematical Notation \\
                 Pseudo-Code \\
                 Contributors \\
                 I: 2D Geometry and Algorithms \\
                 Introduction \\
                 1: The Area of a Simple Polygon \\
                 2: Intersection of Line Segments \\
                 3: Distance from a Point to a Line \\
                 4: An Easy Bounding Circle \\
                 5: The Smallest Circle Containing the Intersection of
                 Two Circles \\
                 6: Appolonius's 10th Problem \\
                 7: A Peano Curve Generation Algorithm \\
                 8: Space-Filling Curves and a Measure of Coherence \\
                 9: Scanline Coherent Shape Algebra \\
                 II: Image Processing \\
                 Introduction \\
                 1: Image Smoothing and Sharpening by Discrete
                 Convolution \\
                 2: A Comparison of Digital Halftoning Techniques \\
                 3: Color Dithering \\
                 4: Fast Anamorphic Image Scaling \\
                 5: Real Pixels \\
                 6: A Fast 90-Degree Bitmap Rotator \\
                 7: Rotation of Run-Length Encoded Image Data \\
                 8: Adaptive Run-Length Encoding \\
                 9: Image File Compression Made Easy \\
                 10: An Optimal Filter for Image Reconstruction \\
                 11: Noise Thresholding in Edge Images \\
                 12: Computing the Area, the Circumference, and the
                 Genus of a Binary Digital Image \\
                 III: Frame Buffer Techniques \\
                 Introduction \\
                 1: Efficient Inverse Color Map Computation \\
                 2. Efficient Statistical Computations for Optimal Color
                 Quantization \\
                 3: A Random Color Map Animation Algorithm \\
                 4: A Fast Approach to PHIGS PLUS Pseudo Color Mapping
                 \\
                 5: Mapping RGB Triples onto 16 Distinct Values \\
                 6: Television Color Encoding and ``Hot'' Broadcast
                 Colors \\
                 7: An Inexpensive Method of Setting the Monitor White
                 Point \\
                 8: Some Tips for Making Color Hardcopy \\
                 IV: 3D Geometry and Algorithms \\
                 Introduction \\
                 1: Area of Planar Polygons and Volume of Polyhedra \\
                 2: Getting Around on a Sphere \\
                 3: Exact Dihedral Metrics for Common Polyhedra \\
                 4: A Simple Viewing Geometry \\
                 5: View Correlation \\
                 6: Maintaining Winged-Edge Models \\
                 7: Quadtree\slash Octree-to-Boundary Conversion \\
                 8: Three-Dimensional Homogeneous Clipping of Triangle
                 Strips \\
                 9: InterPhong Shading \\
                 V: Ray Tracing \\
                 Introduction \\
                 1: Fast Ray-Convex Polyhedron Intersection \\
                 2: Intersecting a Ray with an Elliptical Torus \\
                 3: Ray-Triangle Intersection Using Binary Recursive
                 Subdivision \\
                 4: Improved Ray Tagging for Voxel-Based Ray Tracing \\
                 5: Efficiency Improvements for Hierarchy Traversal in
                 Ray Tracing \\
                 6: A Recursive Shadow Voxel Cache for Ray Tracing \\
                 7: Avoiding Incorrect Shadow Intersections for Ray
                 Tracing \\
                 8: A Body Color Model: Absorption of Light through
                 Translucent Media \\
                 9: More Shadow Attenuation for Ray Tracing Transparent
                 or Translucent Objects \\
                 VI: Radiosity \\
                 Introduction \\
                 1: Implementing Progressive Radiosity with
                 User-Provided Polygon Display Routines \\
                 2: A Cubic Tetrahedral Adaptation of the Hemi-Cube
                 Algorithm \\
                 3: Fast Vertex Radiosity Update \\
                 4: Radiosity via Ray Tracing \\
                 5: Detection of Shadow Boundaries for Adaptive Meshing
                 in Radiosity \\
                 [data unavailable] \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Balsara:1991:DSM
author: Poras T. Balsara and Robert M. Owens and Mary Jane Irwin
title: Digit serial multipliers
journal: j-J-PAR-DIST-COMP
volume: 11
number: 2
pages: 156--162
month: feb
monthnumber: 2
year: 1991
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliation: Univ of Texas at Dallas
affiliationaddress: Richardson, TX, USA
corpsource: Erik Jonsson Sch. of Eng. and Computer Science, Texas University, Richardson, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Poras T. Balsara and Robert M. Owens and Mary Jane Irwin
rawtitle: Digit serial multipliers
keywords:
communication; Computers, Digital; data; digit pipelined multipliers; digit pipelining; digit serial multipliers; digital arithmetic; Integrated Circuits, VLSI; Multiplying Circuits; multiplying circuits; parallel; pipeline processing; Pipelined Multipliers; processing; programmable multipliers; semisystolic; Signal Processing --- Digital Techniques; special purpose computers; special purpose processors; systolic; systolic multiplier; Systolic Multipliers; transmission; VLSI; VLSI signal processing

entry:
@Article{Balsara:1991:DSM,
  author =       "Poras T. Balsara and Robert M. Owens and Mary Jane
                 Irwin",
  title =        "Digit serial multipliers",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "11",
  number =       "2",
  pages =        "156--162",
  month =        feb,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Texas at Dallas",
  affiliationaddress = "Richardson, TX, USA",
  classification = "713; 723; B2570 (Semiconductor integrated circuits);
                 C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Erik Jonsson Sch. of Eng. and Computer Science, Texas
                 University, Richardson, TX, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "communication; Computers, Digital; data; digit
                 pipelined multipliers; digit pipelining; digit serial
                 multipliers; digital arithmetic; Integrated Circuits,
                 VLSI; Multiplying Circuits; multiplying circuits;
                 parallel; pipeline processing; Pipelined Multipliers;
                 processing; programmable multipliers; semisystolic;
                 Signal Processing --- Digital Techniques; special
                 purpose computers; special purpose processors;
                 systolic; systolic multiplier; Systolic Multipliers;
                 transmission; VLSI; VLSI signal processing",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Barrenechea:1991:NEH
author: M. J. Barrenechea
title: Numeric exception handling
journal: j-PROGRAM-J
volume: 9
number: 3
pages: 40--42, 44--49
month: may
monthnumber: 5
year: 1991
ISSN: 0747-5861 OR 07475861
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:20:21 MST
fjournal: Programmer's Journal
acknowledgement: ack-nhfb
affiliation: Microway Inc., Plymouth, MA, USA
thesaurus: C language; C listings; Standards
rawauthor: M. J. Barrenechea
rawtitle: Numeric exception handling
abstract:
Numeric exception handling is a facet of compiler runtime support that is not well understood by many application programmers, or even by some compiler vendors. Floating-point errors have puzzled programmers for too long. The author demystifies the IEEE 754 and 854 floating-point standards and explains how the Intel 80287/80387 and i860 chips fit into the puzzle. He gives some techniques for handling numeric exceptions in C++.

keywords:
C++; Compiler runtime support; Floating point errors; Floating-point standards; I860 chips; IEEE 754; IEEE 854; Intel 80287/80387; Numeric exceptions

rawabstract:
Numeric exception handling is a facet of compiler runtime support that is not well understood by many application programmers, or even by some compiler vendors. Floating-point errors have puzzled programmers for too long. The author demystifies the IEEE 754 and 854 floating-point standards and explains how the Intel 80287/80387 and i860 chips fit into the puzzle. He gives some techniques for handling numeric exceptions in C++.

entry:
@Article{Barrenechea:1991:NEH,
  author =       "M. J. Barrenechea",
  title =        "Numeric exception handling",
  journal =      j-PROGRAM-J,
  volume =       "9",
  number =       "3",
  pages =        "40--42, 44--49",
  month =        may # "--" # jun,
  year =         "1991",
  ISSN =         "0747-5861",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Numeric exception handling is a facet of compiler
                 runtime support that is not well understood by many
                 application programmers, or even by some compiler
                 vendors. Floating-point errors have puzzled programmers
                 for too long. The author demystifies the IEEE 754 and
                 854 floating-point standards and explains how the Intel
                 80287/80387 and i860 chips fit into the puzzle. He
                 gives some techniques for handling numeric exceptions
                 in C++.",
  acknowledgement = ack-nhfb,
  affiliation =  "Microway Inc., Plymouth, MA, USA",
  classification = "C6110 (Systems analysis and programming)",
  fjournal =     "Programmer's Journal",
  keywords =     "C++; Compiler runtime support; Floating point errors;
                 Floating-point standards; I860 chips; IEEE 754; IEEE
                 854; Intel 80287/80387; Numeric exceptions",
  thesaurus =    "C language; C listings; Standards",
}


bibtype: article
filename: fparith.bib
label: Barsi:1991:MAB
author: Ferruccio Barsi
title: Mod $m$ arithmetic in binary systems
journal: j-INFO-PROC-LETT
volume: 40
number: 6
pages: 303--309
year: 1991
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07 (68Q35)
MRnumber: MR1156823 (92m:68009)
bibdate: Thu Nov 8 14:50:34 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:34 ???
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Ferruccio Barsi
rawtitle: Mod $m$ arithmetic in binary systems
entry:
@Article{Barsi:1991:MAB,
  author =       "Ferruccio Barsi",
  title =        "Mod $m$ arithmetic in binary systems",
  journal =      j-INFO-PROC-LETT,
  volume =       "40",
  number =       "6",
  pages =        "303--309",
  year =         "1991",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07 (68Q35)",
  MRnumber =     "MR1156823 (92m:68009)",
  bibdate =      "Thu Nov 8 14:50:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: article
filename: fparith.bib
label: Bartholomew-Biggs:1991:AST
author: M. C. Bartholomew-Biggs
title: Ada Software for Teaching Modern Computer Arithmetic
journal: j-SIGNUM
volume: 26
number: 3
pages: 17--26
month: jul
monthnumber: 7
year: 1991
CODEN: SNEWD6
DOI: https://doi.org/10.1145/122649.122651
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:20 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.04.12 07:50:20 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
affiliation: Numerical Optimisation Centre, Hatfield Polytech., UK
journalURL: https://dl.acm.org/loi/signum
rawauthor: M. C. Bartholomew-Biggs
rawtitle: {Ada} Software for Teaching Modern Computer Arithmetic
abstract:
Describes three Ada packages which support the teaching of some recent and important ideas in numerical computation. The first is designed to enable students to write and use applications programs demonstrating the behavior of floating point arithmetic with different precisions and roundings. It also underpins the other two packages which provide simple computational tools for interval arithmetic and for accurate arithmetic.

keywords:
Accurate arithmetic; Ada software; Computer arithmetic; Floating point arithmetic; Interval arithmetic; Numerical computation; Precisions; Roundings; Students; Teaching

thesaurus:
Computer aided instruction; Computer science education; Digital arithmetic; Numerical analysis; Software packages; Teaching

rawabstract:
Describes three Ada packages which support the teaching of some recent and important ideas in numerical computation. The first is designed to enable students to write and use applications programs demonstrating the behavior of floating point arithmetic with different precisions and roundings. It also underpins the other two packages which provide simple computational tools for interval arithmetic and for accurate arithmetic.

entry:
@Article{Bartholomew-Biggs:1991:AST,
  author =       "M. C. Bartholomew-Biggs",
  title =        "{Ada} Software for Teaching Modern Computer
                 Arithmetic",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "17--26",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/122649.122651",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:20 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes three Ada packages which support the
                 teaching of some recent and important ideas in
                 numerical computation. The first is designed to enable
                 students to write and use applications programs
                 demonstrating the behavior of floating point arithmetic
                 with different precisions and roundings. It also
                 underpins the other two packages which provide simple
                 computational tools for interval arithmetic and for
                 accurate arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Numerical Optimisation Centre, Hatfield Polytech.,
                 UK",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods); C7430 (Computer engineering);
                 C7810C (Computer-aided instruction)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Accurate arithmetic; Ada software; Computer
                 arithmetic; Floating point arithmetic; Interval
                 arithmetic; Numerical computation; Precisions;
                 Roundings; Students; Teaching",
  thesaurus =    "Computer aided instruction; Computer science
                 education; Digital arithmetic; Numerical analysis;
                 Software packages; Teaching",
  xxpages =      "16--26",
}


bibtype: article
filename: fparith.bib
label: BartholomewBiggs:1991:AST
author: M. C. Bartholomew-Biggs
title: Ada software for teaching modern computer arithmetic
journal: j-SIGNUM
volume: 26
number: 3
pages: 16--26
month: jul
monthnumber: 7
year: 1991
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Wed Dec 13 13:13:34 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 13:13:34 MST
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
affiliation: Numerical Optimisation Centre, Hatfield Polytech., UK
journalURL: https://dl.acm.org/loi/signum
rawauthor: M. C. Bartholomew-Biggs
rawtitle: {Ada} software for teaching modern computer arithmetic
abstract:
Describes three Ada packages which support the teaching of some recent and important ideas in numerical computation. The first is designed to enable students to write and use applications programs demonstrating the behavior of floating point arithmetic with different precisions and roundings. It also underpins the other two packages which provide simple computational tools for interval arithmetic and for accurate arithmetic.

keywords:
Accurate arithmetic; Ada software; Computer arithmetic; Floating point arithmetic; Interval arithmetic; Numerical computation; Precisions; Roundings; Students; Teaching

thesaurus:
Computer aided instruction; Computer science education; Digital arithmetic; Numerical analysis; Software packages; Teaching

entry:
@Article{BartholomewBiggs:1991:AST,
  author =       "M. C. Bartholomew-Biggs",
  title =        "{Ada} software for teaching modern computer
                 arithmetic",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "16--26",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes three Ada packages which support the
                 teaching of some recent and important ideas in
                 numerical computation. The first is designed to enable
                 students to write and use applications programs
                 demonstrating the behavior of floating point arithmetic
                 with different precisions and roundings. It also
                 underpins the other two packages which provide simple
                 computational tools for interval arithmetic and for
                 accurate arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Numerical Optimisation Centre, Hatfield Polytech.,
                 UK",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods); C7430 (Computer engineering);
                 C7810C (Computer-aided instruction)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Accurate arithmetic; Ada software; Computer
                 arithmetic; Floating point arithmetic; Interval
                 arithmetic; Numerical computation; Precisions;
                 Roundings; Students; Teaching",
  thesaurus =    "Computer aided instruction; Computer science
                 education; Digital arithmetic; Numerical analysis;
                 Software packages; Teaching",
}


bibtype: article
filename: fparith.bib
label: Bartoloni:1991:MFU
title: MAD, a floating-point unit for massively-parallel processors
journal: Particle World
volume: 2
number: 3
pages: 65--73
year: 1991
ISSN: 1043-6790 OR 10436790
bibdate: Tue Dec 12 09:26:54 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:26:54 MST
acknowledgement: ack-nhfb
affiliation: Roma University, Italy
thesaurus: Digital arithmetic; Microprocessor chips; Parallel architectures; Physics computing
rawtitle: {MAD}, a floating-point unit for massively-parallel processors
author:
A. Bartoloni and C. Battista and S. Cabasino and N. Cabibbo and F. Del Prete and F. Marzano and P. S. Paolucci and R. Sarno and G. Salina and G. M. Todesco and M. Torelli and R. Tripiccione and W. Tross and E. Zanetti

abstract:
The authors describe in detail the architecture and implementation of the MAD chip. It is a floating point unit, used as the elementary processing element of the APE100 array processor. The design has been accurately tailored to the requirements of a SIMD floating point intensive machine.

keywords:
APE100 array processor; Architecture; Elementary processing element; Floating-point unit; Massively-parallel processors; SIMD floating point intensive machine

rawabstract:
The authors describe in detail the architecture and implementation of the MAD chip. It is a floating point unit, used as the elementary processing element of the APE100 array processor. The design has been accurately tailored to the requirements of a SIMD floating point intensive machine.

rawauthor:
A. Bartoloni and C. Battista and S. Cabasino and N. Cabibbo and F. Del Prete and F. Marzano and P. S. Paolucci and R. Sarno and G. Salina and G. M. Todesco and M. Torelli and R. Tripiccione and W. Tross and E. Zanetti

entry:
@Article{Bartoloni:1991:MFU,
  author =       "A. Bartoloni and C. Battista and S. Cabasino and N.
                 Cabibbo and F. Del Prete and F. Marzano and P. S.
                 Paolucci and R. Sarno and G. Salina and G. M. Todesco
                 and M. Torelli and R. Tripiccione and W. Tross and E.
                 Zanetti",
  title =        "{MAD}, a floating-point unit for massively-parallel
                 processors",
  journal =      "Particle World",
  volume =       "2",
  number =       "3",
  pages =        "65--73",
  month =        "????",
  year =         "1991",
  ISSN =         "1043-6790",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors describe in detail the architecture and
                 implementation of the MAD chip. It is a floating point
                 unit, used as the elementary processing element of the
                 APE100 array processor. The design has been accurately
                 tailored to the requirements of a SIMD floating point
                 intensive machine.",
  acknowledgement = ack-nhfb,
  affiliation =  "Roma University, Italy",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods); C7320 (Physics and
                 Chemistry)",
  keywords =     "APE100 array processor; Architecture; Elementary
                 processing element; Floating-point unit;
                 Massively-parallel processors; SIMD floating point
                 intensive machine",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Parallel
                 architectures; Physics computing",
}


bibtype: inproceedings
filename: fparith.bib
label: Bass:1991:BSF
author: S. C. Bass and G. M. Butler and R. L. Williams and F. Barlos and D. R. Miller
booktitle: [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing
title: A bit-serial, floating point CORDIC processor in VLSI
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1165--1168 (vol. 2)
year: 1991
DOI: https://doi.org/10.1109/ICASSP.1991.150583
bibdate: Mon Oct 27 10:32:44 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2025.10.27 10:32:44 ???
acknowledgement: ack-nhfb
rawauthor: S. C. Bass and G. M. Butler and R. L. Williams and F. Barlos and D. R. Miller
rawtitle: A bit-serial, floating point {CORDIC} processor in {VLSI}
keywords:
Application software; Circuits; CMOS technology; Computer architecture; Equations; Hardware; Process design; Signal processing; Signal processing algorithms; Very large scale integration

rawbooktitle:
{[Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing}

entry:
@InProceedings{Bass:1991:BSF,
  author =       "S. C. Bass and G. M. Butler and R. L. Williams and F.
                 Barlos and D. R. Miller",
  booktitle =    "{[Proceedings] ICASSP 91: 1991 International
                 Conference on Acoustics, Speech, and Signal
                 Processing}",
  title =        "A bit-serial, floating point {CORDIC} processor in
                 {VLSI}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1165--1168 (vol. 2)",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ICASSP.1991.150583",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application software; Circuits; CMOS technology;
                 Computer architecture; Equations; Hardware; Process
                 design; Signal processing; Signal processing
                 algorithms; Very large scale integration",
}


bibtype: inproceedings
filename: fparith.bib
label: Beal:1991:GAP
author: D. Beal and C. Lambrinoudakis
crossref: IEEE:1991:PSA
pages: 348--357
year: 1991
bibdate: Wed Apr 15 16:28:01 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.15 16:28:01 MDT
acknowledgement: ack-nhfb
corpsource: Department of Computer Science, Queen Mary and Westfield Coll., London University, UK
treatment: P Practical
rawauthor: D. Beal and C. Lambrinoudakis
title:
GPFP: an array processing element for the next generation of massively parallel supercomputer architectures

keywords:
1.6 micron; 2.5 GFLOPS; 50 MHz; 50-MHz clock; ALU; arithmetic and logic unit; array processing element; CMOS integrated circuits; CMOSIC; cost-effective extra functionality; digital arithmetic; floating point arithmetic; general purpose with floating point support; GPFP; MasPar; massively parallel SIMD arrays; massively parallel supercomputer architectures; microprocessor chips; on-chip memory; parallel architectures; processing element; VLSI

rawtitle:
{GPFP}: an array processing element for the next generation of massively parallel supercomputer architectures

entry:
@InProceedings{Beal:1991:GAP,
  author =       "D. Beal and C. Lambrinoudakis",
  title =        "{GPFP}: an array processing element for the next
                 generation of massively parallel supercomputer
                 architectures",
  crossref =     "IEEE:1991:PSA",
  pages =        "348--357",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220P (Parallel architecture); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Science, Queen Mary and
                 Westfield Coll., London University, UK",
  keywords =     "1.6 micron; 2.5 GFLOPS; 50 MHz; 50-MHz clock; ALU;
                 arithmetic and logic unit; array processing element;
                 CMOS integrated circuits; CMOSIC; cost-effective extra
                 functionality; digital arithmetic; floating point
                 arithmetic; general purpose with floating point
                 support; GPFP; MasPar; massively parallel SIMD arrays;
                 massively parallel supercomputer architectures;
                 microprocessor chips; on-chip memory; parallel
                 architectures; processing element; VLSI",
  sponsororg =   "IEEE; ACM",
  treatment =    "P Practical",
}


bibtype: techreport
filename: fparith.bib
label: Beebe:1991:ASR
author: Nelson H. F. Beebe
title: Accurate Square Root Computation
institution: inst-CSC
address: inst-CSC:adr
pages: 23
day: 4
month: feb
monthnumber: 2
year: 1991
bibdate: Sat Feb 8 10:28:55 2020
bibtimestamp: 2020.02.08 10:28:55 ???
note: Supplemental class notes prepared for Mathematics 118.
acknowledgement: ack-nhfb
rawauthor: Nelson H. F. Beebe
rawnote: Supplemental class notes prepared for Mathematics 118.
rawtitle: Accurate Square Root Computation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Beebe:1991:ASR,
  author =       "Nelson H. F. Beebe",
  title =        "Accurate Square Root Computation",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  pages =        "23",
  day =          "4",
  month =        feb,
  year =         "1991",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supplemental class notes prepared for Mathematics
                 118.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bohlender:1991:DFP
author: G. Bohlender
title: Decimal floating-point arithmetic in binary representation
crossref: Kaucher:1991:CAS
pages: 13--27
year: 1991
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nj
affiliation: Inst. fur Angewandte Math., Karlsruhe University, Germany
thesaurus: Digital arithmetic; Standards
rawauthor: G. Bohlender
rawtitle: Decimal floating-point arithmetic in binary representation
abstract:
The binary representation of decimal floating-point numbers permits an efficient implementation of the proposed radix independent IEEE standard for floating-point arithmetic, as far as storage space is concerned. Unfortunately the left and right shifts occurring in the arithmetic operations are very complicated and slow in this representation. The paper proposes methods which speed up these shifts; in particular a kind of carry look-ahead technique is used for division. These methods can be combined to construct a decimal shifter which is needed in an ALU for decimal arithmetic.

keywords:
ALU; Binary representation; Carry look-ahead; Decimal arithmetic; decimal floating-point arithmetic; Decimal floating-point numbers; Decimal shifter; Division; Floating-point arithmetic; IEEE standard; Left shifts; Radix independent; Right shifts; Storage space

rawabstract:
The binary representation of decimal floating-point numbers permits an efficient implementation of the proposed radix independent IEEE standard for floating-point arithmetic, as far as storage space is concerned. Unfortunately the left and right shifts occurring in the arithmetic operations are very complicated and slow in this representation. The paper proposes methods which speed up these shifts; in particular a kind of carry look-ahead technique is used for division. These methods can be combined to construct a decimal shifter which is needed in an ALU for decimal arithmetic.

entry:
@InProceedings{Bohlender:1991:DFP,
  author =       "G. Bohlender",
  title =        "Decimal floating-point arithmetic in binary
                 representation",
  crossref =     "Kaucher:1991:CAS",
  pages =        "13--27",
  year =         "1991",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The binary representation of decimal floating-point
                 numbers permits an efficient implementation of the
                 proposed radix independent IEEE standard for
                 floating-point arithmetic, as far as storage space is
                 concerned. Unfortunately the left and right shifts
                 occurring in the arithmetic operations are very
                 complicated and slow in this representation. The paper
                 proposes methods which speed up these shifts; in
                 particular a kind of carry look-ahead technique is used
                 for division. These methods can be combined to
                 construct a decimal shifter which is needed in an ALU
                 for decimal arithmetic.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ALU; Binary representation; Carry look-ahead; Decimal
                 arithmetic; decimal floating-point arithmetic; Decimal
                 floating-point numbers; Decimal shifter; Division;
                 Floating-point arithmetic; IEEE standard; Left shifts;
                 Radix independent; Right shifts; Storage space",
  thesaurus =    "Digital arithmetic; Standards",
}


bibtype: inproceedings
filename: fparith.bib
label: Bohlender:1991:SEF
author: G. Bohlender and W. Walter and P. Kornerup and D. W. Matula
title: Semantics for exact floating point operations
crossref: Kornerup:1991:PIS
pages: 22--26
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
note: See cite Boldo:2003:RCT for some special cases that this paper may have overlooked.
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Bohlender.pdf
acknowledgement: ack-nhfb
affiliation: Inst. fur Angewandte Math., Karlsruhe University, Germany
thesaurus: Digital arithmetic; Number theory
rawauthor: G. Bohlender and W. Walter and P. Kornerup and D. W. Matula
rawnote: See \cite{Boldo:2003:RCT} for some special cases that this paper may have overlooked.
rawtitle: Semantics for exact floating point operations
abstract:
Semantics are given for the four elementary arithmetic operations and the square root, to characterize what are termed exact floating point operations. The operands of the arithmetic operations and the argument of the square root are all floating point numbers in one format. In every case, the result is a pair of floating point numbers in the same format with no accuracy lost in the computation. These semantics make it possible to realize the following principle: it shall be a user option to discard any information in the result of a floating point arithmetic operation. The reliability and portability previously associated with only mathematical software implementations in integer arithmetic can thus be attained exploiting the generally higher efficiency of floating point hardware.

keywords:
accurate floating-point summation; argument; ARITH-10; elementary arithmetic operations; exact floating point operations; floating point arithmetic; floating point hardware; floating point numbers; integer arithmetic; mathematical software; operands; portability; reliability; semantics; square root

rawabstract:
Semantics are given for the four elementary arithmetic operations and the square root, to characterize what are termed exact floating point operations. The operands of the arithmetic operations and the argument of the square root are all floating point numbers in one format. In every case, the result is a pair of floating point numbers in the same format with no accuracy lost in the computation. These semantics make it possible to realize the following principle: it shall be a user option to discard any information in the result of a floating point arithmetic operation. The reliability and portability previously associated with only mathematical software implementations in integer arithmetic can thus be attained exploiting the generally higher efficiency of floating point hardware.

entry:
@InProceedings{Bohlender:1991:SEF,
  author =       "G. Bohlender and W. Walter and P. Kornerup and D. W.
                 Matula",
  title =        "Semantics for exact floating point operations",
  crossref =     "Kornerup:1991:PIS",
  pages =        "22--26",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boldo:2003:RCT} for some special cases that
                 this paper may have overlooked.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Bohlender.pdf",
  abstract =     "Semantics are given for the four elementary arithmetic
                 operations and the square root, to characterize what
                 are termed exact floating point operations. The
                 operands of the arithmetic operations and the argument
                 of the square root are all floating point numbers in
                 one format. In every case, the result is a pair of
                 floating point numbers in the same format with no
                 accuracy lost in the computation. These semantics make
                 it possible to realize the following principle: it
                 shall be a user option to discard any information in
                 the result of a floating point arithmetic operation.
                 The reliability and portability previously associated
                 with only mathematical software implementations in
                 integer arithmetic can thus be attained exploiting the
                 generally higher efficiency of floating point
                 hardware.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  keywords =     "accurate floating-point summation; argument; ARITH-10;
                 elementary arithmetic operations; exact floating point
                 operations; floating point arithmetic; floating point
                 hardware; floating point numbers; integer arithmetic;
                 mathematical software; operands; portability;
                 reliability; semantics; square root",
  thesaurus =    "Digital arithmetic; Number theory",
}


bibtype: inproceedings
filename: fparith.bib
label: Bohlender:1991:SPH
author: Gerd Bohlender and Andreas Knofel
title: A Survey of Pipelined Hardware Support for Accurate Scalar Products
crossref: Kaucher:1991:CAS
pages: 29--43
year: 1991
bibdate: Sat Sep 17 19:05:23 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.17 19:05:23 ???
acknowledgement: ack-nhfb
rawauthor: Gerd Bohlender and Andreas Kn{\"o}fel
rawtitle: A Survey of Pipelined Hardware Support for Accurate Scalar Products
entry:
@InProceedings{Bohlender:1991:SPH,
  author =       "Gerd Bohlender and Andreas Kn{\"o}fel",
  title =        "A Survey of Pipelined Hardware Support for Accurate
                 Scalar Products",
  crossref =     "Kaucher:1991:CAS",
  pages =        "29--43",
  year =         "1991",
  bibdate =      "Sat Sep 17 19:05:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bohlender:1991:VEI
author: Gerd Bohlender
title: A Vector Extension of the IEEE Standard for Floating-Point Arithmetic
crossref: Kaucher:1991:CAS
pages: 3--12
year: 1991
bibdate: Wed Dec 13 18:41:16 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:41:16 ???
acknowledgement: ack-nhfb
affiliation: Inst. fur Angewandte Math., Karlsruhe University, Germany
thesaurus: Digital arithmetic; Standards; Vector processor systems
rawauthor: Gerd Bohlender
rawtitle: A Vector Extension of the {IEEE} Standard for Floating-Point Arithmetic
abstract:
The IEEE standard for floating-point arithmetic aims at improving security, accuracy, reliability, and compatibility of floating-point computations. However, the standard only specifies single, double, and extended precision operations for real operands. Therefore, often only these operations are available in hardware on customary floating-point processors. Vector and matrix operations, complex operations, and interval operations, in contrast have to be simulated in the traditional way, using sequences of rounded operations. This method leads to an unnecessary loss of accuracy and efficiency. As floating-point processors more and more evolve into vector processors for sophisticated numerical applications, the same aims should be satisfied for all operations on the customary numerical data types. The paper proposes a vector extension of the IEEE standard which leads to improved operations in higher numerical spaces.

keywords:
Floating-point arithmetic; Floating-point processors; IEEE standard; Numerical data types; Vector processors

rawabstract:
The IEEE standard for floating-point arithmetic aims at improving security, accuracy, reliability, and compatibility of floating-point computations. However, the standard only specifies single, double, and extended precision operations for real operands. Therefore, often only these operations are available in hardware on customary floating-point processors. Vector and matrix operations, complex operations, and interval operations, in contrast have to be simulated in the traditional way, using sequences of rounded operations. This method leads to an unnecessary loss of accuracy and efficiency. As floating-point processors more and more evolve into vector processors for sophisticated numerical applications, the same aims should be satisfied for all operations on the customary numerical data types. The paper proposes a vector extension of the IEEE standard which leads to improved operations in higher numerical spaces.

entry:
@InProceedings{Bohlender:1991:VEI,
  author =       "Gerd Bohlender",
  title =        "A Vector Extension of the {IEEE} Standard for
                 Floating-Point Arithmetic",
  crossref =     "Kaucher:1991:CAS",
  pages =        "3--12",
  year =         "1991",
  bibdate =      "Wed Dec 13 18:41:16 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IEEE standard for floating-point arithmetic aims
                 at improving security, accuracy, reliability, and
                 compatibility of floating-point computations. However,
                 the standard only specifies single, double, and
                 extended precision operations for real operands.
                 Therefore, often only these operations are available in
                 hardware on customary floating-point processors. Vector
                 and matrix operations, complex operations, and interval
                 operations, in contrast have to be simulated in the
                 traditional way, using sequences of rounded operations.
                 This method leads to an unnecessary loss of accuracy
                 and efficiency. As floating-point processors more and
                 more evolve into vector processors for sophisticated
                 numerical applications, the same aims should be
                 satisfied for all operations on the customary numerical
                 data types. The paper proposes a vector extension of
                 the IEEE standard which leads to improved operations in
                 higher numerical spaces.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C5220P (Parallel architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Floating-point arithmetic; Floating-point processors;
                 IEEE standard; Numerical data types; Vector
                 processors",
  thesaurus =    "Digital arithmetic; Standards; Vector processor
                 systems",
}


bibtype: techreport
filename: fparith.bib
label: Boughton:1991:CSG
author: G. A. Boughton (editor)
title: Computation Structures Group Progress Report 1990--91
type: CSG Memo
number: 337
institution: MIT Laboratory for Computer Science
address: Cambridge, MA, USA
pages: 3--12
month: jun
monthnumber: 6
year: 1991
bibdate: Wed Jan 29 16:27:14 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.01.29 16:27:14 ???
acknowledgement: ack-nhfb
rawauthor: G. A. {Boughton (editor)}
rawtitle: {Computation Structures Group} Progress Report 1990--91
remark:
Utilities for accurate reading and printing of double precision floating point numbers (cited in cite Steele:2004:RHP).

entry:
@TechReport{Boughton:1991:CSG,
  author =       "G. A. {Boughton (editor)}",
  title =        "{Computation Structures Group} Progress Report
                 1990--91",
  type =         "{CSG} Memo",
  number =       "337",
  institution =  "MIT Laboratory for Computer Science",
  address =      "Cambridge, MA, USA",
  month =        jun,
  year =         "1991",
  bibdate =      "Wed Jan 29 16:27:14 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Utilities for accurate reading and printing of double
                 precision floating point numbers (cited in
                 \cite{Steele:2004:RHP}).",
}


bibtype: article
filename: fparith.bib
label: Briggs:1991:PCF
author: Keith Briggs
title: A Precise Calculation of the Feigenbaum Constants
journal: j-MATH-COMPUT
volume: 57
number: 195
pages: 435--439
month: jul
monthnumber: 7
year: 1991
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y60 (39B12 58F14 65Q05)
MRnumber: 91j:11117
MRreviewer: Jeffrey O. Shallit
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
corpsource: Department of Math., La Trobe University, Bundoora, Vic., Australia
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Keith Briggs
rawtitle: A Precise Calculation of the {Feigenbaum} Constants
keywords:
Feigenbaum constants; Feigenbaum functional equation; functional equations; iteration; iterative methods; multiple precision floating point; period-doubling bifurcations; real functions

classcodes:
B0290F (Interpolation and function approximation); B0290K (Nonlinear and functional equations); C4130 (Interpolation and function approximation); C4150 (Nonlinear and functional equations)

entry:
@Article{Briggs:1991:PCF,
  author =       "Keith Briggs",
  title =        "A Precise Calculation of the {Feigenbaum} Constants",
  journal =      j-MATH-COMPUT,
  volume =       "57",
  number =       "195",
  pages =        "435--439",
  month =        jul,
  year =         "1991",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y60 (39B12 58F14 65Q05)",
  MRnumber =     "91j:11117",
  MRreviewer =   "Jeffrey O. Shallit",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290K (Nonlinear and functional equations); C4130
                 (Interpolation and function approximation); C4150
                 (Nonlinear and functional equations)",
  corpsource =   "Department of Math., La Trobe University, Bundoora,
                 Vic., Australia",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Feigenbaum constants; Feigenbaum functional equation;
                 functional equations; iteration; iterative methods;
                 multiple precision floating point; period-doubling
                 bifurcations; real functions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Bromley:1991:FAT
author: Mark Bromley and Steven Heller and Tim McNerney and Guy L. Steele Jr.
title: Fortran at ten gigaflops: the Connection Machine convolution compiler
journal: j-SIGPLAN
volume: 26
number: 6
pages: 145--156
month: jun
monthnumber: 6
year: 1991
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Thu May 13 12:37:27 MDT 1999
bibtimestamp: 1999.05.13 12:37:27 MDT
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p145-bromley/
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: Thinking Machines Corp., Cambridge, MA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
thesaurus: FORTRAN; Parallel machines; Parallel programming; Program compilers
rawauthor: Mark Bromley and Steven Heller and Tim McNerney and Guy L. {Steele Jr.}
rawtitle: {Fortran} at ten gigaflops: the {Connection Machine} convolution compiler
bibsource:
http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The authors have implemented a prototype of a specialized compiler module and associated run-time support that allows a Fortran user to achieve sustained floating-point performance of over 10 gigaflops on the Connection Machine Model CM-2. This improves substantially over the previous record of 5.6 gigaflops, which was achieved by means of hand-crafted low-level coding techniques. The compiler module processes array assignment statements of a certain form: the right-hand side must be a sum of products and the products must use the Fortran 90 array shifting intrinsics in a certain stylized pattern. Such assignment statements are suitable for expressing array convolution (stencil) computations and can be executed efficiently by chained multiply-add operations.

keywords:
Array assignment statements; Array convolution; Chained multiply-add operations; Connection Machine convolution compiler; Connection Machine Model CM-2; Fortran 90 array shifting intrinsics; Fortran user; Hand-crafted low-level coding techniques; languages; performance; Run-time support; Specialized compiler module; Sustained floating-point performance

subject:
bf D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Compilers.

rawabstract:
The authors have implemented a prototype of a specialized compiler module and associated run-time support that allows a Fortran user to achieve sustained floating-point performance of over 10 gigaflops on the Connection Machine Model CM-2. This improves substantially over the previous record of 5.6 gigaflops, which was achieved by means of hand-crafted low-level coding techniques. The compiler module processes array assignment statements of a certain form: the right-hand side must be a sum of products and the products must use the Fortran 90 array shifting intrinsics in a certain stylized pattern. Such assignment statements are suitable for expressing array convolution (stencil) computations and can be executed efficiently by chained multiply-add operations.

entry:
@Article{Bromley:1991:FAT,
  author =       "Mark Bromley and Steven Heller and Tim McNerney and
                 Guy L. {Steele Jr.}",
  title =        "{Fortran} at ten gigaflops: the {Connection Machine}
                 convolution compiler",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "6",
  pages =        "145--156",
  month =        jun,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu May 13 12:37:27 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p145-bromley/",
  abstract =     "The authors have implemented a prototype of a
                 specialized compiler module and associated run-time
                 support that allows a Fortran user to achieve sustained
                 floating-point performance of over 10 gigaflops on the
                 Connection Machine Model CM-2. This improves
                 substantially over the previous record of 5.6
                 gigaflops, which was achieved by means of hand-crafted
                 low-level coding techniques. The compiler module
                 processes array assignment statements of a certain
                 form: the right-hand side must be a sum of products and
                 the products must use the Fortran 90 array shifting
                 intrinsics in a certain stylized pattern. Such
                 assignment statements are suitable for expressing array
                 convolution (stencil) computations and can be executed
                 efficiently by chained multiply-add operations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Thinking Machines Corp., Cambridge, MA, USA",
  classification = "C5440 (Multiprocessor systems and techniques); C6110
                 (Systems analysis and programming); C6140D (High level
                 languages); C6150C (Compilers, interpreters and other
                 processors)",
  confdate =     "26-28 June 1991",
  conflocation = "Toronto, Ont., Canada",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Array assignment statements; Array convolution;
                 Chained multiply-add operations; Connection Machine
                 convolution compiler; Connection Machine Model CM-2;
                 Fortran 90 array shifting intrinsics; Fortran user;
                 Hand-crafted low-level coding techniques; languages;
                 performance; Run-time support; Specialized compiler
                 module; Sustained floating-point performance",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Compilers.",
  thesaurus =    "FORTRAN; Parallel machines; Parallel programming;
                 Program compilers",
}


bibtype: book
filename: fparith.bib
label: Brunner:1991:VAR
editor: Richard A. Brunner and Dileep P. Bhandarkar and others
title: VAX Architecture Reference Manual
publisher: pub-DP
address: pub-DP:adr
pages: xv + 560
year: 1991
LCCN: QA76.8.V32 V39 1991
bibdate: Wed Nov 01 08:09:54 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.11.01 08:09:54 ???
acknowledgement: ack-nhfb
raweditor: Richard A. Brunner and Dileep P. Bhandarkar and others
rawtitle: {VAX} Architecture Reference Manual
ISBN:
1-55558-057-2 (Digital Press), 0-13-929522-4 (Prentice-Hall) OR 1555580572 (Digital Press), 0139295224 (PrenticeHall)

ISBN13:
978-1-55558-057-5 (Digital Press), 978-0-13-929522-5 (Prentice-Hall) OR 9781555580575 (Digital Press), 9780139295225 (PrenticeHall)

entry:
@Book{Brunner:1991:VAR,
  editor =       "Richard A. Brunner and Dileep P. Bhandarkar and
                 others",
  title =        "{VAX} Architecture Reference Manual",
  publisher =    pub-DP # " and " # pub-PH,
  address =      pub-DP:adr # " and " # pub-PH:adr,
  pages =        "xv + 560",
  year =         "1991",
  ISBN =         "1-55558-057-2 (Digital Press), 0-13-929522-4
                 (Prentice-Hall)",
  ISBN-13 =      "978-1-55558-057-5 (Digital Press), 978-0-13-929522-5
                 (Prentice-Hall)",
  LCCN =         "QA76.8.V32 V39 1991",
  bibdate =      "Wed Nov 01 08:09:54 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Bruss:1991:RMF
author: Rolf-Jurgen Bruss
title: RISC --- The MIPS-R3000 Family
publisher: pub-SIEMENS
address: pub-SIEMENS:adr
pages: 340
year: 1991
ISBN: 3-8009-4103-1 OR 3800941031
ISBN13: 978-3-8009-4103-2 OR 9783800941032
LCCN: QA76.5 R48 1991
bibdate: Sat Jan 29 23:10:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.01.29 23:10:50 ???
acknowledgement: ack-nhfb
rawauthor: Rolf-J{\"u}rgen Br{\"u}{\ss}
rawtitle: {RISC}\emdash The {MIPS-R3000} Family
entry:
@Book{Bruss:1991:RMF,
  author =       "Rolf-J{\"u}rgen Br{\"u}{\ss}",
  title =        "{RISC}\emdash The {MIPS-R3000} Family",
  publisher =    pub-SIEMENS,
  address =      pub-SIEMENS:adr,
  pages =        "340",
  year =         "1991",
  ISBN =         "3-8009-4103-1",
  ISBN-13 =      "978-3-8009-4103-2",
  LCCN =         "QA76.5 R48 1991",
  bibdate =      "Sat Jan 29 23:10:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Bryant:1991:CVI
author: R. E. Bryant
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 2
pages: 205--213
month: feb
monthnumber: 2
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.73590
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 12:52:19 MDT 2011
bibtimestamp: 2011.07.07 12:52:19 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73590
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. E. Bryant
title:
On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication

rawtitle:
On the complexity of {VLSI} implementations and graph representations of {Boolean} functions with application to integer multiplication

entry:
@Article{Bryant:1991:CVI,
  author =       "R. E. Bryant",
  title =        "On the complexity of {VLSI} implementations and graph
                 representations of {Boolean} functions with application
                 to integer multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "205--213",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.73590",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73590",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Calvetti:1991:REF
author: Daniela Calvetti
title: Roundoff error for floating point representation of real data
journal: j-COMMUN-STAT-THEORY-METH
volume: 20
number: 8
pages: 2687--2695
year: 1991
CODEN: CSTMDC
DOI: https://doi.org/10.1080/03610929108830658
ISSN: 0361-0926 (print), 1532-415X (electronic) OR 03610926 (print), 1532415X (electronic)
ISSNL: 0361-0926 OR 03610926
MRclass: 62E99 (65C20)
MRnumber: 93d:62031
bibdate: Wed Jan 27 05:39:04 MST 2016
bibtimestamp: 2016.01.27 05:39:04 MST
fjournal: Communications in Statistics: Theory and Methods
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/lsta20
reviewer: Evdokia Xekalaki
rawauthor: Daniela Calvetti
rawtitle: Roundoff error for floating point representation of real data
bibsource:
https://www.math.utah.edu/pub/tex/bib/communstattheorymeth1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Calvetti:1991:REF,
  author =       "Daniela Calvetti",
  title =        "Roundoff error for floating point representation of
                 real data",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "20",
  number =       "8",
  pages =        "2687--2695",
  year =         "1991",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1080/03610929108830658",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  MRclass =      "62E99 (65C20)",
  MRnumber =     "93d:62031",
  bibdate =      "Wed Jan 27 05:39:04 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
  reviewer =     "Evdokia Xekalaki",
}


bibtype: article
filename: fparith.bib
label: Calvetti:1991:SRE
author: Daniela Calvetti
title: A stochastic roundoff error analysis for the Fast Fourier Transform
journal: j-MATH-COMPUT
volume: 56
number: 194
pages: 755--774
month: apr
monthnumber: 4
year: 1991
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65T20 (65G05)
MRnumber: 91m:65341
MRreviewer: Harald E. Krogstad
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
corpsource: Dept. of Math., Southern Colorado Univ., Pueblo, CO, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Daniela Calvetti
rawtitle: A stochastic roundoff error analysis for the {Fast Fourier Transform}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib; JSTOR database

keywords:
addition; discrete Fourier transform; error analysis; expected value; fast Fourier transform; fast Fourier transforms; linear forms; multiplication; stochastic roundoff error analysis; variance

classcodes:
B0290Z (Other numerical methods); B0290B (Error analysis in numerical methods); C4190 (Other numerical methods); C4110 (Error analysis in numerical methods)

entry:
@Article{Calvetti:1991:SRE,
  author =       "Daniela Calvetti",
  title =        "A stochastic roundoff error analysis for the {Fast
                 Fourier Transform}",
  journal =      j-MATH-COMPUT,
  volume =       "56",
  number =       "194",
  pages =        "755--774",
  month =        apr,
  year =         "1991",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65T20 (65G05)",
  MRnumber =     "91m:65341",
  MRreviewer =   "Harald E. Krogstad",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290Z (Other numerical methods); B0290B (Error
                 analysis in numerical methods); C4190 (Other numerical
                 methods); C4110 (Error analysis in numerical methods)",
  corpsource =   "Dept. of Math., Southern Colorado Univ., Pueblo, CO,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "addition; discrete Fourier transform; error analysis;
                 expected value; fast Fourier transform; fast Fourier
                 transforms; linear forms; multiplication; stochastic
                 roundoff error analysis; variance",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: fparith.bib
label: Catanzaro:1991:STP
editor: Ben J. Catanzaro
title: The SPARC Technical Papers
publisher: pub-SV
address: pub-SV:adr
pages: xvi + 501
year: 1991
ISBN: 0-387-97634-5, 3-540-97634-5 OR 0387976345, 3540976345
ISBN13: 978-0-387-97634-1, 978-3-540-97634-9 OR 9780387976341, 9783540976349
LCCN: QA76.9.A73 S65 1991
bibdate: Wed Feb 9 01:57:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.02.09 01:57:02 ???
acknowledgement: ack-nhfb
raweditor: Ben J. Catanzaro
rawtitle: The {SPARC} Technical Papers
entry:
@Book{Catanzaro:1991:STP,
  editor =       "Ben J. Catanzaro",
  title =        "The {SPARC} Technical Papers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 501",
  year =         "1991",
  ISBN =         "0-387-97634-5, 3-540-97634-5",
  ISBN-13 =      "978-0-387-97634-1, 978-3-540-97634-9",
  LCCN =         "QA76.9.A73 S65 1991",
  bibdate =      "Wed Feb 9 01:57:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Celarier:1991:AML
author: Donald A. Celarier and Donald W. Sando
title: An Ada math library for real-time avionics
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 274--284
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:43 MDT 2003
bibtimestamp: 2003.08.09 09:05:43 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C7460 (Aerospace engineering); C7150 (Military); C7310 (Mathematics); C6140D (High level languages)
corpsource: Boeing Defense and Space Group, Seattle, WA, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Donald A. Celarier and Donald W. Sando
rawtitle: An {Ada} math library for real-time avionics
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

keywords:
accuracy testing; Ada; Ada math library; aerospace computing; applications; avionics; computing; implementation; library; mathematics computing; military; military avionics processor; real-time avionics; real-time systems; subroutines

entry:
@Article{Celarier:1991:AML,
  author =       "Donald A. Celarier and Donald W. Sando",
  title =        "An {Ada} math library for real-time avionics",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "274--284",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:43 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C7460 (Aerospace engineering); C7150 (Military); C7310
                 (Mathematics); C6140D (High level languages)",
  corpsource =   "Boeing Defense and Space Group, Seattle, WA, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "accuracy testing; Ada; Ada math library; aerospace
                 computing; applications; avionics; computing;
                 implementation; library; mathematics computing;
                 military; military avionics processor; real-time
                 avionics; real-time systems; subroutines",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Chai:1991:MCF
title: A 120 MFLOPS CMOS Floating-Point Processor
crossref: IEEE:1991:PIC
pages: 15.1/1--4
year: 1991
bibdate: Wed Sep 7 22:32:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.07 22:32:42 ???
acknowledgement: ack-nj
rawtitle: A 120 {MFLOPS CMOS} Floating-Point Processor
author:
P. Chai and T. Chuk and Y. H. Fong and L. Hu and K. Ng and J. Prabhu and A. Quek and A. Samuels and J. Yeun

rawauthor:
P. Chai and T. Chuk and Y. H. Fong and L. Hu and K. Ng and J. Prabhu and A. Quek and A. Samuels and J. Yeun

entry:
@Article{Chai:1991:MCF,
  author =       "P. Chai and T. Chuk and Y. H. Fong and L. Hu and K. Ng
                 and J. Prabhu and A. Quek and A. Samuels and J. Yeun",
  title =        "A 120 {MFLOPS CMOS} Floating-Point Processor",
  crossref =     "IEEE:1991:PIC",
  pages =        "15.1/1--4",
  year =         "1991",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Chan:1991:DOC
author: Pak K. Chan and Martine D. F. Schlag and Clark D. Thomborson and Vojin G. Oklobdzija
title: Delay optimization of carry-skip adders and block carry-lookahead adders
crossref: Kornerup:1991:PIS
pages: 154--164
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.11.27 12:40:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chan.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Pak K. Chan and Martine D. F. Schlag and Clark D. Thomborson and Vojin G. Oklobdzija
rawtitle: Delay optimization of carry-skip adders and block carry-lookahead adders
entry:
@InProceedings{Chan:1991:DOC,
  author =       "Pak K. Chan and Martine D. F. Schlag and Clark D.
                 Thomborson and Vojin G. Oklobdzija",
  title =        "Delay optimization of carry-skip adders and block
                 carry-lookahead adders",
  crossref =     "Kornerup:1991:PIS",
  pages =        "154--164",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Chance:1991:EPA
author: R. J. Chance
title: The effect of processor architecture on an efficient floating point table look-up algorithm
journal: j-MICROPROC-MICROSYS
volume: 15
number: 8
pages: 411--416 (or 411--415??)
month: oct
monthnumber: 10
year: 1991
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: R. J. Chance
rawtitle: The effect of processor architecture on an efficient floating point table look-up algorithm
abstract:
R J Chance investigates the performance that can be achieved using linear interpolation and partitioning techniques in look-up tables

rawabstract:
R J Chance investigates the performance that can be achieved using linear interpolation and partitioning techniques in look-up tables

entry:
@Article{Chance:1991:EPA,
  author =       "R. J. Chance",
  title =        "The effect of processor architecture on an efficient
                 floating point table look-up algorithm",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "15",
  number =       "8",
  pages =        "411--416 (or 411--415??)",
  month =        oct,
  year =         "1991",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "R J Chance investigates the performance that can be
                 achieved using linear interpolation and partitioning
                 techniques in look-up tables",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: article
filename: fparith.bib
label: Chang:1991:PLA
author: Yuh-Huu Chang and Ching-Kae Tzou and N. J. Bershad
title: Postsmoothing for the LMS algorithm and a fixed point roundoff error analysis
journal: j-IEEE-TRANS-SIG-PROC
volume: 39
number: 4
pages: 959--962
month: apr
monthnumber: 4
year: 1991
CODEN: ITPRED
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: Yuh-Huu Chang and Ching-Kae Tzou and N. J. Bershad
rawtitle: Postsmoothing for the {LMS} algorithm and a fixed point roundoff error analysis
entry:
@Article{Chang:1991:PLA,
  author =       "Yuh-Huu Chang and Ching-Kae Tzou and N. J. Bershad",
  title =        "Postsmoothing for the {LMS} algorithm and a fixed
                 point roundoff error analysis",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "4",
  pages =        "959--962",
  month =        apr,
  year =         "1991",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The effect of post-algorithm smoothing on digital
                 implementations of the least mean square (LMS)
                 algorithm is studied. An expression is derived for the
                 mean square error (MSE) with post-algorithm (PA)
                 smoothing but without finite wordlength effects.
                 \ldots{}",
}


