# bibtab

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: http://portal.acm.org/browse_dl.cfm?idx=J89
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 =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}


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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57039
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57039",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: http://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/stamp/stamp.jsp?tp=&arnumber=57044; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2065

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/stamp/stamp.jsp?tp=&arnumber=57044;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2065",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "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: J. 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57047
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. E. Vuillemin
rawtitle: Exact real computer arithmetic with continued fractions
entry:
@Article{Vuillemin:1990:ERC,
  author =       "J. 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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57047",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: 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
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
raweditor: Peter J. L. Wallis
rawtitle: Improving Floating-Point Programming
keywords:
Computation by computer systems --- Floating point representation; Electronic digital computers --- Programming.; Floating-point arithmetic.; Floating-point arithmetic., Compiling (Electronic computers)

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/fparith.bib",
  price =        "US\$60.00",
  acknowledgement = ack-nhfb,
  keywords =     "Computation by computer systems --- Floating point
                 representation; Electronic digital computers ---
                 Programming.; Floating-point arithmetic.;
                 Floating-point arithmetic., Compiling (Electronic
                 computers)",
}


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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57045
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57045",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: http://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 =  "http://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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61062
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61062",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83626
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83626",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: 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
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",
  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: http://portal.acm.org/browse_dl.cfm?idx=J690
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 =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
  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: http://portal.acm.org/browse_dl.cfm?idx=J690
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 =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
  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: 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73590
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73590",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: 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: 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: http://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 =  "http://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{}",
}


bibtype: article
filename: fparith.bib
label: Chassaing:1991:DSP
author: Chassaing and Horning
title: Digital Signal Processing with Fixed- and Floating-Point Processors
journal: j-COED
volume: II
number: 1
pages: 1--4
month: jan
monthnumber: 1
year: 1991
CODEN: CWLJDP
ISSN: 0736-8607 OR 07368607
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: CoED
acknowledgement: ack-nhfb
rawauthor: Chassaing and Horning
rawtitle: Digital Signal Processing with Fixed- and Floating-Point Processors
entry:
@Article{Chassaing:1991:DSP,
  author =       "Chassaing and Horning",
  title =        "Digital Signal Processing with Fixed- and
                 Floating-Point Processors",
  journal =      j-COED,
  volume =       "II",
  number =       "1",
  pages =        "1--4",
  month =        jan,
  year =         "1991",
  CODEN =        "CWLJDP",
  ISSN =         "0736-8607",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "CoED",
}


bibtype: inproceedings
filename: fparith.bib
label: Chatelin:1991:AAA
author: F. Chatelin and V. Fraysse
title: Analysis of arithmetic algorithms: a statistical study
crossref: Kornerup:1991:PIS
pages: 10--16
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_Chatelin.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: F. Chatelin and V. Frayss{\'e}
rawtitle: Analysis of arithmetic algorithms: a statistical study
entry:
@InProceedings{Chatelin:1991:AAA,
  author =       "F. Chatelin and V. Frayss{\'e}",
  title =        "Analysis of arithmetic algorithms: a statistical
                 study",
  crossref =     "Kornerup:1991:PIS",
  pages =        "10--16",
  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_Chatelin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Chen:1991:BDR
author: F. Chen and C. S. Chen
title: A 20~b dynamic-range floating-point data acquisition system
journal: j-IEEE-TRANS-IND-ELECTRON
volume: 38
number: 1
pages: 10--14
month: feb
monthnumber: 2
year: 1991
CODEN: ITIED6
DOI: https://doi.org/10.1109/41.103477
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: F. Chen and C. S. Chen
rawtitle: A {20~b} dynamic-range floating-point data acquisition system
entry:
@Article{Chen:1991:BDR,
  author =       "F. Chen and C. S. Chen",
  title =        "A {20~b} dynamic-range floating-point data acquisition
                 system",
  journal =      j-IEEE-TRANS-IND-ELECTRON,
  volume =       "38",
  number =       "1",
  pages =        "10--14",
  month =        feb,
  year =         "1991",
  CODEN =        "ITIED6",
  DOI =          "https://doi.org/10.1109/41.103477",
  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 design and engineering of a floating-point
                 data-acquisition system are described. The system has
                 both automatic gain and software-programmable gain
                 adjustment features. In automatic gain adjustment mode,
                 the gain is set automatically dependent on \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Chiang:1991:FNR
author: Jen-Shiun Chiang and Mi Lu
title: Floating-point numbers in residue number systems
journal: j-COMPUT-MATH-APPL
volume: 22
number: 10
pages: 127--140
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65Y10
MRnumber: 92h:65212
bibdate: Wed Dec 13 18:13:40 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.13 18:13:40 ???
fjournal: Computers and Mathematics with Applications
keywords: Floating-point RNS; Residue number system; RNS
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Texas A&M University, College Station, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: Digital arithmetic
rawauthor: Jen-Shiun Chiang and Mi Lu
rawtitle: Floating-point numbers in residue number systems
abstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement. (6 Refs.)

rawabstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement. (6 Refs.)

entry:
@Article{Chiang:1991:FNR,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65Y10",
  MRnumber =     "92h:65212",
  bibdate =      "Wed Dec 13 18:13:40 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A\&M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Chiang:1991:FPNa
author: Jen-Shiun Chiang and Mi Lu
title: Floating-point numbers in residue number systems
journal: j-COMPUT-MATH-APPL
volume: 22
number: 10
pages: 127--140
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65Y10
MRnumber: 92h:65212
bibdate: Wed Dec 13 18:13:40 1995
bibtimestamp: 1995.12.13 18:13:40 ???
fjournal: Computers and Mathematics with Applications
keywords: Floating-point RNS; Residue number system; RNS
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Texas A&M University, College Station, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: Digital arithmetic
rawauthor: Jen-Shiun Chiang and Mi Lu
rawtitle: Floating-point numbers in residue number systems
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement. (6 Refs.)

entry:
@Article{Chiang:1991:FPNa,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65Y10",
  MRnumber =     "92h:65212",
  bibdate =      "Wed Dec 13 18:13:40 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A\&M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Chiang:1991:FPNb
author: Jen-Shiun Chiang and Mi Lu
title: Floating-point numbers in residue number systems
journal: j-COMPUT-MATH-APPL
volume: 22
number: 10
pages: 127--140
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:01 MST 2017
bibtimestamp: 2017.03.01 19:11:01 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219190200N
fjournal: Computers and Mathematics with Applications
keywords: Floating-point RNS; Residue number system; RNS
acknowledgement: ack-nhfb
affiliation: Department of Electr. Eng., Texas A and M University, College Station, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: Digital arithmetic
rawauthor: Jen-Shiun Chiang and Mi Lu
rawtitle: Floating-point numbers in residue number systems
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement.

rawabstract:
Introduce a new type of the residue number system (RNS), floating-point RNS, which can significantly increase the range of the numbers represented by RNS. The concept of the RNS floating-point arithmetics are presented, and the approaches to perform these arithmetic operations are proposed. The introduced methods are simple, efficient and easy to implement.

entry:
@Article{Chiang:1991:FPNb,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:01 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219190200N",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A and M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Chiang:1991:GDA
author: J.-S. Chiang and M. Lu
title: A general division algorithm for residue number systems
crossref: Kornerup:1991:PIS
pages: 76--83
year: 1991
DOI: https://doi.org/10.1109/ARITH.1991.145537
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chiang.pdf
keywords: ARITH-10; residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: J.-S. Chiang and M. Lu
rawtitle: A general division algorithm for residue number systems
entry:
@InProceedings{Chiang:1991:GDA,
  author =       "J.-S. Chiang and M. Lu",
  title =        "A general division algorithm for residue number
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "76--83",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145537",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chiang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; residue arithmetic; residue number system",
  summary =      "A general algorithm for signed number division in
                 residue number systems (RNSs) is presented. A parity
                 checking technique is used to accomplish the sign and
                 overflow detection in this algorithm. Compared with
                 conventional methods of sign and \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Cmelik:1991:AMS
author: Robert F. Cmelik and Shing I. Kong and David R. Ditzel and Edmund J. Kelly
title: An Analysis of MIPS and SPARC Instruction Set Utilization on the SPEC Benchmarks
journal: j-SIGPLAN
volume: 26
number: 4
pages: 290--301 (or 290--302??)
month: apr
monthnumber: 4
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: 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: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: Sun Microsyst. Inc., Mountain View, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
thesaurus: Instruction sets; Performance evaluation; Reduced instruction set computing
rawauthor: Robert F. Cmelik and Shing I. Kong and David R. Ditzel and Edmund J. Kelly
rawtitle: An Analysis of {MIPS} and {SPARC} Instruction Set Utilization on the {SPEC} Benchmarks
abstract:
The dynamic instruction counts of MIPS and SPARC are compared using the SPEC benchmarks. MIPS typically executes more user-level instructions than SPARC. This difference can be accounted for by architectural differences, compiler differences, and library differences. The most significant differences are that SPARC's double-precision floating point load/store is an architectural advantage in the SPEC floating point benchmarks while MIPS's compare-and-branch instruction is an architectural advantage in the SPEC integer benchmarks. After the differences in the two architectures are isolated, it appears that although MIPS and SPARC each have strengths and weaknesses in their compilers and library routines, the combined effect of compilers and library routines does not give either MIPS or SPARC a clear advantage in these areas.

keywords:
Architectural differences; Compare-and-branch instruction; Compiler differences; Double-precision floating point load/store; Dynamic instruction counts; Instruction set utilization; Library differences; MIPS; SPARC; SPEC floating point benchmarks; SPEC integer benchmarks; User-level instructions

rawabstract:
The dynamic instruction counts of MIPS and SPARC are compared using the SPEC benchmarks. MIPS typically executes more user-level instructions than SPARC. This difference can be accounted for by architectural differences, compiler differences, and library differences. The most significant differences are that SPARC's double-precision floating point load/store is an architectural advantage in the SPEC floating point benchmarks while MIPS's compare-and-branch instruction is an architectural advantage in the SPEC integer benchmarks. After the differences in the two architectures are isolated, it appears that although MIPS and SPARC each have strengths and weaknesses in their compilers and library routines, the combined effect of compilers and library routines does not give either MIPS or SPARC a clear advantage in these areas.

entry:
@Article{Cmelik:1991:AMS,
  author =       "Robert F. Cmelik and Shing I. Kong and David R. Ditzel
                 and Edmund J. Kelly",
  title =        "An Analysis of {MIPS} and {SPARC} Instruction Set
                 Utilization on the {SPEC} Benchmarks",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "4",
  pages =        "290--301 (or 290--302??)",
  month =        apr,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The dynamic instruction counts of MIPS and SPARC are
                 compared using the SPEC benchmarks. MIPS typically
                 executes more user-level instructions than SPARC. This
                 difference can be accounted for by architectural
                 differences, compiler differences, and library
                 differences. The most significant differences are that
                 SPARC's double-precision floating point load/store is
                 an architectural advantage in the SPEC floating point
                 benchmarks while MIPS's compare-and-branch instruction
                 is an architectural advantage in the SPEC integer
                 benchmarks. After the differences in the two
                 architectures are isolated, it appears that although
                 MIPS and SPARC each have strengths and weaknesses in
                 their compilers and library routines, the combined
                 effect of compilers and library routines does not give
                 either MIPS or SPARC a clear advantage in these
                 areas.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sun Microsyst. Inc., Mountain View, CA, USA",
  classification = "C5220 (Computer architecture); C5470 (Performance
                 evaluation and testing); C6140B (Machine-oriented
                 languages)",
  confdate =     "8-11 April 1991",
  conflocation = "Santa Clara, CA, USA",
  confsponsor =  "IEEE; ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Architectural differences; Compare-and-branch
                 instruction; Compiler differences; Double-precision
                 floating point load/store; Dynamic instruction counts;
                 Instruction set utilization; Library differences; MIPS;
                 SPARC; SPEC floating point benchmarks; SPEC integer
                 benchmarks; User-level instructions",
  thesaurus =    "Instruction sets; Performance evaluation; Reduced
                 instruction set computing",
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1991:KAA
author: W. J. Cody
title: Keynote Address: Arithmetic Standards: The Long Road
crossref: Kornerup:1991:PIS
pages: ix--ix
year: 1991
bibdate: Sat Nov 17 08:46:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 08:46:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_keynote.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: Keynote Address: Arithmetic Standards: The Long Road
entry:
@InProceedings{Cody:1991:KAA,
  author =       "W. J. Cody",
  title =        "Keynote Address: Arithmetic Standards: The Long Road",
  crossref =     "Kornerup:1991:PIS",
  pages =        "ix--ix",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_keynote.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Cody:1991:PEP
author: W. J. Cody
title: Performance Evaluation of Programs Related to the Real Gamma Function
journal: j-TOMS
volume: 17
number: 1
pages: 46--54
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65Y20)
MRnumber: 91m:65052
bibdate: Sun Sep 04 23:33:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.04 23:33:02 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: measurement; performance; reliability
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawtitle: Performance Evaluation of Programs Related to the Real Gamma Function
URL:
http://doi.acm.org/10.1145/103147.103153; http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/

abstract:
Methods are presented for evaluating the performance of programs for the functions $ Gamma (x) $, $ ln Gamma (x) $, and $ psi (x) $. Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.

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

rawabstract:
Methods are presented for evaluating the performance of programs for the functions $ \Gamma (x) $, $ \ln \Gamma (x) $, and $ \psi (x) $. Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.

entry:
@Article{Cody:1991:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs Related to the Real
                 Gamma Function",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "46--54",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65052",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103153;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/",
  abstract =     "Methods are presented for evaluating the performance
                 of programs for the functions $ \Gamma (x) $, $ \ln
                 \Gamma (x) $, and $ \psi (x) $. Accuracy estimates are
                 based on comparisons using the manipulation theorem.
                 Ideas for checking robustness are also given, and
                 details on specific implementations of test programs
                 are included.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance; reliability",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}


bibtype: article
filename: fparith.bib
label: Cody:1991:UTS
author: W. J. Cody and L. Stoltz
title: The Use of Taylor Series to Test Accuracy of Function Programs
journal: j-TOMS
volume: 17
number: 1
pages: 55--63
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65Y20)
MRnumber: 91m:65053
bibdate: Sun Sep 04 23:36:36 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 23:36:36 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; measurement; performance; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody and L. Stoltz
rawtitle: The Use of {Taylor} Series to Test Accuracy of Function Programs
URL:
http://doi.acm.org/10.1145/103147.103154; http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/

abstract:
This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applications include testing of programs for certain Bessel functions, Dawson's integral, and error functions.

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

rawabstract:
This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applications include testing of programs for certain Bessel functions, Dawson's integral, and error functions.

entry:
@Article{Cody:1991:UTS,
  author =       "W. J. Cody and L. Stoltz",
  title =        "The Use of {Taylor} Series to Test Accuracy of
                 Function Programs",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "55--63",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65053",
  bibdate =      "Sun Sep 04 23:36:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103154;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/",
  abstract =     "This paper discusses the use of local Taylor series
                 expansions for determining the accuracy of computer
                 programs for special functions. The main example is
                 testing of programs for exponential integrals.
                 Additional applications include testing of programs for
                 certain Bessel functions, Dawson's integral, and error
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; verification",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}


bibtype: article
filename: fparith.bib
label: Compan:1991:GPS
author: A. Compan and P. Debaud and V. Delorme and J. A. Francois and H. Mehrez and F. Pecheux
title: GAF: a portable standard-cell floating point adder generator using the CXgen function library
journal: j-MICROPROC-MICROPROG
volume: 32
number: 1
pages: 637--644
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: 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: Microprocessing and Microprogramming
acknowledgement: ack-nhfb
rawauthor: A. Compan and P. Debaud and V. Delorme and J. A. Fran{\c{c}}ois and H. Mehrez and F. Pecheux
rawtitle: {GAF}: a portable standard-cell floating point adder generator using the {CXgen} function library
entry:
@Article{Compan:1991:GPS,
  author =       "A. Compan and P. Debaud and V. Delorme and J. A.
                 Fran{\c{c}}ois and H. Mehrez and F. Pecheux",
  title =        "{GAF}: a portable standard-cell floating point adder
                 generator using the {CXgen} function library",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "32",
  number =       "1",
  pages =        "637--644",
  month =        aug,
  year =         "1991",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
}


bibtype: book
filename: fparith.bib
label: Counihan:1991:F
author: Martin Counihan
title: Fortran 90
publisher: pub-PITMAN
address: pub-PITMAN:adr
pages: 309
year: 1991
ISBN: 0-273-03073-6 OR 0273030736
ISBN13: 978-0-273-03073-7 OR 9780273030737
LCCN: QA76.73.F25 C68 1991
bibdate: Sun May 02 07:48:16 1999
bibtimestamp: 1999.05.02 07:48:16 ???
note: See cite ANSI:ftn92.
acknowledgement: ack-nhfb
rawauthor: Martin Counihan
rawnote: See \cite{ANSI:ftn92}.
rawtitle: {Fortran 90}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

keywords:
Fortran 90 (computer program language); Programming languages; Fortran 90 (Computer program language)

TOC:
1: Introduction 1.1: Fortran 90 / 1 1.2: Programs and Programming / 2 2: What is Fortran 90? 2.1: Program Structure / 5 2.2: Intrinsic Procedures / 6 2.3: Statement Types / 7 2.4: What Fortran 90 Isn't / 7 2.5: New Features in Fortran 90 / 8 Notes / 10 3: Getting Started 3.1: The Character Set / 11 3.2: A Simple Program / 14 3.3: Arithmetic Operators / 18 Exercises 3A / 19 3.4: Names and Other Lexical Tokens / 20 3.5: Fortran Source Form / 21 Exercises 3B / 24 Notes / 25 4: Intrinsic Data Types 4.1: Integers / 26 4.2: Real Numbers / 29 Exercises A / 31 4.3: Simple Form of the Type Declaration Statement / 32 4.4: Kinds Real Numbers / 32 4.5: Complex Numbers / 33 4.6: Logical Data; Logical and Relational Operators / 35 4.7: Characters and Strings / 38 Exercises 4B / 40 Notes / 42 5: Some Intrinsic Procedures 5.1: An Intrinsic Subroutine / 43 5.2: Mathematical Functions / 44 5.3: Numeric Functions / 46 Exercises 5A / 50 Notes / 52 6: More About Characters 6.1: Declaring Character Data / 53 6.2: Character Constants / 54 6.3: Character Operators / 55 6.4: Intrinsic Character Functions / 56 6.5: Substrings / 59 Exercises / 61 Notes / 62 7: Arrays 7.1: Declaring Arrays / 63 7.2: Using Arrays / 65 7.3: Array Constructors / 67 7.4: Array Sections / 68 7.5: Array Sections, Character Strings and Substrings / 70 7.6: Where / 72 7.7: Arrays and Intrinsic Functions / 73 Exercises 7B / 74 8: Execution Control 8.1: The ``CASE'' Construct / 76 8.2: The ``IF'' Construct / 80 Exercises / 81 8.3: The ``DO'' Construct / 82 8.4: Stop / 88 Exercises 8B / 88 Notes / 89 9: Functions and Subroutines (1) 9.1: Functions / 90 Exercises 9A / 93 9.2: Subroutines / 93 9.3: Procedures and Arrays / 96 Exercises 9B / 99 Notes / 100 10: More Intrinsic Procedures; Statement Labels 10.1: Intrinsic Subroutines / 102 10.2: Functions for Use with Arrays / 104 Exercises 10A / 110 10.3: Numeric Inquiry Functions and Floating-Point Manipulation Functions / 110 10.4: Statement Labels and ``GO TO'' / 111 Notes / 114 11: Modules 11.1: Data Modules / 116 Module Procedures / 120 11.3: More About ``USE'' Statements / 124 Exercises / 126 Notes / 127 12: Functions and Subroutines (2) 12.1: Recursive Procedures / 128 Exercises 12A / 130 12.2: Interface Blocks / 131 12.3: Argument Keywords / 132 12.4: More About Arguments: ``PRESENT'' / 133 12.5: Functions / 134 12.6: Operators / 135 12.7: Generic Names / 138 12.8: Parallel Processing / 141 Exercises 12B / 142 Notes / 143 13: The Type Declaration Statement 13.1: General Form of the TDS / 144 13.2: Character Length Selectors / 147 13.3: Attribute Specifications / 149 13.4: Array Specifications / 152 13.5: The Entity Declaration List / 157 13.6: Summary / 158 Exercises 13A / 159 Notes / 161 14: Derived Types 14.1: Derived-Type Definition / 164 14.2: Structure Constructors / 166 14.3: Structure Components / 168 Exercises 14A / 169 14.4: Structures of Structures / 170 Exercises 14B / 171 14.5: Functions and Operators with Derived Types / 172 14.6: Defined Assignment / 174 Exercises 14C / 178 Notes / 180 15: Arrays and Pointers 15.1: Array Element Order, Array Constructors; RESHAPE / 181 15.2: Vector Subscripts / 184 15.3: Allocatable Arrays / 187 Exercises 15A / 190 15.4: LBOUND, SHAPE and SIZE / 190 Exercises 15B / 191 15.5: Simple Pointers / 192 15.6: Pointers as Structures and as Structure Components / 197 15.7: Pointers and Procedures / 204 15.8: Array Pointers / 205 Exercises 15C / 207 Notes / 208 16: Input and Output; Data Format Specifications 16.1: Data Transfer Statements / 209 16.2: The Item List / 210 16.3: List-Directed Input / 212 16.4: List-Directed Output / 216 16.5: Explicit Formats / 217 Exercises 16A / 219 16.6: Data Edit Descriptors and Character Edit Descriptors / 219 16.7: Control Edit Descriptors / 223 Exercises 16B / 225 16.8: Namelists / 226 16.9: Unformatted / 228 16.10: The TRANSFER Function / 229 16.11: Summary / 231 Notes / 232 17: File Handling 17.1: Units, Files and Records / 233 17.2: Opening and Closing Files / 235 17.3: BACKSPACE, ENDFTLE and REWIND / 240 17.4: Control Specifications for / 240 17.5: The ``INQUIRE'' Statement / 242 17.6: Internal Files / 246 Exercises 17A / 248 Notes / 249 18: Bits 18.1: Inside Integers / 250 18.2: Bit Logic / 251 18.3: A Warning / 252 Exercises 18A / 253 19: Programming Conventions and Program Architecture: Putting It All Together 19.1: Coding Conventions / 254 19.2: Towards Fortran 90 / 255 Fortran 90 Recommended Statements / 256 Intrinsic Functions / 257 19.3: Program Unit Structure / 258 19.4: Program Structure / 261 19.5: Final Remarks / 262 Answers to Selected Exercises / 263 Appendices A: Fortran 90 Statements B: Intrinsic Procedures / 286 C: Intrinsic Procedures: Names / 292 D: Argument Keywords in Intrinsic Procedures / 294 E: Edit Descriptors / 297 F: The ASCII Character Set / 301 Index / 304

rawTOC:
1: Introduction \\ 1.1: Fortran 90 / 1 \\ 1.2: Programs and Programming / 2 \\ 2: What is Fortran 90? \\ 2.1: Program Structure / 5 \\ 2.2: Intrinsic Procedures / 6 \\ 2.3: Statement Types / 7 \\ 2.4: What Fortran 90 Isn't / 7 \\ 2.5: New Features in Fortran 90 / 8 \\ Notes / 10 \\ 3: Getting Started \\ 3.1: The Character Set / 11 \\ 3.2: A Simple Program / 14 \\ 3.3: Arithmetic Operators / 18 \\ Exercises 3A / 19 \\ 3.4: Names and Other Lexical Tokens / 20 \\ 3.5: Fortran Source Form / 21 \\ Exercises 3B / 24 \\ Notes / 25 \\ 4: Intrinsic Data Types \\ 4.1: Integers / 26 \\ 4.2: Real Numbers / 29 \\ Exercises A / 31 \\ 4.3: Simple Form of the Type Declaration Statement / 32 \\ 4.4: Kinds Real Numbers / 32 \\ 4.5: Complex Numbers / 33 \\ 4.6: Logical Data; Logical and Relational Operators / 35 \\ 4.7: Characters and Strings / 38 \\ Exercises 4B / 40 \\ Notes / 42 \\ 5: Some Intrinsic Procedures \\ 5.1: An Intrinsic Subroutine / 43 \\ 5.2: Mathematical Functions / 44 \\ 5.3: Numeric Functions / 46 \\ Exercises 5A / 50 \\ Notes / 52 \\ 6: More About Characters \\ 6.1: Declaring Character Data / 53 \\ 6.2: Character Constants / 54 \\ 6.3: Character Operators / 55 \\ 6.4: Intrinsic Character Functions / 56 \\ 6.5: Substrings / 59 \\ Exercises / 61 \\ Notes / 62 \\ 7: Arrays \\ 7.1: Declaring Arrays / 63 \\ 7.2: Using Arrays / 65 \\ 7.3: Array Constructors / 67 \\ 7.4: Array Sections / 68 \\ 7.5: Array Sections, Character Strings and Substrings / 70 \\ 7.6: Where / 72 \\ 7.7: Arrays and Intrinsic Functions / 73 \\ Exercises 7B / 74 \\ 8: Execution Control \\ 8.1: The ``CASE'' Construct / 76 \\ 8.2: The ``IF'' Construct / 80 \\ Exercises / 81 \\ 8.3: The ``DO'' Construct / 82 \\ 8.4: Stop / 88 \\ Exercises 8B / 88 \\ Notes / 89 \\ 9: Functions and Subroutines (1) \\ 9.1: Functions / 90 \\ Exercises 9A / 93 \\ 9.2: Subroutines / 93 \\ 9.3: Procedures and Arrays / 96 \\ Exercises 9B / 99 \\ Notes / 100 \\ 10: More Intrinsic Procedures; Statement Labels \\ 10.1: Intrinsic Subroutines / 102 \\ 10.2: Functions for Use with Arrays / 104 \\ Exercises 10A / 110 \\ 10.3: Numeric Inquiry Functions and Floating-Point Manipulation Functions / 110 \\ 10.4: Statement Labels and ``GO TO'' / 111 \\ Notes / 114 \\ 11: Modules \\ 11.1: Data Modules / 116 \\ Module Procedures / 120 \\ 11.3: More About ``USE'' Statements / 124 \\ Exercises / 126 \\ Notes / 127 \\ 12: Functions and Subroutines (2) \\ 12.1: Recursive Procedures / 128 \\ Exercises 12A / 130 \\ 12.2: Interface Blocks / 131 \\ 12.3: Argument Keywords / 132 \\ 12.4: More About Arguments: ``PRESENT'' / 133 \\ 12.5: Functions / 134 \\ 12.6: Operators / 135 \\ 12.7: Generic Names / 138 \\ 12.8: Parallel Processing / 141 \\ Exercises 12B / 142 \\ Notes / 143 \\ 13: The Type Declaration Statement \\ 13.1: General Form of the TDS / 144 \\ 13.2: Character Length Selectors / 147 \\ 13.3: Attribute Specifications / 149 \\ 13.4: Array Specifications / 152 \\ 13.5: The Entity Declaration List / 157 \\ 13.6: Summary / 158 \\ Exercises 13A / 159 \\ Notes / 161 \\ 14: Derived Types \\ 14.1: Derived-Type Definition / 164 \\ 14.2: Structure Constructors / 166 \\ 14.3: Structure Components / 168 \\ Exercises 14A / 169 \\ 14.4: Structures of Structures / 170 \\ Exercises 14B / 171 \\ 14.5: Functions and Operators with Derived Types / 172 \\ 14.6: Defined Assignment / 174 \\ Exercises 14C / 178 \\ Notes / 180 \\ 15: Arrays and Pointers \\ 15.1: Array Element Order, Array Constructors; RESHAPE / 181 \\ 15.2: Vector Subscripts / 184 \\ 15.3: Allocatable Arrays / 187 \\ Exercises 15A / 190 \\ 15.4: LBOUND, SHAPE and SIZE / 190 \\ Exercises 15B / 191 \\ 15.5: Simple Pointers / 192 \\ 15.6: Pointers as Structures and as Structure Components / 197 \\ 15.7: Pointers and Procedures / 204 \\ 15.8: Array Pointers / 205 \\ Exercises 15C / 207 \\ Notes / 208 \\ 16: Input and Output; Data Format Specifications \\ 16.1: Data Transfer Statements / 209 \\ 16.2: The Item List / 210 \\ 16.3: List-Directed Input / 212 \\ 16.4: List-Directed Output / 216 \\ 16.5: Explicit Formats / 217 \\ Exercises 16A / 219 \\ 16.6: Data Edit Descriptors and Character Edit Descriptors / 219 \\ 16.7: Control Edit Descriptors / 223 \\ Exercises 16B / 225 \\ 16.8: Namelists / 226 \\ 16.9: Unformatted / 228 \\ 16.10: The TRANSFER Function / 229 \\ 16.11: Summary / 231 \\ Notes / 232 \\ 17: File Handling \\ 17.1: Units, Files and Records / 233 \\ 17.2: Opening and Closing Files / 235 \\ 17.3: BACKSPACE, ENDFTLE and REWIND / 240 \\ 17.4: Control Specifications for / 240 \\ 17.5: The ``INQUIRE'' Statement / 242 \\ 17.6: Internal Files / 246 \\ Exercises 17A / 248 \\ Notes / 249 \\ 18: Bits \\ 18.1: Inside Integers / 250 \\ 18.2: Bit Logic / 251 \\ 18.3: A Warning / 252 \\ Exercises 18A / 253 \\ 19: Programming Conventions and Program Architecture: Putting It All Together \\ 19.1: Coding Conventions / 254 \\ 19.2: Towards Fortran 90 / 255 \\ Fortran 90 Recommended Statements / 256 \\ Intrinsic Functions / 257 \\ 19.3: Program Unit Structure / 258 \\ 19.4: Program Structure / 261 \\ 19.5: Final Remarks / 262 \\ Answers to Selected Exercises / 263 \\ Appendices \\ A: Fortran 90 Statements \\ B: Intrinsic Procedures / 286 \\ C: Intrinsic Procedures: Names / 292 \\ D: Argument Keywords in Intrinsic Procedures / 294 \\ E: Edit Descriptors / 297 \\ F: The ASCII Character Set / 301 \\ Index / 304

entry:
@Book{Counihan:1991:F,
  author =       "Martin Counihan",
  title =        "{Fortran 90}",
  publisher =    pub-PITMAN,
  address =      pub-PITMAN:adr,
  pages =        "309",
  year =         "1991",
  ISBN =         "0-273-03073-6",
  ISBN-13 =      "978-0-273-03073-7",
  LCCN =         "QA76.73.F25 C68 1991",
  bibdate =      "Sun May 02 07:48:16 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See \cite{ANSI:ftn92}.",
  acknowledgement = ack-nhfb,
  keywords =     "Fortran 90 (computer program language); Programming
                 languages; {Fortran 90} (Computer program language)",
  libnote =      "Not yet in my library.",
  tableofcontents = "1: Introduction \\
                 1.1: Fortran 90 / 1 \\
                 1.2: Programs and Programming / 2 \\
                 2: What is Fortran 90? \\
                 2.1: Program Structure / 5 \\
                 2.2: Intrinsic Procedures / 6 \\
                 2.3: Statement Types / 7 \\
                 2.4: What Fortran 90 Isn't / 7 \\
                 2.5: New Features in Fortran 90 / 8 \\
                 Notes / 10 \\
                 3: Getting Started \\
                 3.1: The Character Set / 11 \\
                 3.2: A Simple Program / 14 \\
                 3.3: Arithmetic Operators / 18 \\
                 Exercises 3A / 19 \\
                 3.4: Names and Other Lexical Tokens / 20 \\
                 3.5: Fortran Source Form / 21 \\
                 Exercises 3B / 24 \\
                 Notes / 25 \\
                 4: Intrinsic Data Types \\
                 4.1: Integers / 26 \\
                 4.2: Real Numbers / 29 \\
                 Exercises A / 31 \\
                 4.3: Simple Form of the Type Declaration Statement / 32
                 \\
                 4.4: Kinds Real Numbers / 32 \\
                 4.5: Complex Numbers / 33 \\
                 4.6: Logical Data; Logical and Relational Operators /
                 35 \\
                 4.7: Characters and Strings / 38 \\
                 Exercises 4B / 40 \\
                 Notes / 42 \\
                 5: Some Intrinsic Procedures \\
                 5.1: An Intrinsic Subroutine / 43 \\
                 5.2: Mathematical Functions / 44 \\
                 5.3: Numeric Functions / 46 \\
                 Exercises 5A / 50 \\
                 Notes / 52 \\
                 6: More About Characters \\
                 6.1: Declaring Character Data / 53 \\
                 6.2: Character Constants / 54 \\
                 6.3: Character Operators / 55 \\
                 6.4: Intrinsic Character Functions / 56 \\
                 6.5: Substrings / 59 \\
                 Exercises / 61 \\
                 Notes / 62 \\
                 7: Arrays \\
                 7.1: Declaring Arrays / 63 \\
                 7.2: Using Arrays / 65 \\
                 7.3: Array Constructors / 67 \\
                 7.4: Array Sections / 68 \\
                 7.5: Array Sections, Character Strings and Substrings /
                 70 \\
                 7.6: Where / 72 \\
                 7.7: Arrays and Intrinsic Functions / 73 \\
                 Exercises 7B / 74 \\
                 8: Execution Control \\
                 8.1: The ``CASE'' Construct / 76 \\
                 8.2: The ``IF'' Construct / 80 \\
                 Exercises / 81 \\
                 8.3: The ``DO'' Construct / 82 \\
                 8.4: Stop / 88 \\
                 Exercises 8B / 88 \\
                 Notes / 89 \\
                 9: Functions and Subroutines (1) \\
                 9.1: Functions / 90 \\
                 Exercises 9A / 93 \\
                 9.2: Subroutines / 93 \\
                 9.3: Procedures and Arrays / 96 \\
                 Exercises 9B / 99 \\
                 Notes / 100 \\
                 10: More Intrinsic Procedures; Statement Labels \\
                 10.1: Intrinsic Subroutines / 102 \\
                 10.2: Functions for Use with Arrays / 104 \\
                 Exercises 10A / 110 \\
                 10.3: Numeric Inquiry Functions and Floating-Point
                 Manipulation Functions / 110 \\
                 10.4: Statement Labels and ``GO TO'' / 111 \\
                 Notes / 114 \\
                 11: Modules \\
                 11.1: Data Modules / 116 \\
                 Module Procedures / 120 \\
                 11.3: More About ``USE'' Statements / 124 \\
                 Exercises / 126 \\
                 Notes / 127 \\
                 12: Functions and Subroutines (2) \\
                 12.1: Recursive Procedures / 128 \\
                 Exercises 12A / 130 \\
                 12.2: Interface Blocks / 131 \\
                 12.3: Argument Keywords / 132 \\
                 12.4: More About Arguments: ``PRESENT'' / 133 \\
                 12.5: Functions / 134 \\
                 12.6: Operators / 135 \\
                 12.7: Generic Names / 138 \\
                 12.8: Parallel Processing / 141 \\
                 Exercises 12B / 142 \\
                 Notes / 143 \\
                 13: The Type Declaration Statement \\
                 13.1: General Form of the TDS / 144 \\
                 13.2: Character Length Selectors / 147 \\
                 13.3: Attribute Specifications / 149 \\
                 13.4: Array Specifications / 152 \\
                 13.5: The Entity Declaration List / 157 \\
                 13.6: Summary / 158 \\
                 Exercises 13A / 159 \\
                 Notes / 161 \\
                 14: Derived Types \\
                 14.1: Derived-Type Definition / 164 \\
                 14.2: Structure Constructors / 166 \\
                 14.3: Structure Components / 168 \\
                 Exercises 14A / 169 \\
                 14.4: Structures of Structures / 170 \\
                 Exercises 14B / 171 \\
                 14.5: Functions and Operators with Derived Types / 172
                 \\
                 14.6: Defined Assignment / 174 \\
                 Exercises 14C / 178 \\
                 Notes / 180 \\
                 15: Arrays and Pointers \\
                 15.1: Array Element Order, Array Constructors; RESHAPE
                 / 181 \\
                 15.2: Vector Subscripts / 184 \\
                 15.3: Allocatable Arrays / 187 \\
                 Exercises 15A / 190 \\
                 15.4: LBOUND, SHAPE and SIZE / 190 \\
                 Exercises 15B / 191 \\
                 15.5: Simple Pointers / 192 \\
                 15.6: Pointers as Structures and as Structure
                 Components / 197 \\
                 15.7: Pointers and Procedures / 204 \\
                 15.8: Array Pointers / 205 \\
                 Exercises 15C / 207 \\
                 Notes / 208 \\
                 16: Input and Output; Data Format Specifications \\
                 16.1: Data Transfer Statements / 209 \\
                 16.2: The Item List / 210 \\
                 16.3: List-Directed Input / 212 \\
                 16.4: List-Directed Output / 216 \\
                 16.5: Explicit Formats / 217 \\
                 Exercises 16A / 219 \\
                 16.6: Data Edit Descriptors and Character Edit
                 Descriptors / 219 \\
                 16.7: Control Edit Descriptors / 223 \\
                 Exercises 16B / 225 \\
                 16.8: Namelists / 226 \\
                 16.9: Unformatted / 228 \\
                 16.10: The TRANSFER Function / 229 \\
                 16.11: Summary / 231 \\
                 Notes / 232 \\
                 17: File Handling \\
                 17.1: Units, Files and Records / 233 \\
                 17.2: Opening and Closing Files / 235 \\
                 17.3: BACKSPACE, ENDFTLE and REWIND / 240 \\
                 17.4: Control Specifications for / 240 \\
                 17.5: The ``INQUIRE'' Statement / 242 \\
                 17.6: Internal Files / 246 \\
                 Exercises 17A / 248 \\
                 Notes / 249 \\
                 18: Bits \\
                 18.1: Inside Integers / 250 \\
                 18.2: Bit Logic / 251 \\
                 18.3: A Warning / 252 \\
                 Exercises 18A / 253 \\
                 19: Programming Conventions and Program Architecture:
                 Putting It All Together \\
                 19.1: Coding Conventions / 254 \\
                 19.2: Towards Fortran 90 / 255 \\
                 Fortran 90 Recommended Statements / 256 \\
                 Intrinsic Functions / 257 \\
                 19.3: Program Unit Structure / 258 \\
                 19.4: Program Structure / 261 \\
                 19.5: Final Remarks / 262 \\
                 Answers to Selected Exercises / 263 \\
                 Appendices \\
                 A: Fortran 90 Statements \\
                 B: Intrinsic Procedures / 286 \\
                 C: Intrinsic Procedures: Names / 292 \\
                 D: Argument Keywords in Intrinsic Procedures / 294 \\
                 E: Edit Descriptors / 297 \\
                 F: The ASCII Character Set / 301 \\
                 Index / 304",
}


bibtype: article
filename: fparith.bib
label: Cox:1991:TSS
author: Christopher L. Cox and James A. Knisely
title: A tridiagonal system solver for distributed memory parallel processors with vector nodes
journal: j-J-PAR-DIST-COMP
volume: 13
number: 3
pages: 325--331
month: nov
monthnumber: 11
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: Clemson Univ
affiliationaddress: Clemson, SC, USA
corpsource: Department of Math. Sci., Clemson University, SC, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: A Application; P Practical
rawauthor: Christopher L. Cox and James A. Knisely
rawtitle: A tridiagonal system solver for distributed memory parallel processors with vector nodes
keywords:
algebraic routine; algorithm; computer; Computer Programming languages--fortran; Computer Programming--Algorithms; Computer Systems, Digital; Cyclic reduction algorithms; Data Storage, Digital; digital arithmetic; Distributed memories; distributed memory parallel; divide and conquer strategy; Floating Point Systems FPS T-20; FORTRAN; Intel iPSC/2-VX; linear algebra; Mathematical Techniques--Matrix Algebra; mathematics computing; odd-even cyclic reduction; parallel architectures; Parallel Processing; partitioning; performance evaluation; processors; programs; redundancy; scaled speedup; tridiagonal system solver; Tridiagonal systems; Vector nodes; vector nodes; vector processors

entry:
@Article{Cox:1991:TSS,
  author =       "Christopher L. Cox and James A. Knisely",
  title =        "A tridiagonal system solver for distributed memory
                 parallel processors with vector nodes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "13",
  number =       "3",
  pages =        "325--331",
  month =        nov,
  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 =  "Clemson Univ",
  affiliationaddress = "Clemson, SC, USA",
  classification = "721; 722; 723; 921; C4140 (Linear algebra); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods); C5470 (Performance evaluation and testing);
                 C7310 (Mathematics)",
  corpsource =   "Department of Math. Sci., Clemson University, SC,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algebraic routine; algorithm; computer; Computer
                 Programming languages--fortran; Computer
                 Programming--Algorithms; Computer Systems, Digital;
                 Cyclic reduction algorithms; Data Storage, Digital;
                 digital arithmetic; Distributed memories; distributed
                 memory parallel; divide and conquer strategy; Floating
                 Point Systems FPS T-20; FORTRAN; Intel iPSC/2-VX;
                 linear algebra; Mathematical Techniques--Matrix
                 Algebra; mathematics computing; odd-even cyclic
                 reduction; parallel architectures; Parallel Processing;
                 partitioning; performance evaluation; processors;
                 programs; redundancy; scaled speedup; tridiagonal
                 system solver; Tridiagonal systems; Vector nodes;
                 vector nodes; vector processors",
  treatment =    "A Application; P Practical",
}


bibtype: article
filename: fparith.bib
label: Crenshaw:1991:SRS
author: J. W. Crenshaw
title: Square roots are simple?
journal: j-EMBED-SYS-PROG
volume: 4
number: 11
pages: 30--52
month: nov
monthnumber: 11
year: 1991
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Wed Sep 14 19:14:52 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 19:14:52 ???
fjournal: Embedded Systems Programming
acknowledgement: ack-nj
rawauthor: J. W. Crenshaw
rawtitle: Square roots are simple?
entry:
@Article{Crenshaw:1991:SRS,
  author =       "J. W. Crenshaw",
  title =        "Square roots are simple?",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "11",
  pages =        "30--52",
  month =        nov,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Wed Sep 14 19:14:52 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 =     "Embedded Systems Programming",
}


bibtype: article
filename: fparith.bib
label: Davida:1991:FPA
author: George I. Davida and Bruce Litow
title: Fast Parallel Arithmetic via Modular Representation
journal: j-SIAM-J-COMPUT
volume: 20
number: 4
pages: 756--765
month: aug
monthnumber: 8
year: 1991
CODEN: SMJCAT
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
MRclass: 68Q10
MRnumber: 92c:68046
bibdate: Mon Nov 29 11:01:48 MST 2010
bibtimestamp: 2010.11.29 11:01:48 MST
fjournal: SIAM Journal on Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
rawauthor: George I. Davida and Bruce Litow
rawtitle: Fast Parallel Arithmetic via Modular Representation
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/20/4; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Davida:1991:FPA,
  author =       "George I. Davida and Bruce Litow",
  title =        "Fast Parallel Arithmetic via Modular Representation",
  journal =      j-SIAM-J-COMPUT,
  volume =       "20",
  number =       "4",
  pages =        "756--765",
  month =        aug,
  year =         "1991",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68Q10",
  MRnumber =     "92c:68046",
  bibdate =      "Mon Nov 29 11:01:48 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/20/4;
                 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: mastersthesis
filename: fparith.bib
label: Davies:1991:FPS
author: Davies, T. C. (Tudor Craddock)
title: A floating point systolic array processing element using serial communication
type: Thesis (M.Eng.)
school: Royal Military College of Canada
address: Kingston, ON, Canada
pages: 756--765
year: 1991
ISBN: 0-315-60644-4 OR 0315606444
ISBN13: 978-0-315-60644-9 OR 9780315606449
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: 2 microfiches. University Microfilms order no. UMI00285885
series: National Library of Canada = Bibliotheque nationale du Canada; Canadian theses = Theses canadiennes
acknowledgement: ack-nhfb
rawauthor: Davies, T. C. (Tudor Craddock)
rawnote: 2 microfiches. University Microfilms order no. UMI00285885
rawtitle: A floating point systolic array processing element using serial communication
entry:
@MastersThesis{Davies:1991:FPS,
  author =       "Davies, T. C. (Tudor Craddock)",
  title =        "A floating point systolic array processing element
                 using serial communication",
  type =         "Thesis ({M.Eng.})",
  school =       "Royal Military College of Canada",
  address =      "Kingston, ON, Canada",
  year =         "1991",
  ISBN =         "0-315-60644-4",
  ISBN-13 =      "978-0-315-60644-9",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "2 microfiches. University Microfilms order no.
                 UMI00285885",
  series =       "National Library of Canada = Bibliotheque nationale du
                 Canada; Canadian theses = Theses canadiennes",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Davis:1991:CC
author: Warren Davis and Kan Yabumoto
title: A coprocessor for a coprocessor?
journal: j-DDJ
volume: 16
number: 5
pages: 16--28, 84--88
month: may
monthnumber: 5
year: 1991
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Sep 10 09:11:02 MDT 1996
bibtimestamp: 1996.09.10 09:11:02 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
affiliation: Pixelab Inc., Lisle, IL, USA
rawauthor: Warren Davis and Kan Yabumoto
rawtitle: A coprocessor for a coprocessor?
bibsource:
http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib; UnCover database

abstract:
When fast graphics aren't fast enough, the TI 34020 graphics coprocessor employs its own coprocessor -- the 34082 FPU -- for even higher system performance.

keywords:
Built-in graphics-related instructions; Floating point coprocessor; General-purpose microprocessor; Graphics System Processor; Programmable graphics coprocessor; Texas Instruments; TMS34020; TMS34082; Video control circuitry

thesaurus:
Assembly language listings; C listings; Computer graphic equipment; Microprocessor chips; Satellite computers; Texas Instruments computers

rawabstract:
When fast graphics aren't fast enough, the TI 34020 graphics coprocessor employs its own coprocessor -- the 34082 FPU -- for even higher system performance.

entry:
@Article{Davis:1991:CC,
  author =       "Warren Davis and Kan Yabumoto",
  title =        "A coprocessor for a coprocessor?",
  journal =      j-DDJ,
  volume =       "16",
  number =       "5",
  pages =        "16--28, 84--88",
  month =        may,
  year =         "1991",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 09:11:02 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "When fast graphics aren't fast enough, the TI 34020
                 graphics coprocessor employs its own coprocessor -- the
                 34082 FPU -- for even higher system performance.",
  acknowledgement = ack-nhfb,
  affiliation =  "Pixelab Inc., Lisle, IL, USA",
  classification = "C5130 (Microprocessor chips); C5540 (Terminals and
                 graphic displays)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "Built-in graphics-related instructions; Floating point
                 coprocessor; General-purpose microprocessor; Graphics
                 System Processor; Programmable graphics coprocessor;
                 Texas Instruments; TMS34020; TMS34082; Video control
                 circuitry",
  thesaurus =    "Assembly language listings; C listings; Computer
                 graphic equipment; Microprocessor chips; Satellite
                 computers; Texas Instruments computers",
}


bibtype: phdthesis
filename: fparith.bib
label: Deb:1991:BFF
author: Kalyanmoy Deb
title: Binary and floating-point function optimization using messy genetic algorithms
type: Thesis (Ph.D.)
school: Department of Engineering Mechanics, University of Alabama
address: Tuscaloosa, AL, USA
pages: xvii + 166
year: 1991
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: Algorithms.; Combinatorial optimization.
acknowledgement: ack-nhfb
rawauthor: Kalyanmoy Deb
rawtitle: Binary and floating-point function optimization using messy genetic algorithms
entry:
@PhdThesis{Deb:1991:BFF,
  author =       "Kalyanmoy Deb",
  title =        "Binary and floating-point function optimization using
                 messy genetic algorithms",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Engineering Mechanics, University of
                 Alabama",
  address =      "Tuscaloosa, AL, USA",
  pages =        "xvii + 166",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Combinatorial optimization.",
}


bibtype: inproceedings
filename: fparith.bib
label: deLange:1991:DIF
author: Alfons A. J. de Lange and Ed F. Deprettere
crossref: Kornerup:1991:PIS
pages: 272--281
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_Lange.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Alfons A. J. de Lange and Ed F. Deprettere
title:
Design and implementation of a floating-point quasi-systolic general purpose CORDIC rotator for high-rate parallel data and signal processing

rawtitle:
Design and implementation of a floating-point quasi-systolic general purpose {CORDIC} rotator for high-rate parallel data and signal processing

entry:
@InProceedings{deLange:1991:DIF,
  author =       "Alfons A. J. de Lange and Ed F. Deprettere",
  title =        "Design and implementation of a floating-point
                 quasi-systolic general purpose {CORDIC} rotator for
                 high-rate parallel data and signal processing",
  crossref =     "Kornerup:1991:PIS",
  pages =        "272--281",
  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_Lange.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Demmel:1991:OIA
author: James W. Demmel
title: On the odor of IEEE arithmetic
journal: j-NA-DIGEST
volume: 91
number: 39
pages: 272--281
day: 29
month: sep
monthnumber: 9
year: 1991
bibdate: Thu Aug 23 06:19:41 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.23 06:19:41 ???
note: Rebuttal to cite Grcar:1991:IAS.
URL: http://www.netlib.org/na-digest/91/v91n39
fjournal: NA Digest
acknowledgement: ack-nhfb
rawauthor: James W. Demmel
rawnote: Rebuttal to \cite{Grcar:1991:IAS}.
rawtitle: On the odor of {IEEE} arithmetic
entry:
@Article{Demmel:1991:OIA,
  author =       "James W. Demmel",
  title =        "On the odor of {IEEE} arithmetic",
  journal =      j-NA-DIGEST,
  volume =       "91",
  number =       "39",
  day =          "29",
  month =        sep,
  year =         "1991",
  bibdate =      "Thu Aug 23 06:19:41 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Rebuttal to \cite{Grcar:1991:IAS}.",
  URL =          "http://www.netlib.org/na-digest/91/v91n39",
  acknowledgement = ack-nhfb,
  fjournal =     "NA Digest",
}


bibtype: inproceedings
filename: fparith.bib
label: Dongarra:1991:GBP
author: J. J. Dongarra and A. Karp and K. Miura and H. D. Simon
title: Gordon Bell Prize lectures (supercomputer applications)
crossref: IEEE:1991:PSA
pages: 328--337
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, Tennessee University, Knoxville, TN, USA
treatment: G General Review; P Practical
rawauthor: J. J. Dongarra and A. Karp and K. Miura and H. D. Simon
rawtitle: {Gordon Bell Prize} lectures (supercomputer applications)
keywords:
128-node Intel iPSC/860; compiler speedup; Connections Machine; electronic structure; floating point processors; Fortran 77; Fortran 90; grid generation program; parallel processing; partial differential equation; price/performance award; scientific and engineering problems; supercomputers

entry:
@InProceedings{Dongarra:1991:GBP,
  author =       "J. J. Dongarra and A. Karp and K. Miura and H. D.
                 Simon",
  title =        "{Gordon Bell Prize} lectures (supercomputer
                 applications)",
  crossref =     "IEEE:1991:PSA",
  pages =        "328--337",
  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 = "C5440 (Multiprocessor systems and techniques)",
  corpsource =   "Department of Computer Science, Tennessee University,
                 Knoxville, TN, USA",
  keywords =     "128-node Intel iPSC/860; compiler speedup; Connections
                 Machine; electronic structure; floating point
                 processors; Fortran 77; Fortran 90; grid generation
                 program; parallel processing; partial differential
                 equation; price/performance award; scientific and
                 engineering problems; supercomputers",
  sponsororg =   "IEEE; ACM",
  treatment =    "G General Review; P Practical",
}


bibtype: article
filename: fparith.bib
label: Dunham:1991:ABA
author: C. Dunham
title: Applications of Best Approximation
journal: j-SIGNUM
volume: 26
number: 2
pages: 2--10
month: apr
monthnumber: 4
year: 1991
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Sep 1 10:15:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:40 ???
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nj
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J690
rawauthor: C. Dunham
rawtitle: Applications of Best Approximation
entry:
@Article{Dunham:1991:ABA,
  author =       "C. Dunham",
  title =        "Applications of Best Approximation",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "2",
  pages =        "2--10",
  month =        apr,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J690",
}


bibtype: inproceedings
filename: fparith.bib
label: Duprat:1991:NRR
author: Jean Duprat and Yvan Herreros and Sylvanus Kla
title: New redundant representations of complex numbers and vectors
crossref: Kornerup:1991:PIS
pages: 2--9
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_Duprat.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Jean Duprat and Yvan Herreros and Sylvanus Kla
rawtitle: New redundant representations of complex numbers and vectors
entry:
@InProceedings{Duprat:1991:NRR,
  author =       "Jean Duprat and Yvan Herreros and Sylvanus Kla",
  title =        "New redundant representations of complex numbers and
                 vectors",
  crossref =     "Kornerup:1991:PIS",
  pages =        "2--9",
  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_Duprat.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Duprat:1991:WND
author: J. Duprat and Jean-Michel Muller
title: Writing numbers differently for faster calculation
journal: j-TECHNIQUE-SCI-INFORMATIQUES
volume: 10
number: 3
pages: 211--224
year: 1991
CODEN: TTSIDJ
ISSN: 0752-4072, 0264-7419 OR 07524072, 02647419
ISSNL: 0752-4072 OR 07524072
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: Technique et science informatiques : TSI
language: French
acknowledgement: ack-nhfb
affiliation: Ecole Normale Superieure de Lyon, France
thesaurus: Digital arithmetic
rawauthor: J. Duprat and Jean-Michel Muller
rawtitle: Writing numbers differently for faster calculation
abstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

keywords:
Addition; Borrow save; Carry save methods; Cordic algorithm; Floating point arithmetic; Multiplication; Pseudo normalisation; Shifting; Subtraction; Zero

rawabstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

entry:
@Article{Duprat:1991:WND,
  author =       "J. Duprat and Jean-Michel Muller",
  title =        "Writing numbers differently for faster calculation",
  journal =      j-TECHNIQUE-SCI-INFORMATIQUES,
  volume =       "10",
  number =       "3",
  pages =        "211--224",
  month =        "????",
  year =         "1991",
  CODEN =        "TTSIDJ",
  ISSN =         "0752-4072, 0264-7419",
  ISSN-L =       "0752-4072",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Instead of Avizienis' or the carry save methods a
                 borrow save (BS) notation is proposed. Examples are
                 given of BS addition, subtraction, shifting and
                 multiplication with the necessary elementary cells
                 being proposed and circuits for testing zero and sign
                 being described. Floating point arithmetic is
                 explained, involving pseudo normalisation and
                 applications are covered including the Cordic
                 algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Technique et science informatiques : TSI",
  keywords =     "Addition; Borrow save; Carry save methods; Cordic
                 algorithm; Floating point arithmetic; Multiplication;
                 Pseudo normalisation; Shifting; Subtraction; Zero",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic",
}


bibtype: article
filename: fparith.bib
label: Ercegovac:1991:MPM
author: Milos D. Ercegovac and Tomas Lang
journal: j-J-PAR-DIST-COMP
volume: 11
number: 3
pages: 212--221
month: mar
monthnumber: 3
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 California Los Angeles
affiliationaddress: Los Angeles, CA, USA
corpsource: Department of Computer Science, California University, Los Angeles, CA, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Milo{\v{s}} D. Ercegovac and Tomas Lang
title:
Module to perform multiplication, division, and square root in systolic arrays for matrix computations

keywords:
Applications; carry-save; complexity; Computer Programming --- Algorithms; Computers; digital arithmetic; division; matrix algebra; Matrix Computations; matrix computations; module; multiplication; Multiplication/Division/Square Root Module; Normalization; On-The-Fly Conversion; radix-2 divider; result-digit selection; Rounding; signed-digit; square root; Systolic Arrays; systolic arrays

rawtitle:
Module to perform multiplication, division, and square root in systolic arrays for matrix computations

entry:
@Article{Ercegovac:1991:MPM,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "Module to perform multiplication, division, and square
                 root in systolic arrays for matrix computations",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "11",
  number =       "3",
  pages =        "212--221",
  month =        mar,
  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 California Los Angeles",
  affiliationaddress = "Los Angeles, CA, USA",
  classification = "722; 723; 921; C4140 (Linear algebra); C5220
                 (Computer architecture); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Applications; carry-save; complexity; Computer
                 Programming --- Algorithms; Computers; digital
                 arithmetic; division; matrix algebra; Matrix
                 Computations; matrix computations; module;
                 multiplication; Multiplication/Division/Square Root
                 Module; Normalization; On-The-Fly Conversion; radix-2
                 divider; result-digit selection; Rounding;
                 signed-digit; square root; Systolic Arrays; systolic
                 arrays",
  treatment =    "P Practical",
}


bibtype: article
filename: fparith.bib
label: Even:1991:SMM
author: Shimon Even
title: Systolic Modular Multiplication
journal: j-LECT-NOTES-COMP-SCI
volume: 537
pages: 619--??
year: 1991
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:48:02 MST 2002
bibtimestamp: 2002.02.05 11:48:02 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Shimon Even
rawtitle: Systolic Modular Multiplication
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t0537.htm; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/0537/05370619.htm; http://link.springer-ny.com/link/service/series/0558/papers/0537/05370619.pdf

entry:
@Article{Even:1991:SMM,
  author =       "Shimon Even",
  title =        "Systolic Modular Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "537",
  pages =        "619--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:48:02 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0537.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0537/05370619.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0537/05370619.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: fparith.bib
label: Ferguson:1991:AMA
author: Warren E. Ferguson, Jr. and Tom Brightman
title: Accurate and Monotone Approximations of Some Transcendental Functions
crossref: Kornerup:1991:PIS
pages: 237--244
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; 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_Ferguson.pdf
keywords: ARITH-10
acknowledgement: ack-nj
rawauthor: Warren E. {Ferguson, Jr.} and Tom Brightman
rawtitle: Accurate and Monotone Approximations of Some Transcendental Functions
entry:
@InProceedings{Ferguson:1991:AMA,
  author =       "Warren E. {Ferguson, Jr.} and Tom Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  crossref =     "Kornerup:1991:PIS",
  pages =        "237--244",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Ferguson.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Ferguson:1991:SMC
author: Warren E. Ferguson, Jr.
title: Selecting math coprocessors
journal: j-IEEE-SPECTRUM
volume: 28
number: 7
pages: 38--41
month: jul
monthnumber: 7
year: 1991
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.83469
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Thu Sep 01 16:17:34 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.01 16:17:34 ???
fjournal: IEEE Spectrum
keywords: floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Warren E. {Ferguson, Jr.}
rawtitle: Selecting math coprocessors
remark:
Contains performance-comparison tables for Cyrix, Intel, Motorola, and Weitek floating-point coprocessor chips.

entry:
@Article{Ferguson:1991:SMC,
  author =       "Warren E. {Ferguson, Jr.}",
  title =        "Selecting math coprocessors",
  journal =      j-IEEE-SPECTRUM,
  volume =       "28",
  number =       "7",
  pages =        "38--41",
  month =        jul,
  year =         "1991",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.83469",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:17:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "floating-point arithmetic",
  remark =       "Contains performance-comparison tables for Cyrix,
                 Intel, Motorola, and Weitek floating-point coprocessor
                 chips.",
}


bibtype: inproceedings
filename: fparith.bib
label: Fleurkens:1991:HLD
author: H. Fleurkens and R. Tangelder
title: The high level design of the long accumulator chip
crossref: IEEE:1991:PFC
pages: 299--301
year: 1991
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
acknowledgement: ack-nhfb
affiliation: Eindhoven University of Technol., Netherlands
thesaurus: Circuit CAD; Digital arithmetic; Integrated logic circuits; Logic CAD; Parallel architectures
rawauthor: H. Fleurkens and R. Tangelder
rawtitle: The high level design of the long accumulator chip
abstract:
The authors discuss an architecture and its high level description of a long accumulator chip suited for the exact calculation of the inner products of floating point numbers. A highly parallel implementation is developed using eight independent adder stations, which add products to two circular long accumulators. A dispatcher schedules each product to the best available station. To validate this architecture and to calculate its performance, a high level description is created. This description is made with ESCHER+, an interactive schematic entry tool with a built-in simulator. The resulting description showed to be the basis for the further implementation of the chip.

keywords:
Built-in simulator; ESCHER+; Floating point numbers; High level description; High level design; Highly parallel implementation; Inner products calculation; Interactive schematic entry tool; Long accumulator chip

rawabstract:
The authors discuss an architecture and its high level description of a long accumulator chip suited for the exact calculation of the inner products of floating point numbers. A highly parallel implementation is developed using eight independent adder stations, which add products to two circular long accumulators. A dispatcher schedules each product to the best available station. To validate this architecture and to calculate its performance, a high level description is created. This description is made with ESCHER+, an interactive schematic entry tool with a built-in simulator. The resulting description showed to be the basis for the further implementation of the chip.

entry:
@InProceedings{Fleurkens:1991:HLD,
  author =       "H. Fleurkens and R. Tangelder",
  title =        "The high level design of the long accumulator chip",
  crossref =     "IEEE:1991:PFC",
  pages =        "299--301",
  year =         "1991",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors discuss an architecture and its high level
                 description of a long accumulator chip suited for the
                 exact calculation of the inner products of floating
                 point numbers. A highly parallel implementation is
                 developed using eight independent adder stations, which
                 add products to two circular long accumulators. A
                 dispatcher schedules each product to the best available
                 station. To validate this architecture and to calculate
                 its performance, a high level description is created.
                 This description is made with ESCHER+, an interactive
                 schematic entry tool with a built-in simulator. The
                 resulting description showed to be the basis for the
                 further implementation of the chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Eindhoven University of Technol., Netherlands",
  classification = "B1130B (Computer-aided circuit analysis and design);
                 B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5210B (Computer-aided logic design); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods); C7410D (Electronic engineering)",
  keywords =     "Built-in simulator; ESCHER+; Floating point numbers;
                 High level description; High level design; Highly
                 parallel implementation; Inner products calculation;
                 Interactive schematic entry tool; Long accumulator
                 chip",
  thesaurus =    "Circuit CAD; Digital arithmetic; Integrated logic
                 circuits; Logic CAD; Parallel architectures",
}


bibtype: article
filename: fparith.bib
label: Fossmeier:1991:ALH
author: R. Foss meier
journal: j-COMPUTING
volume: 46
number: 2
pages: 175--182
month: jun
monthnumber: 6
year: 1991
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65G99
MRnumber: 92e:65064
bibdate: Tue Oct 12 16:33:42 MDT 1999
bibtimestamp: 1999.10.12 16:33:42 MDT
fjournal: Computing
language: German
acknowledgement: ack-nhfb
affiliation: Inst. fur Inf., Tech. University of Munchen, Germany
journalURL: http://link.springer.com/journal/607
journalabr: Comput Vienna New York
thesaurus: Number theory; Numerical analysis
rawauthor: R. F{\"o}{\ss}meier
title:
Zur Axiomatisierung logarithmischer und halblogarithmischer Zahlensysteme. (German) [On the axiomatization of logarithmic and semi-logarithmic number systems]

bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database; OCLC Contents1st database

abstract:
In the history of numerical analysis there have been various approaches to gain stricter control of numerical computation by axiomatization of approximative arithmetic systems. In the case of floating-point-like systems, the limitations to this approach originate essentially in the fact that addition is not associative. By suitably weakening the axiomatic system of the real numbers the author arrives at a system which can be fulfilled by approximative arithmetic structures. Comparisons show that structures fulfilling this system cannot be arbitrarily distant from reasonable approximative structures. This shows that it is possible to describe approximative structures by approximations of the laws of the original structure.

keywords:
Approximative arithmetic structures; Axiomatization; computers, digital --- Computational Methods; Floating-Point Arithmetic; Logarithmic; mathematical techniques; Number systems; Number Systems; Numerical analysis; Semi-logarithmic number systems

rawabstract:
In the history of numerical analysis there have been various approaches to gain stricter control of numerical computation by axiomatization of approximative arithmetic systems. In the case of floating-point-like systems, the limitations to this approach originate essentially in the fact that addition is not associative. By suitably weakening the axiomatic system of the real numbers the author arrives at a system which can be fulfilled by approximative arithmetic structures. Comparisons show that structures fulfilling this system cannot be arbitrarily distant from reasonable approximative structures. This shows that it is possible to describe approximative structures by approximations of the laws of the original structure.

rawtitle:
{Zur Axiomatisierung logarithmischer und halblogarithmischer Zahlensysteme}. ({German}) [{On} the axiomatization of logarithmic and semi-logarithmic number systems]

entry:
@Article{Fossmeier:1991:ALH,
  author =       "R. F{\"o}{\ss}meier",
  title =        "{Zur Axiomatisierung logarithmischer und
                 halblogarithmischer Zahlensysteme}. ({German}) [{On}
                 the axiomatization of logarithmic and semi-logarithmic
                 number systems]",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "2",
  pages =        "175--182",
  month =        jun,
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G99",
  MRnumber =     "92e:65064",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  abstract =     "In the history of numerical analysis there have been
                 various approaches to gain stricter control of
                 numerical computation by axiomatization of
                 approximative arithmetic systems. In the case of
                 floating-point-like systems, the limitations to this
                 approach originate essentially in the fact that
                 addition is not associative. By suitably weakening the
                 axiomatic system of the real numbers the author arrives
                 at a system which can be fulfilled by approximative
                 arithmetic structures. Comparisons show that structures
                 fulfilling this system cannot be arbitrarily distant
                 from reasonable approximative structures. This shows
                 that it is possible to describe approximative
                 structures by approximations of the laws of the
                 original structure.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. f{\"u}r Inf., Tech. University of Munchen,
                 Germany",
  classification = "723; 921; C4100 (Numerical analysis)",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Approximative arithmetic structures; Axiomatization;
                 computers, digital --- Computational Methods;
                 Floating-Point Arithmetic; Logarithmic; mathematical
                 techniques; Number systems; Number Systems; Numerical
                 analysis; Semi-logarithmic number systems",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Number theory; Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Fossmeier:1991:ALS
author: R. Fossmeier
title: On the axiomatization of logarithmic and semi-logarithmic number systems
journal: j-COMPUTING
volume: 46
number: 2
pages: 175--182
year: 1991
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
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: Computing: Archiv fur informatik und numerik
language: German
acknowledgement: ack-nhfb
affiliation: Inst. fur Inf., Tech. University of Munchen, Germany
journalURL: http://link.springer.com/journal/607
thesaurus: Number theory; Numerical analysis
rawauthor: R. Fossmeier
rawtitle: On the axiomatization of logarithmic and semi-logarithmic number systems
abstract:
In the history of numerical analysis there have been various approaches to gain stricter control of numerical computation by axiomatization of approximative arithmetic systems. In the case of floating-point-like systems, the limitations to this approach originate essentially in the fact that addition is not associative. By suitably weakening the axiomatic system of the real numbers the author arrives at a system which can be fulfilled by approximative arithmetic structures. Comparisons show that structures fulfilling this system cannot be arbitrarily distant from reasonable approximative structures. This shows that it is possible to describe approximative structures by approximations of the laws of the original structure.

keywords:
Approximative arithmetic structures; Axiomatization; Logarithmic; Number systems; Numerical analysis; Semi-logarithmic number systems

entry:
@Article{Fossmeier:1991:ALS,
  author =       "R. Fossmeier",
  title =        "On the axiomatization of logarithmic and
                 semi-logarithmic number systems",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "2",
  pages =        "175--182",
  month =        "????",
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the history of numerical analysis there have been
                 various approaches to gain stricter control of
                 numerical computation by axiomatization of
                 approximative arithmetic systems. In the case of
                 floating-point-like systems, the limitations to this
                 approach originate essentially in the fact that
                 addition is not associative. By suitably weakening the
                 axiomatic system of the real numbers the author arrives
                 at a system which can be fulfilled by approximative
                 arithmetic structures. Comparisons show that structures
                 fulfilling this system cannot be arbitrarily distant
                 from reasonable approximative structures. This shows
                 that it is possible to describe approximative
                 structures by approximations of the laws of the
                 original structure.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Inf., Tech. University of Munchen, Germany",
  classification = "C4100 (Numerical analysis)",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Approximative arithmetic structures; Axiomatization;
                 Logarithmic; Number systems; Numerical analysis;
                 Semi-logarithmic number systems",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Number theory; Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Foster:1991:PM
author: Kenneth R. Foster
title: Prepackaged math
journal: j-IEEE-SPECTRUM
volume: 28
number: 11
pages: 44--50
month: nov
monthnumber: 11
year: 1991
CODEN: IEESAM
DOI: https://doi.org/10.1109/6.99016
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Wed Jan 15 16:15:28 2020
bibtimestamp: 2020.01.15 16:15:28 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Kenneth R. Foster
rawtitle: Prepackaged math
bibsource:
https://www.math.utah.edu/pub/tex/bib/axiom.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib; https://www.math.utah.edu/pub/tex/bib/macsyma.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib

keywords:
Chemical analysis; Data engineering; Data visualization; Differential equations; Graphics; Hard disks; manipulation; mathematical problems; mathematics computing; matrices; matrix algebra; Packaging; Personal communication networks; software packages; Software packages; Workstations

entry:
@Article{Foster:1991:PM,
  author =       "Kenneth R. Foster",
  title =        "Prepackaged math",
  journal =      j-IEEE-SPECTRUM,
  volume =       "28",
  number =       "11",
  pages =        "44--50",
  month =        nov,
  year =         "1991",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.99016",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 16:15:28 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Chemical analysis; Data engineering; Data
                 visualization; Differential equations; Graphics; Hard
                 disks; manipulation; mathematical problems; mathematics
                 computing; matrices; matrix algebra; Packaging;
                 Personal communication networks; software packages;
                 Software packages; Workstations",
}


bibtype: inproceedings
filename: fparith.bib
label: Frougny:1991:RNN
author: Christiane Frougny
title: Representation of numbers in nonclassical numeration systems
crossref: Kornerup:1991:PIS
pages: 17--21
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_Frougny.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Christiane Frougny
rawtitle: Representation of numbers in nonclassical numeration systems
entry:
@InProceedings{Frougny:1991:RNN,
  author =       "Christiane Frougny",
  title =        "Representation of numbers in nonclassical numeration
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "17--21",
  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_Frougny.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Gal:1991:AEM
author: Shmuel Gal and Boris Bachelis
title: An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard
journal: j-TOMS
volume: 17
number: 1
pages: 26--45
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65-04 65D15)
MRnumber: 92a:65069
bibdate: Sun Sep 04 23:33:02 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 23:33:02 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; correct rounding; floating-point arithmetic; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Shmuel Gal and Boris Bachelis
rawtitle: An Accurate Elementary Mathematical Library for the {IEEE} Floating Point Standard
URL:
http://doi.acm.org/10.1145/103147.103151; http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/

abstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values.par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation.

rawabstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values.\par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

entry:
@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103151;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument
                 values.\par

                 Our main idea in the accurate tables method is to use
                 ``nonstandard tables,'' which are different from the
                 natural tables of equally spaced points in which the
                 rounding error prevents obtaining last bit accuracy. In
                 order to achieve a small error we use the following
                 idea: Perturb the original, equally spaced, points in
                 such a way that the table value (or tables values in
                 case we need several tables) will be very close to
                 numbers which can be exactly represented by the
                 computer (much closer than the usual double precision
                 representation). Thus we were able to control the error
                 introduced by the computer representation of real
                 numbers and extended the accuracy without actually
                 using extended precision arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; correct rounding; floating-point
                 arithmetic; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation.",
}


bibtype: inproceedings
filename: fparith.bib
label: Gamberger:1991:NAI
author: Dragan Gamberger
title: New approach to integer division in residue number systems
crossref: Kornerup:1991:PIS
pages: 84--91
year: 1991
DOI: https://doi.org/10.1109/ARITH.1991.145538
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Gamberger.pdf
keywords: ARITH-10; residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Dragan Gamberger
rawtitle: New approach to integer division in residue number systems
entry:
@InProceedings{Gamberger:1991:NAI,
  author =       "Dragan Gamberger",
  title =        "New approach to integer division in residue number
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "84--91",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145538",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Gamberger.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; residue arithmetic; residue number system",
  summary =      "A novel division algorithm that is especially
                 appropriate for residue number systems (RNSs) is
                 presented. It makes use of the fact that the
                 multiplicative inverse element of a divisor which is
                 relatively prime to system moduli can be easily
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gladshtein:1991:MDD
author: M. A. Gladshtein
title: A method of designing a decimal arithmetic processor
journal: j-AUTO-CTL-COMP-SCI
volume: 25
number: 6
pages: 51--56
year: 1991
CODEN: ACCSCE
ISSN: 0132-4160 OR 01324160
ISSNL: 0146-4116 OR 01464116
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Automatic Control and Computer Sciences
remark: English translation of: Avtomatika i Vychislitel'naya Tekhnika
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic; Microprocessor chips
rawauthor: M. A. Gladshtein
rawtitle: A method of designing a decimal arithmetic processor
abstract:
The advantages and drawbacks of binary numeric coding in digital computers are considered. This type of coding has is shown to be ineffective in processing large data arrays especially when represented in the floating-point form. Also, the low efficiency of conventionally employed decimal computational procedures using the so-called corrections is noted. It is proposed, in designing digital computers, to renounce the principle of binary computations in favor of decimal operations on the basis of stored addition and multiplication tables using binary-decimal numeric coding. A version of circuit design for a decimal processor, algorithms and microprograms for addition and multiplication operations are described. Advantages inherent in the method proposed are analyzed. (10 Refs.)

keywords:
Addition tables; BCD code; Binary numeric coding; Binary-decimal numeric coding; Circuit design; Decimal arithmetic processor; decimal floating-point arithmetic; Decimal operations; Digital computers; Microprograms; Multiplication tables

rawabstract:
The advantages and drawbacks of binary numeric coding in digital computers are considered. This type of coding has is shown to be ineffective in processing large data arrays especially when represented in the floating-point form. Also, the low efficiency of conventionally employed decimal computational procedures using the so-called corrections is noted. It is proposed, in designing digital computers, to renounce the principle of binary computations in favor of decimal operations on the basis of stored addition and multiplication tables using binary-decimal numeric coding. A version of circuit design for a decimal processor, algorithms and microprograms for addition and multiplication operations are described. Advantages inherent in the method proposed are analyzed. (10 Refs.)

entry:
@Article{Gladshtein:1991:MDD,
  author =       "M. A. Gladshtein",
  title =        "A method of designing a decimal arithmetic processor",
  journal =      j-AUTO-CTL-COMP-SCI,
  volume =       "25",
  number =       "6",
  pages =        "51--56",
  month =        "????",
  year =         "1991",
  CODEN =        "ACCSCE",
  ISSN =         "0132-4160",
  ISSN-L =       "0146-4116",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The advantages and drawbacks of binary numeric coding
                 in digital computers are considered. This type of
                 coding has is shown to be ineffective in processing
                 large data arrays especially when represented in the
                 floating-point form. Also, the low efficiency of
                 conventionally employed decimal computational
                 procedures using the so-called corrections is noted. It
                 is proposed, in designing digital computers, to
                 renounce the principle of binary computations in favor
                 of decimal operations on the basis of stored addition
                 and multiplication tables using binary-decimal numeric
                 coding. A version of circuit design for a decimal
                 processor, algorithms and microprograms for addition
                 and multiplication operations are described. Advantages
                 inherent in the method proposed are analyzed. (10
                 Refs.)",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Automatic Control and Computer Sciences",
  keywords =     "Addition tables; BCD code; Binary numeric coding;
                 Binary-decimal numeric coding; Circuit design; Decimal
                 arithmetic processor; decimal floating-point
                 arithmetic; Decimal operations; Digital computers;
                 Microprograms; Multiplication tables",
  pubcountry =   "Latvia",
  remark =       "English translation of: Avtomatika i Vychislitel'naya
                 Tekhnika",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}


bibtype: article
filename: fparith.bib
label: Goldberg:1991:CWE
author: David Goldberg
title: Corrigendum: ``What Every Computer Scientist Should Know About Floating-Point Arithmetic''
journal: j-COMP-SURV
volume: 23
number: 3
pages: 413--413
month: sep
monthnumber: 9
year: 1991
CODEN: CMSVAN
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Sun Sep 25 09:58:43 1994
bibtimestamp: 1994.09.25 09:58:43 ???
note: See cite Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW.
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: David Goldberg
rawnote: See \cite{Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW}.
rawtitle: Corrigendum: {``What Every Computer Scientist Should Know About Floating-Point Arithmetic''}
bibsource:
https://www.math.utah.edu/pub/tex/bib/compsurv.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Goldberg:1991:CWE,
  author =       "David Goldberg",
  title =        "Corrigendum: {``What Every Computer Scientist Should
                 Know About Floating-Point Arithmetic''}",
  journal =      j-COMP-SURV,
  volume =       "23",
  number =       "3",
  pages =        "413--413",
  month =        sep,
  year =         "1991",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Sun Sep 25 09:58:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}


bibtype: article
filename: fparith.bib
label: Goldberg:1991:WEC
author: David Goldberg
title: What Every Computer Scientist Should Know About Floating-Point Arithmetic
journal: j-COMP-SURV
volume: 23
number: 1
pages: 5--48
month: mar
monthnumber: 3
year: 1991
CODEN: CMSVAN
DOI: https://doi.org/10.1145/103162.103163
ISSN: 0360-0300 (print), 1557-7341 (electronic) OR 03600300 (print), 15577341 (electronic)
ISSNL: 0360-0300 OR 03600300
bibdate: Thu Jun 19 09:40:16 MDT 2008
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.06.19 09:40:16 MDT
note: See also cite Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW.
URL: http://www.acm.org/pubs/toc/Abstracts/0360-0300/103163.html
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
affiliation: Xerox Palo Alto Res. Center, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
thesaurus: digital arithmetic; roundoff errors
rawauthor: David Goldberg
rawnote: See also \cite{Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW}.
rawtitle: What Every Computer Scientist Should Know About Floating-Point Arithmetic
abstract:
Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with examples of how computer system builders can better support floating point.

keywords:
algorithms; compilers; computer scientist; computer systems; denormalized number; design; exception; floating-point; floating-point accelerators; floating-point algorithms; floating-point datatype; floating-point exceptions; floating-point representation; floating-point standard; gradual underflow; guard digit; IEEE floating-point standard; languages; NaN; operating system; overflow; PCs; relative error; rounding error; rounding mode; standardization; supercomputers; ulp; underflow

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf K.1: Computing Milieux, THE COMPUTER INDUSTRY, Standards. bf C.0: Computer Systems Organization, GENERAL, Instruction set design. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with examples of how computer system builders can better support floating point.

entry:
@Article{Goldberg:1991:WEC,
  author =       "David Goldberg",
  title =        "What Every Computer Scientist Should Know About
                 Floating-Point Arithmetic",
  journal =      j-COMP-SURV,
  volume =       "23",
  number =       "1",
  pages =        "5--48",
  month =        mar,
  year =         "1991",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/103162.103163",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:40:16 MDT 2008",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also
                 \cite{Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW}.",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0360-0300/103163.html",
  abstract =     "Floating-point arithmetic is considered an esoteric
                 subject by many people. This is rather surprising,
                 because floating-point is ubiquitous in computer
                 systems: almost every language has a floating-point
                 datatype; computers from PCs to supercomputers have
                 floating-point accelerators; most compilers will be
                 called upon to compile floating-point algorithms from
                 time to time; and virtually every operating system must
                 respond to floating-point exceptions such as overflow.
                 This paper presents a tutorial on the aspects of
                 floating-point that have a direct impact on designers
                 of computer systems. It begins with background on
                 floating-point representation and rounding error,
                 continues with a discussion of the IEEE floating-point
                 standard, and concludes with examples of how computer
                 system builders can better support floating point.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Xerox Palo Alto Res. Center, CA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "algorithms; compilers; computer scientist; computer
                 systems; denormalized number; design; exception;
                 floating-point; floating-point accelerators;
                 floating-point algorithms; floating-point datatype;
                 floating-point exceptions; floating-point
                 representation; floating-point standard; gradual
                 underflow; guard digit; IEEE floating-point standard;
                 languages; NaN; operating system; overflow; PCs;
                 relative error; rounding error; rounding mode;
                 standardization; supercomputers; ulp; underflow",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf K.1}:
                 Computing Milieux, THE COMPUTER INDUSTRY, Standards.
                 {\bf C.0}: Computer Systems Organization, GENERAL,
                 Instruction set design. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "digital arithmetic; roundoff errors",
}


bibtype: techreport
filename: fparith.bib
label: Golubev:1991:FPM
author: Yu. F. Golubev and I. A. Seregin and R. Z. Khaui rullin
type: Inst. Prikl. Mat. Preprint
number: 50
institution: Akad. Nauk SSSR
pages: 28
year: 1991
MRclass: 65K10 (49N55 70-08 70Q05)
MRnumber: 166 839
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
language: Russian
acknowledgement: ack-nhfb
rawauthor: Yu. F. Golubev and I. A. Seregin and R. Z. Kha{\u\i}rullin
title:
The floating point method in problems of the optimization of motion during the descent of a spacecraft into the atmosphere. (Russian)

rawtitle:
The floating point method in problems of the optimization of motion during the descent of a spacecraft into the atmosphere. ({Russian})

entry:
@TechReport{Golubev:1991:FPM,
  author =       "Yu. F. Golubev and I. A. Seregin and R. Z.
                 Kha{\u\i}rullin",
  title =        "The floating point method in problems of the
                 optimization of motion during the descent of a
                 spacecraft into the atmosphere. ({Russian})",
  type =         "{Inst. Prikl. Mat.} Preprint",
  number =       "50",
  institution =  "Akad. Nauk SSSR",
  pages =        "28",
  year =         "1991",
  MRclass =      "65K10 (49N55 70-08 70Q05)",
  MRnumber =     "166 839",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: fparith.bib
label: Gonnella:1991:ACF
author: J. Gonnella
title: The application of core functions to residue number systems
journal: j-IEEE-TRANS-SIG-PROC
volume: 39
number: 1
pages: 69--75
month: jan
monthnumber: 1
year: 1991
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.80766
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2655
fjournal: IEEE Transactions on Signal Processing
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: J. Gonnella
rawtitle: The application of core functions to residue number systems
entry:
@Article{Gonnella:1991:ACF,
  author =       "J. Gonnella",
  title =        "The application of core functions to residue number
                 systems",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "1",
  pages =        "69--75",
  month =        jan,
  year =         "1991",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.80766",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2655",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A theory of core functions is presented, and the
                 application of this theory to the difficult residue
                 number system (RNS) operations is described. Potential
                 applications for special-purpose core-based RNS
                 processors include adaptive array processing,
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gotze:1991:SRD
author: J. Gotze and U. Schwiegelshohn
journal: j-SIAM-J-SCI-STAT-COMP
volume: 12
number: 4
pages: 800--807
month: jul
monthnumber: 7
year: 1991
CODEN: SIJCD4
ISSN: 0196-5204 OR 01965204
MRclass: 65F20 (65F25)
MRnumber: 92a:65125
bibdate: Sat Oct 24 13:20:45 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.10.24 13:20:45 MDT
fjournal: SIAM Journal on Scientific and Statistical Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/loi/sijcd4
rawauthor: J. G{\"o}tze and U. Schwiegelshohn
title:
A Square Root and Division Free Givens Rotation for Solving Least Squares Problems on Systolic Arrays

rawtitle:
A Square Root and Division Free {Givens} Rotation for Solving Least Squares Problems on Systolic Arrays

entry:
@Article{Gotze:1991:SRD,
  author =       "J. G{\"o}tze and U. Schwiegelshohn",
  title =        "A Square Root and Division Free {Givens} Rotation for
                 Solving Least Squares Problems on Systolic Arrays",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "12",
  number =       "4",
  pages =        "800--807",
  month =        jul,
  year =         "1991",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65F20 (65F25)",
  MRnumber =     "92a:65125",
  bibdate =      "Sat Oct 24 13:20:45 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
}


bibtype: article
filename: fparith.bib
label: Grcar:1991:IAS
author: Joe Grcar
title: IEEE Arithmetic Stinks
journal: j-NA-DIGEST
volume: 91
number: 33
pages: 800--807
day: 18
month: aug
monthnumber: 8
year: 1991
bibdate: Thu Aug 23 06:22:13 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.23 06:22:13 ???
note: See rebuttal cite Demmel:1991:OIA.
URL: http://www.netlib.org/na-digest/91/v91n33
fjournal: NA Digest
acknowledgement: ack-nhfb
rawauthor: Joe Grcar
rawnote: See rebuttal \cite{Demmel:1991:OIA}.
rawtitle: {IEEE} Arithmetic Stinks
entry:
@Article{Grcar:1991:IAS,
  author =       "Joe Grcar",
  title =        "{IEEE} Arithmetic Stinks",
  journal =      j-NA-DIGEST,
  volume =       "91",
  number =       "33",
  day =          "18",
  month =        aug,
  year =         "1991",
  bibdate =      "Thu Aug 23 06:22:13 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See rebuttal \cite{Demmel:1991:OIA}.",
  URL =          "http://www.netlib.org/na-digest/91/v91n33",
  acknowledgement = ack-nhfb,
  fjournal =     "NA Digest",
}


bibtype: article
filename: fparith.bib
label: Griffin:1991:REA
author: C. Griffin and P. Rao and F. Taylor
title: Roundoff error analysis of the discrete Wigner distribution using fixed-point arithmetic
journal: j-IEEE-TRANS-SIG-PROC
volume: 39
number: 9
pages: 2096--2098
month: sep
monthnumber: 9
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: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: C. Griffin and P. Rao and F. Taylor
rawtitle: Roundoff error analysis of the discrete {Wigner} distribution using fixed-point arithmetic
entry:
@Article{Griffin:1991:REA,
  author =       "C. Griffin and P. Rao and F. Taylor",
  title =        "Roundoff error analysis of the discrete {Wigner}
                 distribution using fixed-point arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "9",
  pages =        "2096--2098",
  month =        sep,
  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 =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The issue of roundoff noise effects in the
                 implementation of the discrete Wigner distribution
                 using fixed-point arithmetic is addressed. The
                 sign-magnitude number representation is assumed
                 throughout the analysis. The measure of roundoff noise
                 \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Gusev:1991:NCS
author: A. V. Gusev and I. V. Melezhnikov
title: Noise in a Constant-Current SQUID with a Floating Operating Point
journal: j-TELECOMM-RADIO-ENG
volume: 46
number: 8
pages: 125--127
year: 1991
CODEN: TCREAG
ISSN: 0040-2508 (print), 1943-6009 (electronic) OR 00402508 (print), 19436009 (electronic)
ISSNL: 0040-2508 OR 00402508
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: Telecommunications and Radio Engineering
acknowledgement: ack-nhfb
rawauthor: A. V. Gusev and I. V. Melezhnikov
rawtitle: Noise in a Constant-Current {SQUID} with a Floating Operating Point
entry:
@Article{Gusev:1991:NCS,
  author =       "A. V. Gusev and I. V. Melezhnikov",
  title =        "Noise in a Constant-Current {SQUID} with a Floating
                 Operating Point",
  journal =      j-TELECOMM-RADIO-ENG,
  volume =       "46",
  number =       "8",
  pages =        "125--127",
  year =         "1991",
  CODEN =        "TCREAG",
  ISSN =         "0040-2508 (print), 1943-6009 (electronic)",
  ISSN-L =       "0040-2508",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Telecommunications and Radio Engineering",
}


bibtype: inproceedings
filename: fparith.bib
label: Guyot:1991:OAV
author: Alain Guyot
title: OCAPI: Architecture of a VLSI Coprocessor for the GCD and the Extended GCD of Large Numbers
crossref: Kornerup:1991:PIS
pages: 226--231
year: 1991
bibdate: Sat Nov 17 08:46:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.17 08:46:25 ???
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Guyot.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Alain Guyot
rawtitle: {OCAPI}: Architecture of a {VLSI} Coprocessor for the {GCD} and the Extended {GCD} of Large Numbers
entry:
@InProceedings{Guyot:1991:OAV,
  author =       "Alain Guyot",
  title =        "{OCAPI}: Architecture of a {VLSI} Coprocessor for the
                 {GCD} and the Extended {GCD} of Large Numbers",
  crossref =     "Kornerup:1991:PIS",
  pages =        "226--231",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Guyot.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Hamza:1991:MBD
author: K. M. Hamza and M. A. H. Abdul-Karim
title: Microprocessor Based Direct Square Root Extractor
journal: Modelling
volume: 34
number: 1
pages: 45--48
year: 1991
bibdate: Thu Sep 1 10:15:42 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:42 ???
acknowledgement: ack-nj
rawauthor: K. M. Hamza and M. A. H. Abdul-Karim
rawtitle: Microprocessor Based Direct Square Root Extractor
entry:
@Article{Hamza:1991:MBD,
  author =       "K. M. Hamza and M. A. H. Abdul-Karim",
  title =        "Microprocessor Based Direct Square Root Extractor",
  journal =      "Modelling",
  volume =       "34",
  number =       "1",
  pages =        "45--48",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:42 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: Heidtmann:1991:ASA
author: K. D. Heidtmann
title: Arithmetic spectrum applied to fault detection for combinational networks
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 3
pages: 320--324
month: mar
monthnumber: 3
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.76409
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=76409
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: K. D. Heidtmann
rawtitle: Arithmetic spectrum applied to fault detection for combinational networks
entry:
@Article{Heidtmann:1991:ASA,
  author =       "K. D. Heidtmann",
  title =        "Arithmetic spectrum applied to fault detection for
                 combinational networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "3",
  pages =        "320--324",
  month =        mar,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.76409",
  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 =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=76409",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: mastersthesis
filename: fparith.bib
label: Holmes:1991:FSD
author: Ian Holmes
title: A feasibility study into the design of a 64-bit floating point processor
type: Thesis (M.Sc. in Electronics)
school: University of Southampton, Department of Electronics and Computer Science
address: Southampton, UK
pages: 320--324
year: 1991
bibdate: Thu May 09 08:35:32 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:35:32 ???
acknowledgement: ack-nhfb
rawauthor: Ian Holmes
rawtitle: A feasibility study into the design of a 64-bit floating point processor
entry:
@MastersThesis{Holmes:1991:FSD,
  author =       "Ian Holmes",
  title =        "A feasibility study into the design of a 64-bit
                 floating point processor",
  type =         "Thesis ({M.Sc. in Electronics})",
  school =       "University of Southampton, Department of Electronics
                 and Computer Science",
  address =      "Southampton, UK",
  year =         "1991",
  bibdate =      "Thu May 09 08:35:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Horiguchi:1991:HFN
author: Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki Kajitori
title: Hamada Floating-Point Numbers and Real Numbers
journal: j-ADV-SOFT-SCI-TECH
volume: 2
pages: 123--??
year: 1991
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 and Tsutomu Tayama and Kazuaki Kajitori
rawtitle: {Hamada} Floating-Point Numbers and Real Numbers
entry:
@Article{Horiguchi:1991:HFN,
  author =       "Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki
                 Kajitori",
  title =        "{Hamada} Floating-Point Numbers and Real Numbers",
  journal =      j-ADV-SOFT-SCI-TECH,
  volume =       "2",
  number =       "??",
  pages =        "123--??",
  year =         "1991",
  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: article
filename: fparith.bib
label: Horiguchi:1991:PEP
author: Susumu Horiguchi and Takeo Nakada
title: Performance Evaluation of Parallel Fast Fourier Transform on a Multiprocessor Workstation
journal: j-J-PAR-DIST-COMP
volume: 12
number: 2
pages: 158--163
month: jun
monthnumber: 6
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 17:13:17 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.04.12 17:13:17 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
corpsource: Department of Inf. Sci., Tohoku University, Sendai, Japan
journalURL: http://www.sciencedirect.com/science/journal/07437315
treatment: P Practical
rawauthor: Susumu Horiguchi and Takeo Nakada
rawtitle: Performance Evaluation of Parallel Fast {Fourier} Transform on a Multiprocessor Workstation
keywords:
algorithms; cache protocols; fast Fourier transform; fast Fourier transforms; FFT; floating-; multiprocess operating system; multiprocessing systems; multiprocessor workstation; multithread operating system; operating systems; parallel; parallel FFT; performance; performance evaluation; point coprocessors

entry:
@Article{Horiguchi:1991:PEP,
  author =       "Susumu Horiguchi and Takeo Nakada",
  title =        "Performance Evaluation of Parallel Fast {Fourier}
                 Transform on a Multiprocessor Workstation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "12",
  number =       "2",
  pages =        "158--163",
  month =        jun,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 17:13:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4190 (Other numerical methods); C4240 (Programming
                 and algorithm theory); C5440 (Multiprocessor systems
                 and techniques)",
  corpsource =   "Department of Inf. Sci., Tohoku University, Sendai,
                 Japan",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "algorithms; cache protocols; fast Fourier transform;
                 fast Fourier transforms; FFT; floating-; multiprocess
                 operating system; multiprocessing systems;
                 multiprocessor workstation; multithread operating
                 system; operating systems; parallel; parallel FFT;
                 performance; performance evaluation; point
                 coprocessors",
  treatment =    "P Practical",
}


bibtype: misc
filename: fparith.bib
label: Hough:1991:TBC
author: David G. Hough and Vern Paxson
title: Testbase: base conversion test program
pages: 158--163
day: 20
month: jul
monthnumber: 7
year: 1991
bibdate: Wed May 26 07:22:52 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2004.05.26 07:22:52 ???
note: See cite Paxson:1991:PTI.
URL: http://www.netlib.org/fp/testbase
keywords: floating-point testing
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: David G. Hough and Vern Paxson
rawnote: See \cite{Paxson:1991:PTI}.
rawtitle: Testbase: base conversion test program
entry:
@Misc{Hough:1991:TBC,
  author =       "David G. Hough and Vern Paxson",
  title =        "Testbase: base conversion test program",
  howpublished = "World-Wide Web document",
  day =          "20",
  month =        jul,
  year =         "1991",
  bibdate =      "Wed May 26 07:22:52 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Paxson:1991:PTI}.",
  URL =          "http://www.netlib.org/fp/testbase",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}


bibtype: inproceedings
filename: fparith.bib
label: Hsiao:1991:CHA
author: Shen-Fu Hsiao and Jean-Marc Delosme
title: The CORDIC Householder algorithm
crossref: Kornerup:1991:PIS
pages: 256--263
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_Hsiao.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Shen-Fu Hsiao and Jean-Marc Delosme
rawtitle: The {CORDIC Householder} algorithm
entry:
@InProceedings{Hsiao:1991:CHA,
  author =       "Shen-Fu Hsiao and Jean-Marc Delosme",
  title =        "The {CORDIC Householder} algorithm",
  crossref =     "Kornerup:1991:PIS",
  pages =        "256--263",
  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_Hsiao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Hu:1991:ERC
author: X. Hu and R. G. Harber and S. C. Bass
title: Expanding the Range of Convergence of the CORDIC Algorithm
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 1
pages: 13--21
month: jan
monthnumber: 1
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.67316
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 08 00:50:12 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 00:50:12 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: X. Hu and R. G. Harber and S. C. Bass
rawtitle: Expanding the Range of Convergence of the {CORDIC} Algorithm
entry:
@Article{Hu:1991:ERC,
  author =       "X. Hu and R. G. Harber and S. C. Bass",
  title =        "Expanding the Range of Convergence of the {CORDIC}
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "1",
  pages =        "13--21",
  month =        jan,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.67316",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 00:50:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Hui:1991:DFD
author: S. Hui and D. P. Brown
booktitle: IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, 9--10 May 1991
title: Digital filter design with a combination of fixed point and residue number systems
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 331--334
year: 1991
DOI: https://doi.org/10.1109/PACRIM.1991.160746
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. Hui and D. P. Brown
rawbooktitle: {IEEE} Pacific Rim Conference on Communications, Computers and Signal Processing, 9--10 May 1991
rawtitle: Digital filter design with a combination of fixed point and residue number systems
entry:
@InProceedings{Hui:1991:DFD,
  author =       "S. Hui and D. P. Brown",
  booktitle =    "{IEEE} Pacific Rim Conference on Communications,
                 Computers and Signal Processing, 9--10 May 1991",
  title =        "Digital filter design with a combination of fixed
                 point and residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "331--334",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/PACRIM.1991.160746",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new design method using a combination of fixed-point
                 and RNS (residue number system) arithmetics is
                 presented. It is proven that an IIR digital filter can
                 be efficiently implemented in a system that combines
                 both fixed-point and RNS arithmetics. \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Hull:1991:SVP
author: T. E. Hull and M. S. Cohen and C. B. Hall
title: Specifications for a variable-precision arithmetic coprocessor
crossref: Kornerup:1991:PIS
pages: 127--131
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_Hull.pdf
acknowledgement: ack-nhfb
affiliation: Department of Computer Science, Toronto University, Ont., Canada
thesaurus: Digital arithmetic; Logic circuits; Microprocessor chips; Satellite computers
rawauthor: T. E. Hull and M. S. Cohen and C. B. Hall
rawtitle: Specifications for a variable-precision arithmetic coprocessor
abstract:
The authors have been developing a programming system intended to be especially convenient for scientific computing. Its main features are variable precision (decimal) floating-point arithmetic and convenient exception handling. The software implementation of the system has evolved over a number of years, and a partial hardware implementation of the arithmetic itself was constructed and used during the early stages of the project. Based on this experience, the authors have developed a set of specifications for an arithmetic coprocessor to support such a system. These specifications are described. An outline of the language features and how they can be used is also provided, to help justify the particular choice of coprocessor specifications. The authors also indicate what other hardware features would be most helpful to the systems programmer, especially for implementation of the exception handling.

keywords:
ARITH-10; decimal floating-point arithmetic; Exception handling; Floating-point arithmetic; Programming system; Scientific computing; Variable-precision arithmetic coprocessor

rawabstract:
The authors have been developing a programming system intended to be especially convenient for scientific computing. Its main features are variable precision (decimal) floating-point arithmetic and convenient exception handling. The software implementation of the system has evolved over a number of years, and a partial hardware implementation of the arithmetic itself was constructed and used during the early stages of the project. Based on this experience, the authors have developed a set of specifications for an arithmetic coprocessor to support such a system. These specifications are described. An outline of the language features and how they can be used is also provided, to help justify the particular choice of coprocessor specifications. The authors also indicate what other hardware features would be most helpful to the systems programmer, especially for implementation of the exception handling.

entry:
@InProceedings{Hull:1991:SVP,
  author =       "T. E. Hull and M. S. Cohen and C. B. Hall",
  title =        "Specifications for a variable-precision arithmetic
                 coprocessor",
  crossref =     "Kornerup:1991:PIS",
  pages =        "127--131",
  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_Hull.pdf",
  abstract =     "The authors have been developing a programming system
                 intended to be especially convenient for scientific
                 computing. Its main features are variable precision
                 (decimal) floating-point arithmetic and convenient
                 exception handling. The software implementation of the
                 system has evolved over a number of years, and a
                 partial hardware implementation of the arithmetic
                 itself was constructed and used during the early stages
                 of the project. Based on this experience, the authors
                 have developed a set of specifications for an
                 arithmetic coprocessor to support such a system. These
                 specifications are described. An outline of the
                 language features and how they can be used is also
                 provided, to help justify the particular choice of
                 coprocessor specifications. The authors also indicate
                 what other hardware features would be most helpful to
                 the systems programmer, especially for implementation
                 of the exception handling.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Toronto University,
                 Ont., Canada",
  classification = "B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); B2570 (Semiconductor integrated
                 circuits); C5120 (Logic and switching circuits); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  keywords =     "ARITH-10; decimal floating-point arithmetic; Exception
                 handling; Floating-point arithmetic; Programming
                 system; Scientific computing; Variable-precision
                 arithmetic coprocessor",
  thesaurus =    "Digital arithmetic; Logic circuits; Microprocessor
                 chips; Satellite computers",
}


bibtype: book
filename: fparith.bib
label: Ince:1991:SQR
author: D. (Darrel) Ince
title: Software quality and reliability tools and methods
publisher: Chapman and Hall
address: London, UK
pages: 178
year: 1991
ISBN: 0-442-31314-4, 0-412-37810-8 OR 0442313144, 0412378108
ISBN13: 978-0-442-31314-2, 978-0-412-37810-2 OR 9780442313142, 9780412378102
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
series: Unicom applied information technology reports; [6]
acknowledgement: ack-nhfb
rawauthor: D. (Darrel) Ince
rawtitle: Software quality and reliability tools and methods
keywords:
Computer software --- Quality control.; Computer software --- Reliability.; Software --- Quality control

remark:
Aspects of path testing and mutation testing / M.R. Woodward --- Quality-- an integrated approach / A. Smith --- Quality management and software engineering / R. Hailstone --- The role of verification and validation tools in the production of critical software / J.T. Webb --- The real importance of software quality and the role of quality systems / A. Voss --- Software testing tools / E. Fergus ldots [et al.] --- FPV-- a floating point validation package / J. Du Croz --- Building in quality through the use of software tools / P.A.V. Hall --- Software requirements analysis, formal methods and software prototyping / D. Ince --- Increasing software quality by objectives and residual fault prognosis / K. Moller --- Towards a software quality control environment / M. Adam ldots [et al.] --- Expert system software quality problems / S. Ronchi and M. Martignano --- Quality assurance management for real-time software systems: the experience of the Spanish Civil Aviation Administration / J.P. Buendia, C. Bravo --- The PRX/A software reliability investigation / A.E.J. van Delft.

entry:
@Book{Ince:1991:SQR,
  author =       "D. (Darrel) Ince",
  title =        "Software quality and reliability tools and methods",
  publisher =    "Chapman and Hall",
  address =      "London, UK",
  pages =        "178",
  year =         "1991",
  ISBN =         "0-442-31314-4, 0-412-37810-8",
  ISBN-13 =      "978-0-442-31314-2, 978-0-412-37810-2",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Unicom applied information technology reports; [6]",
  acknowledgement = ack-nhfb,
  keywords =     "Computer software --- Quality control.; Computer
                 software --- Reliability.; Software --- Quality
                 control",
  remark =       "Aspects of path testing and mutation testing / M.R.
                 Woodward --- Quality-- an integrated approach / A.
                 Smith --- Quality management and software engineering /
                 R. Hailstone --- The role of verification and
                 validation tools in the production of critical software
                 / J.T. Webb --- The real importance of software quality
                 and the role of quality systems / A. Voss --- Software
                 testing tools / E. Fergus \ldots{} [et al.] --- FPV-- a
                 floating point validation package / J. Du Croz ---
                 Building in quality through the use of software tools /
                 P.A.V. Hall --- Software requirements analysis, formal
                 methods and software prototyping / D. Ince ---
                 Increasing software quality by objectives and residual
                 fault prognosis / K. Moller --- Towards a software
                 quality control environment / M. Adam \ldots{} [et al.]
                 --- Expert system software quality problems / S. Ronchi
                 and M. Martignano --- Quality assurance management for
                 real-time software systems: the experience of the
                 Spanish Civil Aviation Administration / J.P. Buendia,
                 C. Bravo --- The PRX/A software reliability
                 investigation / A.E.J. van Delft.",
}


bibtype: incollection
filename: fparith.bib
label: Iri:1991:HAD
author: M. Iri
editor: A. Griewank and G. F. Corliss
booktitle: Automatic Differentiation of Algorithms: Theory, Implementation, and Application
title: History of automatic differentiation and rounding error estimation
crossref: Griewank:1991:ADA
pages: 3--16
year: 1991
bibdate: Thu May 27 07:45:02 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.05.27 07:45:02 ???
acknowledgement: ack-nhfb
rawauthor: M. Iri
rawbooktitle: Automatic Differentiation of Algorithms: Theory, Implementation, and Application
raweditor: A. Griewank and G. F. Corliss
rawtitle: History of automatic differentiation and rounding error estimation
entry:
@InCollection{Iri:1991:HAD,
  author =       "M. Iri",
  editor =       "A. Griewank and G. F. Corliss",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  title =        "History of automatic differentiation and rounding
                 error estimation",
  crossref =     "Griewank:1991:ADA",
  pages =        "3--16",
  year =         "1991",
  bibdate =      "Thu May 27 07:45:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Jain:1991:CSN
author: Suneel Jain
title: Circular scheduling: a new technique to perform software pipelining
journal: j-SIGPLAN
volume: 26
number: 6
pages: 219--228
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: Sun Dec 14 09:16:07 MST 2003
bibtimestamp: 2003.12.14 09:16:07 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p219-jain/
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
affiliation: MIPS Comput. Syst. Inc., Sunnyvale, CA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Suneel Jain
rawtitle: Circular scheduling: a new technique to perform software pipelining
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
With the advent of deeply pipelined RISC processors, static instruction scheduling by the compiler has become extremely important to obtain high processor performance. This is especially true for floating point code. The author suggests using a new algorithm called circular scheduling to perform software pipelining. Software pipelining has previously been investigated mostly for VLIW architectures. The algorithm described is shown to be quite effective for a scalar architecture. Register renaming, an idea that originates from dynamic instruction scheduling, is used in conjunction with this algorithm to augment its performance. The techniques described here have been implemented as part of a commercial, production quality optimizing compiler for a RISC architecture. The resulting performance improvement has verified the feasibility and practicality of the techniques.

keywords:
algorithms; Circular scheduling; Deeply pipelined RISC processors; Dynamic instruction scheduling; experimentation; performance; Production quality optimizing compiler; RISC architecture; Scalar architecture; Software pipelining; Static instruction scheduling; VLIW architectures

subject:
bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Compilers. bf D.3.4 Software, PROGRAMMING LANGUAGES, Processors, Optimization.

thesaurus:
Parallel programming; Pipeline processing; Program compilers; Reduced instruction set computing; Scheduling

rawabstract:
With the advent of deeply pipelined RISC processors, static instruction scheduling by the compiler has become extremely important to obtain high processor performance. This is especially true for floating point code. The author suggests using a new algorithm called circular scheduling to perform software pipelining. Software pipelining has previously been investigated mostly for VLIW architectures. The algorithm described is shown to be quite effective for a scalar architecture. Register renaming, an idea that originates from dynamic instruction scheduling, is used in conjunction with this algorithm to augment its performance. The techniques described here have been implemented as part of a commercial, production quality optimizing compiler for a RISC architecture. The resulting performance improvement has verified the feasibility and practicality of the techniques.

entry:
@Article{Jain:1991:CSN,
  author =       "Suneel Jain",
  title =        "Circular scheduling: a new technique to perform
                 software pipelining",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "6",
  pages =        "219--228",
  month =        jun,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:07 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 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/p219-jain/",
  abstract =     "With the advent of deeply pipelined RISC processors,
                 static instruction scheduling by the compiler has
                 become extremely important to obtain high processor
                 performance. This is especially true for floating point
                 code. The author suggests using a new algorithm called
                 circular scheduling to perform software pipelining.
                 Software pipelining has previously been investigated
                 mostly for VLIW architectures. The algorithm described
                 is shown to be quite effective for a scalar
                 architecture. Register renaming, an idea that
                 originates from dynamic instruction scheduling, is used
                 in conjunction with this algorithm to augment its
                 performance. The techniques described here have been
                 implemented as part of a commercial, production quality
                 optimizing compiler for a RISC architecture. The
                 resulting performance improvement has verified the
                 feasibility and practicality of the techniques.",
  acknowledgement = ack-nhfb,
  affiliation =  "MIPS Comput. Syst. Inc., Sunnyvale, CA, USA",
  classification = "C5220 (Computer architecture); C6110 (Systems
                 analysis and programming); C6150C (Compilers,
                 interpreters and other processors); C6150J (Operating
                 systems)",
  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 =     "algorithms; Circular scheduling; Deeply pipelined RISC
                 processors; Dynamic instruction scheduling;
                 experimentation; performance; Production quality
                 optimizing compiler; RISC architecture; Scalar
                 architecture; Software pipelining; Static instruction
                 scheduling; VLIW architectures",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Compilers. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Optimization.",
  thesaurus =    "Parallel programming; Pipeline processing; Program
                 compilers; Reduced instruction set computing;
                 Scheduling",
}


bibtype: inproceedings
filename: fparith.bib
label: Jain:1991:NRS
author: V. K. Jain and G. E. Perez and J. M. Wills
title: Novel reciprocal and square-root VLSI cell: architecture and application to signal processing
crossref: IEEE:1991:VCA
volume: 2
pages: 1201--1204
year: 1991
bibdate: Sat Jul 16 15:28:14 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 15:28:14 MDT
acknowledgement: ack-nj
rawauthor: V. K. Jain and G. E. Perez and J. M. Wills
rawtitle: Novel reciprocal and square-root {VLSI} cell: architecture and application to signal processing
entry:
@InProceedings{Jain:1991:NRS,
  author =       "V. K. Jain and G. E. Perez and J. M. Wills",
  title =        "Novel reciprocal and square-root {VLSI} cell:
                 architecture and application to signal processing",
  crossref =     "IEEE:1991:VCA",
  volume =       "2",
  pages =        "1201--1204",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  summary =      "A novel high-speed cell, capable of performing a
                 square-root or a reciprocal function in two clock
                 cycles, is presented. Its performance signifies an
                 estimated three-fold increase in speed over existing
                 approaches. Furthermore, since both functions
                 \ldots{}",
}


bibtype: techreport
filename: fparith.bib
label: Kahan:1991:APL
author: William Kahan and J. W. Thomas
title: Augmenting a Programming Language with Complex Arithmetic
number: NCEG/91-039, UCB/CSD 91/667
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
pages: 8
day: 15
month: nov
monthnumber: 11
year: 1991
bibdate: Mon Dec 26 21:13:51 GMT 1994
bibtimestamp: 1994.12.26 21:13:51 GMT
note: Manuscript
acknowledgement: ack-nhfb
rawauthor: William Kahan and J. W. Thomas
rawnote: Manuscript
rawtitle: Augmenting a Programming Language with Complex Arithmetic
entry:
@TechReport{Kahan:1991:APL,
  author =       "William Kahan and J. W. Thomas",
  title =        "Augmenting a Programming Language with Complex
                 Arithmetic",
  number =       "NCEG/91-039, UCB/CSD 91/667",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "8",
  day =          "15",
  month =        nov,
  year =         "1991",
  bibdate =      "Mon Dec 26 21:13:51 GMT 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kahan:1991:ARL
author: W. Kahan
title: Analysis and Refutation of the LCAS
journal: j-SIGNUM
volume: 26
number: 3
pages: 2--15
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: Fri Jan 5 07:58:42 MST 1996
bibtimestamp: 1996.01.05 07:58:42 MST
fjournal: ACM SIGNUM Newsletter
keywords: LCAS (Language Compatible Arithmetic Standard)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: W. Kahan
rawtitle: Analysis and Refutation of the {LCAS}
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-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/signum.bib

entry:
@Article{Kahan:1991:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "2--15",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Fri Jan 5 07:58:42 MST 1996",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-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/signum.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "LCAS (Language Compatible Arithmetic Standard)",
}


bibtype: inproceedings
filename: fparith.bib
label: Kantabutra:1991:DOC
author: Vitit Kantabutra
title: Designing optimum carry-skip adders
crossref: Kornerup:1991:PIS
pages: 146--153
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_Kantabutra.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Vitit Kantabutra
rawtitle: Designing optimum carry-skip adders
entry:
@InProceedings{Kantabutra:1991:DOC,
  author =       "Vitit Kantabutra",
  title =        "Designing optimum carry-skip adders",
  crossref =     "Kornerup:1991:PIS",
  pages =        "146--153",
  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_Kantabutra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: article
filename: fparith.bib
label: Kim:1991:ERB
author: Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee
title: Efficient residue-to-binary conversion technique with rounding error compensation
journal: j-IEEE-TRANS-CIRCUITS-SYST
volume: 38
number: 3
pages: 315--317
month: mar
monthnumber: 3
year: 1991
CODEN: ICSYBT
ISSN: 0098-4094 (print), 1558-1276 (electronic) OR 00984094 (print), 15581276 (electronic)
ISSNL: 0098-4094 OR 00984094
bibdate: Sat Jul 16 11:25:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:03 MDT
fjournal: IEEE Transactions on Circuits and Systems
acknowledgement: ack-nhfb
rawauthor: Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee
rawtitle: Efficient residue-to-binary conversion technique with rounding error compensation
entry:
@Article{Kim:1991:ERB,
  author =       "Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee",
  title =        "Efficient residue-to-binary conversion technique with
                 rounding error compensation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "38",
  number =       "3",
  pages =        "315--317",
  month =        mar,
  year =         "1991",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "An improved scaled-decoding technique (defined as
                 residue-to-binary conversion of which outputs are
                 scaled by a constant) for hardware implementations in
                 the residue number system (RNS) is presented. The
                 technique is based on the Chinese remainder \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Kim:1991:NIC
author: S. W. Kim and T. Stouraitis
booktitle: IEEE International Symposium on Circuits and Systems, 11--14 June 1991
title: New implementations of converters for the residue and quadratic residue number system
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2959--2962
year: 1991
DOI: https://doi.org/10.1109/ISCAS.1991.176166
bibdate: Fri Nov 9 11:38:58 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 11:38:58 MST
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: S. W. Kim and T. Stouraitis
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, 11--14 June 1991
rawtitle: New implementations of converters for the residue and quadratic residue number system
entry:
@InProceedings{Kim:1991:NIC,
  author =       "S. W. Kim and T. Stouraitis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "New implementations of converters for the residue and
                 quadratic residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2959--2962",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176166",
  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 =      "Full adder (FA)-based converters are proposed for
                 efficiently performing complex number calculations. The
                 basic idea is to use FA arrays to decompose 2 i terms
                 into 2 j terms, where j{$<$}i, by modulo arithmetic.
                 \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Klatte:1991:PSB
author: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
title: PASCAL-XSC: Sprachbeschreibung mit Beispielen
publisher: pub-SV
address: pub-SV:adr
pages: x + 345
year: 1991
ISBN: 0-387-53714-7 OR 0387537147
ISBN13: 978-0-387-53714-6 OR 9780387537146
LCCN: QA76.73.P2 P42 1991
bibdate: Mon Dec 18 09:37:18 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.18 09:37:18 ???
note: English translation is available as cite Klatte:1991:PXP.
acknowledgement: ack-nhfb
rawauthor: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
rawnote: English translation is available as \cite{Klatte:1991:PXP}.
rawtitle: {PASCAL-XSC: Sprachbeschreibung mit Beispielen}
entry:
@Book{Klatte:1991:PSB,
  author =       "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
                 Ch. Ullrich",
  title =        "{PASCAL-XSC: Sprachbeschreibung mit Beispielen}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 345",
  year =         "1991",
  ISBN =         "0-387-53714-7",
  ISBN-13 =      "978-0-387-53714-6",
  LCCN =         "QA76.73.P2 P42 1991",
  bibdate =      "Mon Dec 18 09:37:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation is available as
                 \cite{Klatte:1991:PXP}.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Klatte:1991:PXP
author: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
title: PASCAL-XSC: A PASCAL Extension for Scientific Computation
publisher: pub-SV
address: pub-SV:adr
pages: x + 344
year: 1991
ISBN: 0-387-55137-9 (New York), 3-540-55137-9 (Berlin) OR 0387551379 (New York), 3540551379 (Berlin)
LCCN: QA76.73.P2 P4213 1992
bibdate: Thu Nov 8 14:50:35 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:35 ???
note: English translation of cite Klatte:1991:PSB.
acknowledgement: ack-nhfb
rawauthor: R. Klatte and U. Kulisch and M. Neaga and D. Ratz and Ch. Ullrich
rawnote: English translation of \cite{Klatte:1991:PSB}.
rawtitle: {PASCAL-XSC}: {A PASCAL} Extension for Scientific Computation
ISBN13:
978-0-387-55137-1 (New York), 978-3-540-55137-9 (Berlin) OR 9780387551371 (New York), 9783540551379 (Berlin)

entry:
@Book{Klatte:1991:PXP,
  author =       "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
                 Ch. Ullrich",
  title =        "{PASCAL-XSC}: {A PASCAL} Extension for Scientific
                 Computation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 344",
  year =         "1991",
  ISBN =         "0-387-55137-9 (New York), 3-540-55137-9 (Berlin)",
  ISBN-13 =      "978-0-387-55137-1 (New York), 978-3-540-55137-9
                 (Berlin)",
  LCCN =         "QA76.73.P2 P4213 1992",
  bibdate =      "Thu Nov 8 14:50:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation of \cite{Klatte:1991:PSB}.",
  price =        "DM64.00",
  acknowledgement = ack-nhfb,
  referred =     "[Corl91a].",
}


bibtype: inproceedings
filename: fparith.bib
label: Knofel:1991:FHU
author: Andreas Knofel
title: Fast hardware units for the computation of accurate dot products
crossref: Kornerup:1991:PIS
pages: 70--74
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_Knofel.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Andreas Kn{\"o}fel
rawtitle: Fast hardware units for the computation of accurate dot products
entry:
@InProceedings{Knofel:1991:FHU,
  author =       "Andreas Kn{\"o}fel",
  title =        "Fast hardware units for the computation of accurate
                 dot products",
  crossref =     "Kornerup:1991:PIS",
  pages =        "70--74",
  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_Knofel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


bibtype: inproceedings
filename: fparith.bib
label: Knowles:1991:APD
author: S. Knowles
title: Arithmetic Processor Design for the T9000 Transputer
crossref: SPIE:1991:PSI
pages: 230--243
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
rawauthor: S. Knowles
rawtitle: Arithmetic Processor Design for the {T9000} Transputer
entry:
@InProceedings{Knowles:1991:APD,
  author =       "S. Knowles",
  title =        "Arithmetic Processor Design for the {T9000}
                 Transputer",
  crossref =     "SPIE:1991:PSI",
  pages =        "230--243",
  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: article
filename: fparith.bib
label: Koc:1991:FAG
author: Cetin K. Koc and Sarath N. Arachchige
title: A fast algorithm for Gaussian elimination over GF(2) and its implementation on the GAPP
journal: j-J-PAR-DIST-COMP
volume: 13
number: 1
pages: 118--122
day: 1
month: sep
monthnumber: 9
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 Houston
affiliationaddress: Houston, TX, USA
corpsource: Department of Electr. Eng., Houston University, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: T Theoretical or Mathematical
rawauthor: Cetin K. Koc and Sarath N. Arachchige
rawtitle: A fast algorithm for {Gaussian} elimination over {GF(2)} and its implementation on the {GAPP}
keywords:
1s location; Algorithms; algorithms; arithmetic parallel processor; binary matrix; binary search; Binary search technique; bit operations; bit-array; columns; computational complexity; Computer Programming; Computer Systems, Digital--Parallel Processing; Galois fields; GAPP; Gaussian elimination; geometric; Geometric arithmetic parallel processors; GF(2); Large binary matrices; Mathematical Techniques--Matrix Algebra; matrix algebra; ones location; parallel; Triangularization; triangularize; vertical memory

entry:
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  author =       "Cetin K. Koc and Sarath N. Arachchige",
  title =        "A fast algorithm for {Gaussian} elimination over
                 {GF(2)} and its implementation on the {GAPP}",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "13",
  number =       "1",
  pages =        "118--122",
  day =          "1",
  month =        sep,
  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 Houston",
  affiliationaddress = "Houston, TX, USA",
  classification = "722; 723; 921; C4140 (Linear algebra); C4240
                 (Programming and algorithm theory)",
  corpsource =   "Department of Electr. Eng., Houston University, TX,
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  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "1s location; Algorithms; algorithms; arithmetic
                 parallel processor; binary matrix; binary search;
                 Binary search technique; bit operations; bit-array;
                 columns; computational complexity; Computer
                 Programming; Computer Systems, Digital--Parallel
                 Processing; Galois fields; GAPP; Gaussian elimination;
                 geometric; Geometric arithmetic parallel processors;
                 GF(2); Large binary matrices; Mathematical
                 Techniques--Matrix Algebra; matrix algebra; ones
                 location; parallel; Triangularization; triangularize;
                 vertical memory",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: fparith.bib
label: Koc:1991:IAM
author: Cetin K. Koc
title: An improved algorithm for mixed-radix conversion of residue numbers
journal: j-COMPUT-MATH-APPL
volume: 22
number: 8
pages: 63--71
year: 1991
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:04 MST 2017
bibtimestamp: 2017.03.01 19:11:04 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219190014U
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: {\c{C}}etin K. Ko{\c{c}}
rawtitle: An improved algorithm for mixed-radix conversion of residue numbers
entry:
@Article{Koc:1991:IAM,
  author =       "{\c{C}}etin K. Ko{\c{c}}",
  title =        "An improved algorithm for mixed-radix conversion of
                 residue numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "8",
  pages =        "63--71",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219190014U",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: mastersthesis
filename: fparith.bib
label: Kohprasert:1991:FAC
author: Teera Kohprasert
title: 32-bit floating-point arithmetic coprocessor design using VHDL
type: Thesis (M.S.)
school: Florida Institute of Technology
address: Melbourne, FL, USA
pages: xiv + 456
year: 1991
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: Teera Kohprasert
rawtitle: 32-bit floating-point arithmetic coprocessor design using {VHDL}
keywords:
Computer arithmetic and logic units --- Design and construction.; VHDL (Computer hardware description language).

entry:
@MastersThesis{Kohprasert:1991:FAC,
  author =       "Teera Kohprasert",
  title =        "32-bit floating-point arithmetic coprocessor design
                 using {VHDL}",
  type =         "Thesis ({M.S.})",
  school =       "Florida Institute of Technology",
  address =      "Melbourne, FL, USA",
  pages =        "xiv + 456",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units --- Design and
                 construction.; VHDL (Computer hardware description
                 language).",
}


bibtype: article
filename: fparith.bib
label: Kostopoulos:1991:ACB
author: D. K. Kostopoulos
title: An Algorithm for the Computation of Binary Logarithms
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 11
pages: 1267--1270
month: nov
monthnumber: 11
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.102831
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:16:09 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. K. Kostopoulos
rawtitle: An Algorithm for the Computation of Binary Logarithms
entry:
@Article{Kostopoulos:1991:ACB,
  author =       "D. K. Kostopoulos",
  title =        "An Algorithm for the Computation of Binary
                 Logarithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "11",
  pages =        "1267--1270",
  month =        nov,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.102831",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Kramer:1991:EFA
author: David Kramer and Isaac D. Scherson
type: Technical report
number: 91-73
institution: Information and Computer Science, University of California, Irvine
address: Irvine, CA, USA
pages: 18
year: 1991
LCCN: Z699 .C3 no. 91-73
bibdate: Fri Jan 5 11:51:46 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.01.05 11:51:46 MST
acknowledgement: ack-nhfb
rawauthor: David Kramer and Isaac D. Scherson
title:
The effect of FPU architecture on a dynamic precision algorithm for the solution of differential equations

rawtitle:
The effect of {FPU} architecture on a dynamic precision algorithm for the solution of differential equations

entry:
@TechReport{Kramer:1991:EFA,
  author =       "David Kramer and Isaac D. Scherson",
  title =        "The effect of {FPU} architecture on a dynamic
                 precision algorithm for the solution of differential
                 equations",
  type =         "Technical report",
  number =       "91-73",
  institution =  "Information and Computer Science, University of
                 California, Irvine",
  address =      "Irvine, CA, USA",
  pages =        "18",
  year =         "1991",
  LCCN =         "Z699 .C3 no. 91-73",
  bibdate =      "Fri Jan 5 11:51:46 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kuhnel:1991:OPS
author: Lars Kuhnel
title: Optimal purely systolic addition
crossref: Kornerup:1991:PIS
pages: 172--179
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_Kuhnel.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Lars K{\"u}hnel
rawtitle: Optimal purely systolic addition
entry:
@InProceedings{Kuhnel:1991:OPS,
  author =       "Lars K{\"u}hnel",
  title =        "Optimal purely systolic addition",
  crossref =     "Kornerup:1991:PIS",
  pages =        "172--179",
  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_Kuhnel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}


