# bibtab

bibtype: techreport
filename: elefunt.bib
label: Schwarz:1993:UFM
author: Eric Mark Schwarz and M. J. (Michael J.) Flynn
title: Using a floating-point multiplier's internals for high-radix division and square root
type: Technical report
number: CSL-TR-93-554
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: iv + 45
year: 1993
bibdate: Sat Feb 24 15:01:45 MST 1996
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer arithmetic.
acknowledgement: ack-nhfb
rawauthor: Eric Mark Schwarz and M. J. (Michael J.) Flynn
rawtitle: Using a floating-point multiplier's internals for high-radix division and square root
remark:
``January 1993.'' Abstract: ``A method for obtaining high-precision approximations of high-order arithmetic operations at low-cost is presented in this study. Specifically, high-precision approximations of the reciprocal (12 bits worst case) and square root (16 bits) operations are obtained using the internal hardware of a floating-point multiplier without the use of look-up tables. The additional combinatorial logic necessary is very small due to the reuse of existing hardware. These low-cost high-precision approximations are used by iterative algorithms to perform the operations of division and square root. The method presented also applies to several other high-order arithmetic operations. Thus, high-radix algorithms for high-order arithmetic operations such as division and square root are possible at low-cost.''

entry:
@TechReport{Schwarz:1993:UFM,
  author =       "Eric Mark Schwarz and M. J. (Michael J.) Flynn",
  title =        "Using a floating-point multiplier's internals for
                 high-radix division and square root",
  type =         "Technical report",
  number =       "CSL-TR-93-554",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "iv + 45",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.",
  remark =       "``January 1993.'' Abstract: ``A method for obtaining
                 high-precision approximations of high-order arithmetic
                 operations at low-cost is presented in this study.
                 Specifically, high-precision approximations of the
                 reciprocal (12 bits worst case) and square root (16
                 bits) operations are obtained using the internal
                 hardware of a floating-point multiplier without the use
                 of look-up tables. The additional combinatorial logic
                 necessary is very small due to the reuse of existing
                 hardware. These low-cost high-precision approximations
                 are used by iterative algorithms to perform the
                 operations of division and square root. The method
                 presented also applies to several other high-order
                 arithmetic operations. Thus, high-radix algorithms for
                 high-order arithmetic operations such as division and
                 square root are possible at low-cost.''",
}


bibtype: article
filename: elefunt.bib
label: Sellers:1993:CDC
author: H. Sellers
title: The C$^2$-DIIS Convergence Acceleration Algorithm
journal: j-IJQC
volume: 45
number: 1
pages: 31--??
year: 1993
CODEN: IJQCB2
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Wed Jan 3 14:24:13 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.01.03 14:24:13 MST
fjournal: International Journal of Quantum Chemistry
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
rawauthor: H. Sellers
rawtitle: The {C$^2$-DIIS} Convergence Acceleration Algorithm
entry:
@Article{Sellers:1993:CDC,
  author =       "H. Sellers",
  title =        "The {C$^2$-DIIS} Convergence Acceleration Algorithm",
  journal =      j-IJQC,
  volume =       "45",
  number =       "1",
  pages =        "31--??",
  year =         "1993",
  CODEN =        "IJQCB2",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Jan 3 14:24:13 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Shishkov:1993:RDB
author: Dimitcdprime r Shishkov
title: Reduction of domains of basic elementary functions to arbitrary small intervals
journal: Annuaire Univ. Sofia Fac. Math. Inform.
volume: 87
number: 1--2
pages: 3--32 (1999)
year: 1993
ISSN: 0205-0808 OR 02050808
MRclass: 65D20
MRnumber: MR1745336
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
acknowledgement: ack-nhfb
rawauthor: Dimit{\cdprime}r Shishkov
rawtitle: Reduction of domains of basic elementary functions to arbitrary small intervals
fjournal:
Godishnik na Sofiui skiya Universitet ``Sv. Kliment Okhridski''. Fakultet po Matematika i Informatika. Annuaire de l'Universite de Sofia ``St. Kliment Ohridski''. Faculte de Mathematiques et Informatique

entry:
@Article{Shishkov:1993:RDB,
  author =       "Dimit{\cdprime}r Shishkov",
  title =        "Reduction of domains of basic elementary functions to
                 arbitrary small intervals",
  journal =      "Annuaire Univ. Sofia Fac. Math. Inform.",
  volume =       "87",
  number =       "1--2",
  pages =        "3--32 (1999)",
  year =         "1993",
  ISSN =         "0205-0808",
  MRclass =      "65D20",
  MRnumber =     "MR1745336",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Godishnik na Sofi\u\i skiya Universitet ``Sv. Kliment
                 Okhridski''. Fakultet po Matematika i Informatika.
                 Annuaire de l'Universit\'e de Sofia ``St. Kliment
                 Ohridski''. Facult\'e de Math\'ematiques et
                 Informatique",
}


bibtype: article
filename: elefunt.bib
label: Snyder:1993:AFI
author: W. Van Snyder
title: Algorithm 723: Fresnel Integrals
journal: j-TOMS
volume: 19
number: 4
pages: 452--456
month: dec
monthnumber: 12
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/168173.168193
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Apr 29 15:24:56 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1999.04.29 15:24:56 ???
note: See remarks cite Snyder:1996:RAF,Snyder:2021:CRA.
URL: http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Van Snyder
rawnote: See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.
rawtitle: {Algorithm 723}: {Fresnel} Integrals
abstract:
An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

subject:
bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.

rawabstract:
An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

entry:
@Article{Snyder:1993:AFI,
  author =       "W. Van Snyder",
  title =        "{Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "452--456",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168193",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:24:56 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/",
  abstract =     "An implementation of approximations for Fresnel
                 integrals and associated functions is described. The
                 approximations were originally developed by W. J. Cody,
                 but a Fortran implementation using them has not
                 previously been published.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; special functions",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}


bibtype: article
filename: elefunt.bib
label: Thompson:1993:CCQ
author: William J. Thompson
title: Cutting Corners: Quick Square Roots and Trig Functions
journal: j-COMPUT-PHYS
volume: 7
number: 1
pages: 18--??
month: jan
monthnumber: 1
year: 1993
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4823136
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:39 MDT 2019
bibtimestamp: 2019.04.10 08:45:39 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4823136
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William J. Thompson
rawtitle: Cutting Corners: Quick Square Roots and Trig Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computphys.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Thompson:1993:CCQ,
  author =       "William J. Thompson",
  title =        "Cutting Corners: Quick Square Roots and Trig
                 Functions",
  journal =      j-COMPUT-PHYS,
  volume =       "7",
  number =       "1",
  pages =        "18--??",
  month =        jan,
  year =         "1993",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4823136",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:39 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4823136",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Vedder:1993:IAN
author: John D. Vedder
title: An invertible approximation to the normal distribution function
journal: j-COMPUT-STAT-DATA-ANAL
volume: 16
number: 1
pages: 119--123
month: jun
monthnumber: 6
year: 1993
CODEN: CSDADW
ISSN: 0167-9473 (print), 1872-7352 (electronic) OR 01679473 (print), 18727352 (electronic)
ISSNL: 0167-9473 OR 01679473
bibdate: Fri Feb 6 11:39:39 MST 2015
bibtimestamp: 2015.02.06 11:39:39 MST
URL: http://www.sciencedirect.com/science/article/pii/016794739390248R
fjournal: Computational Statistics & Data Analysis
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01679473
rawauthor: John D. Vedder
rawtitle: An invertible approximation to the normal distribution function
bibsource:
https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Vedder:1993:IAN,
  author =       "John D. Vedder",
  title =        "An invertible approximation to the normal distribution
                 function",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "16",
  number =       "1",
  pages =        "119--123",
  month =        jun,
  year =         "1993",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:39:39 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/016794739390248R",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}


bibtype: article
filename: elefunt.bib
label: Zaitsev:1993:IMM
author: A. V. Zaitsev
title: Implementation of Miller's method for evaluation of Bessel functions of first kind
journal: j-J-SOV-MATH
volume: 63
number: 5
pages: 558--560
month: feb
monthnumber: 2
year: 1993
CODEN: JSOMAR
DOI: https://doi.org/10.1007/bf01142530
ISSN: 0090-4104 (print), 2376-5798 (electronic) OR 00904104 (print), 23765798 (electronic)
ISSNL: 0090-4104 OR 00904104
bibdate: Wed Mar 1 09:29:38 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.01 09:29:38 ???
fjournal: Journal of Soviet Mathematics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10958
rawauthor: A. V. Zaitsev
rawtitle: Implementation of {Miller}'s method for evaluation of {Bessel} functions of first kind
entry:
@Article{Zaitsev:1993:IMM,
  author =       "A. V. Zaitsev",
  title =        "Implementation of {Miller}'s method for evaluation of
                 {Bessel} functions of first kind",
  journal =      j-J-SOV-MATH,
  volume =       "63",
  number =       "5",
  pages =        "558--560",
  month =        feb,
  year =         "1993",
  CODEN =        "JSOMAR",
  DOI =          "https://doi.org/10.1007/bf01142530",
  ISSN =         "0090-4104 (print), 2376-5798 (electronic)",
  ISSN-L =       "0090-4104",
  bibdate =      "Wed Mar 1 09:29:38 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Soviet Mathematics",
  journal-URL =  "http://link.springer.com/journal/10958",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1994:C
author: Anonymous
title: Corrigenda
journal: j-TOMS
volume: 20
number: 4
pages: 553--553
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 14 16:17:03 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.03.14 16:17:03 ???
note: See cite Hull:1994:ICE
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Anonymous
rawnote: See \cite{Hull:1994:ICE}
rawtitle: Corrigenda
entry:
@Article{Anonymous:1994:C,
  author =       "Anonymous",
  title =        "Corrigenda",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "553--553",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:03 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hull:1994:ICE}",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Bajard:1994:BNH
author: Jean-Claude Bajard and Sylvanus Kla and Jean-Michel Muller
title: BKM: a new hardware algorithm for complex elementary functions
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 8
pages: 955--963
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.295857
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68M07
MRnumber: 1 294 301
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jean-Claude Bajard and Sylvanus Kla and Jean-Michel Muller
rawtitle: {BKM}: a new hardware algorithm for complex elementary functions
entry:
@Article{Bajard:1994:BNH,
  author =       "Jean-Claude Bajard and Sylvanus Kla and Jean-Michel
                 Muller",
  title =        "{BKM}: a new hardware algorithm for complex elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "955--963",
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295857",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "1 294 301",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Bender:1994:DAS
author: Carl M. Bender and Stefan Boettcher
title: Determination of $ f(infty ) $ from the asymptotic series for $ f(x) $ about $ x = 0 $
journal: j-J-MATH-PHYS
volume: 35
number: 4
pages: 1914--1921
month: apr
monthnumber: 4
year: 1994
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.530577
ISSNL: 0022-2488 OR 00222488
MRclass: 41A60 (41A21 65D15 81Q15)
MRnumber: 95d:41063
bibdate: Tue Nov 1 08:58:10 MDT 2011
bibtimestamp: 2011.11.01 08:58:10 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v35/i4/p1914_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Carl M. Bender and Stefan Boettcher
rawtitle: Determination of $ f(\infty) $ from the asymptotic series for $ f(x) $ about $ x = 0 $
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib

entry:
@Article{Bender:1994:DAS,
  author =       "Carl M. Bender and Stefan Boettcher",
  title =        "Determination of $ f(\infty) $ from the asymptotic
                 series for $ f(x) $ about $ x = 0 $",
  journal =      j-J-MATH-PHYS,
  volume =       "35",
  number =       "4",
  pages =        "1914--1921",
  month =        apr,
  year =         "1994",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.530577",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A60 (41A21 65D15 81Q15)",
  MRnumber =     "95d:41063",
  bibdate =      "Tue Nov 1 08:58:10 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v35/i4/p1914_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "8",
}


bibtype: article
filename: elefunt.bib
label: Brown:1994:CAS
author: Barry W. Brown and Lawrence Levy
title: Certification of Algorithm 708: Significant Digit Computation of the Incomplete Beta
journal: j-TOMS
volume: 20
number: 3
pages: 393--397
month: sep
monthnumber: 9
year: 1994
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 19 12:53:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.11.19 12:53:17 ???
note: See cite DiDonato:1992:ASD.
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; continued fractions; F-distribution
subject: G.1.2 [Numerical Analysis]: Approximation
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Barry W. Brown and Lawrence Levy
rawnote: See \cite{DiDonato:1992:ASD}.
rawtitle: Certification of {Algorithm 708}: Significant Digit Computation of the Incomplete Beta
URL:
http://doi.acm.org/10.1145/192115.192155; http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/

entry:
@Article{Brown:1994:CAS,
  author =       "Barry W. Brown and Lawrence Levy",
  title =        "Certification of {Algorithm 708}: Significant Digit
                 Computation of the Incomplete Beta",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "393--397",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{DiDonato:1992:ASD}.",
  URL =          "http://doi.acm.org/10.1145/192115.192155;
                 http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; continued fractions; F-distribution",
  subject =      "G.1.2 [Numerical Analysis]: Approximation",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1994:AAS
author: B. C. Carlson and J. L. Gustafson
title: Asymptotic Approximations for Symmetric Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 25
number: 2
pages: 288--303
month: mar
monthnumber: 3
year: 1994
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33E05 (41A60)
MRnumber: 95b:33056
MRreviewer: Bruce C. Berndt
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMA/25/2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/22847
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: B. C. Carlson and J. L. Gustafson
rawtitle: Asymptotic Approximations for Symmetric Elliptic Integrals
entry:
@Article{Carlson:1994:AAS,
  author =       "B. C. Carlson and J. L. Gustafson",
  title =        "Asymptotic Approximations for Symmetric Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "25",
  number =       "2",
  pages =        "288--303",
  month =        mar,
  year =         "1994",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05 (41A60)",
  MRnumber =     "95b:33056",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/25/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/22847",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:1994:GIG
author: M. Aslam Chaudhry and S. M. Zubair
title: Generalized incomplete gamma functions with applications
journal: j-J-COMPUT-APPL-MATH
volume: 55
number: 1
pages: 99--123
day: 31
month: oct
monthnumber: 10
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:33 MST 2017
bibtimestamp: 2017.02.25 12:24:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794901872
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Aslam Chaudhry and S. M. Zubair
rawtitle: Generalized incomplete gamma functions with applications
entry:
@Article{Chaudhry:1994:GIG,
  author =       "M. Aslam Chaudhry and S. M. Zubair",
  title =        "Generalized incomplete gamma functions with
                 applications",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "55",
  number =       "1",
  pages =        "99--123",
  day =          "31",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794901872",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Chen:1994:ABB
author: Yang Chen and Mourad E. H. Ismail and K. A. Muttalib
title: Asymptotics of basic Bessel functions and $q$-Laguerre polynomials
journal: j-J-COMPUT-APPL-MATH
volume: 54
number: 3
pages: 263--272
day: 20
month: oct
monthnumber: 10
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:33 MST 2017
bibtimestamp: 2017.02.25 12:24:33 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279200128V
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yang Chen and Mourad E. H. Ismail and K. A. Muttalib
rawtitle: Asymptotics of basic {Bessel} functions and $q$-{Laguerre} polynomials
entry:
@Article{Chen:1994:ABB,
  author =       "Yang Chen and Mourad E. H. Ismail and K. A. Muttalib",
  title =        "Asymptotics of basic {Bessel} functions and
                 $q$-{Laguerre} polynomials",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "54",
  number =       "3",
  pages =        "263--272",
  day =          "20",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279200128V",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chen:1994:EDU
author: Sau-Gee Chen and Chieh-Chih Li
title: Efficient designs of unified $2$'s complement division and square root algorithm and architecture
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 943--947
year: 1994
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Sau-Gee Chen and Chieh-Chih Li
rawtitle: Efficient designs of unified $2$'s complement division and square root algorithm and architecture
booktitle:
Proceedings of TENCON '94. IEEE Region 10's Ninth Annual International Conference. Theme: `Frontiers of Computer Technology'

rawbooktitle:
{Proceedings of TENCON '94. IEEE Region 10's Ninth Annual International Conference. Theme: `Frontiers of Computer Technology'}

entry:
@InProceedings{Chen:1994:EDU,
  author =       "Sau-Gee Chen and Chieh-Chih Li",
  booktitle =    "{Proceedings of TENCON '94. IEEE Region 10's Ninth
                 Annual International Conference. Theme: `Frontiers of
                 Computer Technology'}",
  title =        "Efficient designs of unified $2$'s complement division
                 and square root algorithm and architecture",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "943--947",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Efficient unified 2's complement division and square
                 root algorithm, and their architectures are proposed in
                 this work. The designs are high speed, small area and
                 high compatibility. The architectures provide bit level
                 pipelined operation, as well \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cortadella:1994:HRD
author: J. Cortadella and T. Lang
title: High-Radix Division and Square-Root with Speculation
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 8
pages: 919--931
month: aug
monthnumber: 8
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.295854
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
remark: Selected revised and extended papers from ARITH'11 cite Swartzlander:1993:SCA.
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. Cortadella and T. Lang
rawtitle: High-Radix Division and Square-Root with Speculation
entry:
@Article{Cortadella:1994:HRD,
  author =       "J. Cortadella and T. Lang",
  title =        "High-Radix Division and Square-Root with Speculation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "919--931",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295854",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
  summary =      "The speed of high-radix digit-recurrence dividers and
                 square-root units is mainly determined by the
                 complexity of the result-digit selection. We present a
                 scheme in which a simpler function speculates the
                 result digit, and, when this speculation is \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Damnjanovic:1994:EFL
author: Zlatan Damnjanovic
title: Elementary functions and loop programs
journal: j-NOTRE-DAME-J-FORM-LOG
volume: 35
number: 4
pages: 496--522
year: 1994
CODEN: NDJFAM
ISSN: 0029-4527 (print), 1939-0726 (electronic) OR 00294527 (print), 19390726 (electronic)
ISSNL: 0029-4527 OR 00294527
MRclass: 03D20 (68Q15)
MRnumber: 96i:03036
MRreviewer: John P. Helm
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Notre Dame journal of formal logic
acknowledgement: ack-nhfb
journalURL: http://projecteuclid.org/all/euclid.ndjfl
rawauthor: Zlatan Damnjanovic
rawtitle: Elementary functions and loop programs
entry:
@Article{Damnjanovic:1994:EFL,
  author =       "Zlatan Damnjanovic",
  title =        "Elementary functions and loop programs",
  journal =      j-NOTRE-DAME-J-FORM-LOG,
  volume =       "35",
  number =       "4",
  pages =        "496--522",
  year =         "1994",
  CODEN =        "NDJFAM",
  ISSN =         "0029-4527 (print), 1939-0726 (electronic)",
  ISSN-L =       "0029-4527",
  MRclass =      "03D20 (68Q15)",
  MRnumber =     "96i:03036",
  MRreviewer =   "John P. Helm",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Notre Dame journal of formal logic",
  journal-URL =  "http://projecteuclid.org/all/euclid.ndjfl",
}


bibtype: article
filename: elefunt.bib
label: Das:1994:ATE
author: Mrinal Kanti Das
title: Analysis of two elementary functions
journal: j-INT-J-MATH-EDU-SCI-TECH
volume: 25
number: 1
pages: 17--24
year: 1994
CODEN: IJMEBM
ISSN: 0020-739X (print), 1464-5211 (electronic) OR 0020739X (print), 14645211 (electronic)
ISSNL: 0020-739X OR 0020739X
MRclass: 26-01 (33B10)
MRnumber: 1 257 731
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: International Journal of Mathematical Education in Science and Technology
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/tmes20
rawauthor: Mrinal Kanti Das
rawtitle: Analysis of two elementary functions
entry:
@Article{Das:1994:ATE,
  author =       "Mrinal Kanti Das",
  title =        "Analysis of two elementary functions",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "25",
  number =       "1",
  pages =        "17--24",
  year =         "1994",
  CODEN =        "IJMEBM",
  ISSN =         "0020-739X (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26-01 (33B10)",
  MRnumber =     "1 257 731",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}


bibtype: techreport
filename: elefunt.bib
label: Dunham:1994:PMAa
author: Charles B. Dunham
title: Provably Monotone Approximations, IV
type: Technical report
number: TR-417
institution: Department of Computer Science, University of Western Ontario
address: London, Ontario, Canada
pages: 17--24
day: 8
month: mar
monthnumber: 3
year: 1994
bibdate: Tue Apr 12 11:26:47 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 11:26:47 ???
URL: http://www.csd.uwo.ca/tech-reports/
acknowledgement: ack-nhfb
rawauthor: Charles B. Dunham
rawtitle: Provably Monotone Approximations, {IV}
entry:
@TechReport{Dunham:1994:PMAa,
  author =       "Charles B. Dunham",
  title =        "Provably Monotone Approximations, {IV}",
  type =         "Technical report",
  number =       "TR-417",
  institution =  "Department of Computer Science, University of Western
                 Ontario",
  address =      "London, Ontario, Canada",
  day =          "8",
  month =        mar,
  year =         "1994",
  bibdate =      "Tue Apr 12 11:26:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Dunham:1994:PMAb
author: Charles B. Dunham
title: Provably Monotone Approximations, IV, Revised
type: Technical report
number: TR-422
institution: Department of Computer Science, University of Western Ontario
address: London, Ontario, Canada
pages: 17--24
day: 4
month: apr
monthnumber: 4
year: 1994
bibdate: Tue Apr 12 11:26:47 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 11:26:47 ???
URL: http://www.csd.uwo.ca/tech-reports/
acknowledgement: ack-nhfb
rawauthor: Charles B. Dunham
rawtitle: Provably Monotone Approximations, {IV}, Revised
entry:
@TechReport{Dunham:1994:PMAb,
  author =       "Charles B. Dunham",
  title =        "Provably Monotone Approximations, {IV}, Revised",
  type =         "Technical report",
  number =       "TR-422",
  institution =  "Department of Computer Science, University of Western
                 Ontario",
  address =      "London, Ontario, Canada",
  day =          "4",
  month =        apr,
  year =         "1994",
  bibdate =      "Tue Apr 12 11:26:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dunkl:1994:AHI
author: Charles F. Dunkl and Donald E. Ramirez
title: Algorithm 736: Hyperelliptic Integrals and the Surface Measure of Ellipsoids
journal: j-TOMS
volume: 20
number: 4
pages: 427--435
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
DOI: https://doi.org/10.1145/198429.198431
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D30
MRnumber: 1 368 025
bibdate: Tue Mar 14 16:16:51 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.03.14 16:16:51 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Charles F. Dunkl and Donald E. Ramirez
rawtitle: {Algorithm 736}: Hyperelliptic Integrals and the Surface Measure of Ellipsoids
keywords:
elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure

subject:
G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics

entry:
@Article{Dunkl:1994:AHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "{Algorithm 736}: Hyperelliptic Integrals and the
                 Surface Measure of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "427--435",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198431",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 025",
  bibdate =      "Tue Mar 14 16:16:51 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}


bibtype: article
filename: elefunt.bib
label: Dunkl:1994:CHI
author: Charles F. Dunkl and Donald E. Ramirez
title: Computing Hyperelliptic Integrals for Surface Measure of Ellipsoids
journal: j-TOMS
volume: 20
number: 4
pages: 413--426
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
DOI: https://doi.org/10.1145/198429.198430
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D30
MRnumber: 1 368 024
bibdate: Tue Mar 14 16:16:49 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.03.14 16:16:49 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Charles F. Dunkl and Donald E. Ramirez
rawtitle: Computing Hyperelliptic Integrals for Surface Measure of Ellipsoids
keywords:
elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure

subject:
G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics

entry:
@Article{Dunkl:1994:CHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "Computing Hyperelliptic Integrals for Surface Measure
                 of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "413--426",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198430",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 024",
  bibdate =      "Tue Mar 14 16:16:49 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}


bibtype: book
filename: elefunt.bib
label: Ercegovac:1994:DSR
author: Milos D. (Dragutin) Ercegovac and Tomas Lang
title: Division and Square Root: Digit-recurrence Algorithms and Implementations
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: x + 230
year: 1994
ISBN: 0-7923-9438-0 OR 0792394380
ISBN13: 978-0-7923-9438-9 OR 9780792394389
LCCN: QA76.9.C62 E73 1994
bibdate: Fri Mar 27 09:46:24 1998
bibtimestamp: 1998.03.27 09:46:24 ???
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang
rawtitle: Division and Square Root: Digit-recurrence Algorithms and Implementations
TOC:
Preface / 1 1. General Comments / 5 2. Division by Digit Recurrence / 5 3. Theory of Digit-Recurrence Division / 19 4. Division With Scaling and Prediction /65 5. Higher Radix Division / 91 6. On-The-Fly Conversion and Round / 121 7. Square Root by Digit Recurrence / 135 8. Implementations of Square Root / 153 A: Restoring and Non-Restoring Division / 182 B: Evaluation of Some Implementations / 182 Bibliography / 207 Index / 227

rawTOC:
Preface / 1 \\ 1. General Comments / 5 \\ 2. Division by Digit Recurrence / 5 \\ 3. Theory of Digit-Recurrence Division / 19 \\ 4. Division With Scaling and Prediction /65 \\ 5. Higher Radix Division / 91 \\ 6. On-The-Fly Conversion and Round / 121 \\ 7. Square Root by Digit Recurrence / 135 \\ 8. Implementations of Square Root / 153 \\ A: Restoring and Non-Restoring Division / 182 \\ B: Evaluation of Some Implementations / 182 \\ Bibliography / 207 \\ Index / 227

entry:
@Book{Ercegovac:1994:DSR,
  author =       "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
  title =        "Division and Square Root: Digit-recurrence Algorithms
                 and Implementations",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "x + 230",
  year =         "1994",
  ISBN =         "0-7923-9438-0",
  ISBN-13 =      "978-0-7923-9438-9",
  LCCN =         "QA76.9.C62 E73 1994",
  bibdate =      "Fri Mar 27 09:46:24 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / 1 \\
                 1. General Comments / 5 \\
                 2. Division by Digit Recurrence / 5 \\
                 3. Theory of Digit-Recurrence Division / 19 \\
                 4. Division With Scaling and Prediction /65 \\
                 5. Higher Radix Division / 91 \\
                 6. On-The-Fly Conversion and Round / 121 \\
                 7. Square Root by Digit Recurrence / 135 \\
                 8. Implementations of Square Root / 153 \\
                 A: Restoring and Non-Restoring Division / 182 \\
                 B: Evaluation of Some Implementations / 182 \\
                 Bibliography / 207 \\
                 Index / 227",
}


bibtype: article
filename: elefunt.bib
label: Everitt:1994:GBF
author: W. N. Everitt and C. Markett
title: On a generalization of Bessel functions satisfying higher-order differential equations
journal: j-J-COMPUT-APPL-MATH
volume: 54
number: 3
pages: 325--349
day: 20
month: oct
monthnumber: 10
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:33 MST 2017
bibtimestamp: 2017.02.25 12:24:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794902550
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: W. N. Everitt and C. Markett
rawtitle: On a generalization of {Bessel} functions satisfying higher-order differential equations
entry:
@Article{Everitt:1994:GBF,
  author =       "W. N. Everitt and C. Markett",
  title =        "On a generalization of {Bessel} functions satisfying
                 higher-order differential equations",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "54",
  number =       "3",
  pages =        "325--349",
  day =          "20",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794902550",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Fukushima:1994:NCI
author: Toshio Fukushima and Hideharu Ishizaki
title: Numerical computation of incomplete elliptic integrals of a general form
journal: j-CELEST-MECH-DYN-ASTR
volume: 59
number: 3
pages: 237--251
month: jul
monthnumber: 7
year: 1994
CODEN: CLMCAV
DOI: https://doi.org/10.1007/BF00692874
ISSN: 0923-2958 (print), 1572-9478 (electronic) OR 09232958 (print), 15729478 (electronic)
ISSNL: 0923-2958 OR 09232958
MRclass: 33E05 65R20 65D32 (33E30 70-08 70E15)
MRnumber: 1285916 (95c:65041)
bibdate: Wed Oct 20 21:26:45 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.20 21:26:45 ???
URL: http://www.springerlink.com/content/0923-2958/
fjournal: Celestial Mechanics & Dynamical Astronomy. An International Journal of Space Dynamics
keywords: Incomplete elliptic integrals; numerical computation
ZMnumber: Zbl 0818.33013
acknowledgement: ack-nhfb
rawauthor: Toshio Fukushima and Hideharu Ishizaki
rawtitle: Numerical computation of incomplete elliptic integrals of a general form
abstract:
We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter.

rawabstract:
We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter.

entry:
@Article{Fukushima:1994:NCI,
  author =       "Toshio Fukushima and Hideharu Ishizaki",
  title =        "Numerical computation of incomplete elliptic integrals
                 of a general form",
  journal =      j-CELEST-MECH-DYN-ASTR,
  volume =       "59",
  number =       "3",
  pages =        "237--251",
  month =        jul,
  year =         "1994",
  CODEN =        "CLMCAV",
  DOI =          "https://doi.org/10.1007/BF00692874",
  ISSN =         "0923-2958 (print), 1572-9478 (electronic)",
  ISSN-L =       "0923-2958",
  MRclass =      "33E05 65R20 65D32 (33E30 70-08 70E15)",
  MRnumber =     "1285916 (95c:65041)",
  bibdate =      "Wed Oct 20 21:26:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/0923-2958/",
  ZMnumber =     "Zbl 0818.33013",
  abstract =     "We present an algorithm to compute the incomplete
                 elliptic integral of a general form. The algorithm
                 efficiently evaluates some linear combinations of
                 incomplete elliptic integrals of all kinds to a high
                 precision. Some numerical examples are given as
                 illustrations. This enables us to numerically calculate
                 the values and the partial derivatives of incomplete
                 elliptic integrals of all kinds, which are essential
                 when dealing with many problems in celestial mechanics,
                 including the analytic solution of the torque-free
                 rotational motion of a rigid body around its
                 barycenter.",
  acknowledgement = ack-nhfb,
  fjournal =     "Celestial Mechanics \& Dynamical Astronomy. An
                 International Journal of Space Dynamics",
  keywords =     "Incomplete elliptic integrals; numerical computation",
}


bibtype: article
filename: elefunt.bib
label: Hahn:1994:UDF
author: H. Hahn and D. Timmermann and B. J. Hosticka and B. Rix
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 11
pages: 1339--1344
month: nov
monthnumber: 11
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.324568
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:13:58 MDT 2011
bibtimestamp: 2011.07.07 07:13:58 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: H. Hahn and D. Timmermann and B. J. Hosticka and B. Rix
title:
A unified and division-free CORDIC argument reduction method with unlimited convergence domain including inverse hyperbolic functions

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

rawtitle:
A unified and division-free {CORDIC} argument reduction method with unlimited convergence domain including inverse hyperbolic functions

entry:
@Article{Hahn:1994:UDF,
  author =       "H. Hahn and D. Timmermann and B. J. Hosticka and B.
                 Rix",
  title =        "A unified and division-free {CORDIC} argument
                 reduction method with unlimited convergence domain
                 including inverse hyperbolic functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "11",
  pages =        "1339--1344",
  month =        nov,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.324568",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568",
  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: elefunt.bib
label: Homeier:1994:NCA
author: Herbert H. H. Homeier
editor: Ralf Gruber and Marco Tomassini
title: Nonlinear convergence acceleration for orthogonal series
publisher: European Physical Society, Boite Postale 69, CH-1213 Petit-Lancy, Geneva, Switzerland
address: Lugano
pages: 47--50
year: 1994
ISBN: 2-88270-011-3 OR 2882700113
ISBN13: 978-2-88270-011-7 OR 9782882700117
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA942
keywords: convergence acceleration
rawauthor: Herbert H. H. Homeier
raweditor: Ralf Gruber and Marco Tomassini
rawtitle: Nonlinear convergence acceleration for orthogonal series
booktitle:
Proceedings of the 6th Joint EPS-APS International Conference on Physics Computing, Physics Computing '94

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawbooktitle:
Proceedings of the 6th {Joint EPS-APS International Conference} on {Physics Computing, Physics Computing} '94

entry:
@InProceedings{Homeier:1994:NCA,
  author =       "Herbert H. H. Homeier",
  editor =       "Ralf Gruber and Marco Tomassini",
  booktitle =    "Proceedings of the 6th {Joint EPS-APS International
                 Conference} on {Physics Computing, Physics Computing}
                 '94",
  title =        "Nonlinear convergence acceleration for orthogonal
                 series",
  publisher =    "European Physical Society, Boite Postale 69, CH-1213
                 Petit-Lancy, Geneva, Switzerland",
  address =      "Lugano",
  pages =        "47--50",
  year =         "1994",
  ISBN =         "2-88270-011-3",
  ISBN-13 =      "978-2-88270-011-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA942",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-NA-94-2, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1994",
}


bibtype: article
filename: elefunt.bib
label: Hull:1994:ICE
author: T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang
title: Implementing Complex Elementary Functions Using Exception Handling
journal: j-TOMS
volume: 20
number: 2
pages: 215--244
month: jun
monthnumber: 6
year: 1994
CODEN: ACMSCU
DOI: https://doi.org/10.1145/178365.178404
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 21 15:10:29 1995
bibtimestamp: 1995.03.21 15:10:29 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; complex elementary functions; design; implementation
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang
rawtitle: Implementing Complex Elementary Functions Using Exception Handling
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/toms.bib

note:
See correction cite Anonymous:1994:C, and improved analysis, tightened bounds, and exhibition of worst cases for complex square roots cite Jeannerod:2017:REC.

abstract:
Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in Fortran 77 and Fortran 90, namely cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding Fortran programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results are of these tests are included in the paper, but the Fortran programs are not; the programs are available from Fairgrieve, (tff@cs.toronto.edu).

subject:
G.1.0 [Numerical Analysis]: General--error analysis; numerical algorithms; G.1.2 [Numerical Analysis]: Approximation--elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software--algorithm analysis; reliability and robustness; verification

rawabstract:
Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in Fortran 77 and Fortran 90, namely cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding Fortran programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results are of these tests are included in the paper, but the Fortran programs are not; the programs are available from Fairgrieve, (tff@cs.toronto.edu).

rawnote:
See correction \cite{Anonymous:1994:C}, and improved analysis, tightened bounds, and exhibition of worst cases for complex square roots \cite{Jeannerod:2017:REC}.

entry:
@Article{Hull:1994:ICE,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing Complex Elementary Functions Using
                 Exception Handling",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "215--244",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.178404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 21 15:10:29 1995",
  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/toms.bib",
  note =         "See correction \cite{Anonymous:1994:C}, and improved
                 analysis, tightened bounds, and exhibition of worst
                 cases for complex square roots
                 \cite{Jeannerod:2017:REC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/",
  abstract =     "Algorithms are developed for reliable and accurate
                 evaluations of the complex elementary functions
                 required in Fortran 77 and Fortran 90, namely cabs,
                 csqrt, cexp, clog, csin, and ccos. The algorithms are
                 presented in a pseudocode that has a convenient
                 exception-handling facility. A tight error bound is
                 derived for each algorithm. Corresponding Fortran
                 programs for an IEEE environment have also been
                 developed to illustrate the practicality of the
                 algorithms, and these programs have been tested very
                 carefully to help confirm the correctness of the
                 algorithms and their error bounds. The results are of
                 these tests are included in the paper, but the Fortran
                 programs are not; the programs are available from
                 Fairgrieve, (tff@cs.toronto.edu).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex elementary functions; design;
                 implementation",
  subject =      "G.1.0 [Numerical Analysis]: General--error analysis;
                 numerical algorithms; G.1.2 [Numerical Analysis]:
                 Approximation--elementary function approximation; G.4
                 [Mathematics of Computing]: Mathematical
                 Software--algorithm analysis; reliability and
                 robustness; verification",
}


bibtype: article
filename: elefunt.bib
label: Iserles:1994:CAD
author: A. Iserles
title: Convergence acceleration as a dynamical system
journal: j-APPL-NUM-MATH
volume: 15
number: 2
pages: 101--121
day: 13
month: sep
monthnumber: 9
year: 1994
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 58F23 (30D05 58F08 65D99 65H99)
MRnumber: 95i:58155
MRreviewer: Peter M. Makienko
bibdate: Wed Jul 28 14:35:48 MDT 1999
bibtimestamp: 1999.07.28 14:35:48 MDT
note: Innovative methods in numerical analysis (Bressanone, 1992).
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: A. Iserles
rawnote: Innovative methods in numerical analysis (Bressanone, 1992).
rawtitle: Convergence acceleration as a dynamical system
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=15&issue=2; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=15&issue=2&aid=496

entry:
@Article{Iserles:1994:CAD,
  author =       "A. Iserles",
  title =        "Convergence acceleration as a dynamical system",
  journal =      j-APPL-NUM-MATH,
  volume =       "15",
  number =       "2",
  pages =        "101--121",
  day =          "13",
  month =        sep,
  year =         "1994",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "58F23 (30D05 58F08 65D99 65H99)",
  MRnumber =     "95i:58155",
  MRreviewer =   "Peter M. Makienko",
  bibdate =      "Wed Jul 28 14:35:48 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=15&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Innovative methods in numerical analysis (Bressanone,
                 1992).",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=15&issue=2&aid=496",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Jablonski:1994:NES
author: Aleksander Jablonski
title: Numerical Evaluation of Spherical Bessel Functions of the First Kind
journal: j-J-COMPUT-PHYS
volume: 111
number: 2
pages: 256--259
month: apr
monthnumber: 4
year: 1994
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.1994.1060
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:54:54 MST 2012
bibtimestamp: 2012.01.02 07:54:54 MST
URL: http://www.sciencedirect.com/science/article/pii/S0021999184710606
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Aleksander Jablonski
rawtitle: Numerical Evaluation of Spherical {Bessel} Functions of the First Kind
abstract:
Calculations of cross sections for elastic scattering of electrons require frequent evaluations of the spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $, in a wide range of the argument $x$ and the order $l$. It turns out that the usual algorithms providing the values of the spherical Bessel function of the first kind, $ j_l(x) $, have a rather limited range of stability. It is shown that there is no algorithm implementing a single method which can be used in calculations associated with the theory of elastic scattering of electrons. An attempt is made to select different areas of stability from different algorithms in order to create a relatively fast and universal algorithm.

rawabstract:
Calculations of cross sections for elastic scattering of electrons require frequent evaluations of the spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $, in a wide range of the argument $x$ and the order $l$. It turns out that the usual algorithms providing the values of the spherical Bessel function of the first kind, $ j_l(x) $, have a rather limited range of stability. It is shown that there is no algorithm implementing a single method which can be used in calculations associated with the theory of elastic scattering of electrons. An attempt is made to select different areas of stability from different algorithms in order to create a relatively fast and universal algorithm.

entry:
@Article{Jablonski:1994:NES,
  author =       "Aleksander Jablonski",
  title =        "Numerical Evaluation of Spherical {Bessel} Functions
                 of the First Kind",
  journal =      j-J-COMPUT-PHYS,
  volume =       "111",
  number =       "2",
  pages =        "256--259",
  month =        apr,
  year =         "1994",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1994.1060",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:54:54 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999184710606",
  abstract =     "Calculations of cross sections for elastic scattering
                 of electrons require frequent evaluations of the
                 spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $,
                 in a wide range of the argument $x$ and the order $l$.
                 It turns out that the usual algorithms providing the
                 values of the spherical Bessel function of the first
                 kind, $ j_l(x) $, have a rather limited range of
                 stability. It is shown that there is no algorithm
                 implementing a single method which can be used in
                 calculations associated with the theory of elastic
                 scattering of electrons. An attempt is made to select
                 different areas of stability from different algorithms
                 in order to create a relatively fast and universal
                 algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Jain:1994:SRR
author: V. K. Jain and Lei Lin
title: Square-root, reciprocal, sine / cosine, arctangent cell for signal and image processing
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: II/521--II/524
year: 1994
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: V. K. Jain and Lei Lin
rawtitle: Square-root, reciprocal, sine\slash cosine, arctangent cell for signal and image processing
booktitle:
IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP-94, 19--22 April 1994

rawbooktitle:
{IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP-94, 19--22} April 1994

entry:
@InProceedings{Jain:1994:SRR,
  author =       "V. K. Jain and Lei Lin",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-94, 19--22} April 1994",
  title =        "Square-root, reciprocal, sine\slash cosine, arctangent
                 cell for signal and image processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II/521--II/524",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper discusses an efficient interpolation method
                 for nonlinear function generation. Based on this, a 24
                 bit VLSI cell, capable of computing the (1) square
                 root, (2) reciprocal, (3) sine/cosine, and (4)
                 arctangent functions, is presented for \ldots{}",
}


bibtype: misc
filename: elefunt.bib
label: Karp:1994:FPA
author: Alan H. Karp and Peter Markstein and Dennis Brzezinski
pages: II/521--II/524
day: 23
month: aug
monthnumber: 8
year: 1994
bibdate: Thu Oct 17 10:20:52 2019
bibtimestamp: 2019.10.17 10:20:52 ???
URL: http://patft.uspto.gov/netahtml/PTO/search-bool.html; https://patents.google.com/patent/US5341321A
acknowledgement: ack-nhfb
howpublished: US Patent 5,341,321
rawauthor: Alan H. Karp and Peter Markstein and Dennis Brzezinski
title:
Floating point arithmetic unit using modified Newton--Raphson technique for division and square root

note:
Patent filed 5 May 1993, granted to Hewlett-Packard Company on 23 August 1994. Patent expired 5-May-2013. See criticism in cite Zimmermann:2005:XXX.

abstract:
A floating point processing system which uses a multiplier unit and an adder unit to perform floating point division and square root operations using both a conventional and a modified form of the Newton--Raphson method. The modified form of the Newton--Raphson method is used in place of the final iteration of the conventional Newton--Raphson so as to compute high precision approximated results with a substantial improvement in speed. The invention computes approximated results faster and simplifies hardware requirements because no multiplications of numbers of the precision of the result are required.

rawabstract:
A floating point processing system which uses a multiplier unit and an adder unit to perform floating point division and square root operations using both a conventional and a modified form of the Newton--Raphson method. The modified form of the Newton--Raphson method is used in place of the final iteration of the conventional Newton--Raphson so as to compute high precision approximated results with a substantial improvement in speed. The invention computes approximated results faster and simplifies hardware requirements because no multiplications of numbers of the precision of the result are required.

rawnote:
Patent filed 5 May 1993, granted to Hewlett-Packard Company on 23 August 1994. Patent expired 5-May-2013. See criticism in \cite{Zimmermann:2005:XXX}.

rawtitle:
Floating point arithmetic unit using modified {Newton--Raphson} technique for division and square root

entry:
@Misc{Karp:1994:FPA,
  author =       "Alan H. Karp and Peter Markstein and Dennis
                 Brzezinski",
  title =        "Floating point arithmetic unit using modified
                 {Newton--Raphson} technique for division and square
                 root",
  howpublished = "US Patent 5,341,321",
  day =          "23",
  month =        aug,
  year =         "1994",
  bibdate =      "Thu Oct 17 10:20:52 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Patent filed 5 May 1993, granted to Hewlett-Packard
                 Company on 23 August 1994. Patent expired 5-May-2013.
                 See criticism in \cite{Zimmermann:2005:XXX}.",
  URL =          "http://patft.uspto.gov/netahtml/PTO/search-bool.html;
                 https://patents.google.com/patent/US5341321A",
  abstract =     "A floating point processing system which uses a
                 multiplier unit and an adder unit to perform floating
                 point division and square root operations using both a
                 conventional and a modified form of the Newton--Raphson
                 method. The modified form of the Newton--Raphson method
                 is used in place of the final iteration of the
                 conventional Newton--Raphson so as to compute high
                 precision approximated results with a substantial
                 improvement in speed. The invention computes
                 approximated results faster and simplifies hardware
                 requirements because no multiplications of numbers of
                 the precision of the result are required.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kearfott:1994:AIP
author: R. B. Kearfott and M. Dawande and K. Du and C. Hu
title: Algorithm 737: INTLIB: a Portable Fortran-77 Elementary Function Library
journal: j-TOMS
volume: 20
number: 4
pages: 447--459
month: dec
monthnumber: 12
year: 1994
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat May 20 15:54:18 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.05.20 15:54:18 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: BLAS; Fortran 77; Fortran 90; interval arithmetic; operator overloading; standard functions
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: R. B. Kearfott and M. Dawande and K. Du and C. Hu
rawtitle: Algorithm 737: {INTLIB}: a Portable {Fortran}-77 Elementary Function Library
subject:
D.2.2 [Software Engineering]: Tools and Techniques -- software libraries; D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; portability; G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation

entry:
@Article{Kearfott:1994:AIP,
  author =       "R. B. Kearfott and M. Dawande and K. Du and C. Hu",
  title =        "Algorithm 737: {INTLIB}: a Portable {Fortran}-77
                 Elementary Function Library",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "447--459",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat May 20 15:54:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  accepted =     "December 1993",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; Fortran 77; Fortran 90; interval arithmetic;
                 operator overloading; standard functions",
  subject =      "D.2.2 [Software Engineering]: Tools and Techniques --
                 software libraries; D.2.7 [Software Engineering]:
                 Distribution and Maintenance -- documentation;
                 portability; G.1.0 [Numerical Analysis]: General --
                 computer arithmetic; G.1.2 [Numerical Analysis]:
                 Approximation -- elementary function approximation",
}


bibtype: article
filename: elefunt.bib
label: Khajah:1994:UHP
author: H. G. Khajah and E. L. Ortiz
title: Ultra-high precision computations
journal: j-COMPUT-MATH-APPL
volume: 27
number: 7
pages: 41--57
month: apr
monthnumber: 4
year: 1994
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(94)90148-1
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Mon Jun 13 22:03:39 2011
bibtimestamp: 2011.06.13 22:03:39 ???
URL: http://www.sciencedirect.com/science/article/pii/0898122194901481
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
affiliation: Dept. of Math., Imperial Coll. of Sci., Technol. and Med., London, UK
journalURL: http://www.sciencedirect.com/science/journal/08981221
thesaurus: FORTRAN; Mathematics computing
rawauthor: H. G. Khajah and E. L. Ortiz
rawtitle: Ultra-high precision computations
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We describe a machine independent Fortran subroutine which performs the four basic arithmetic operations with a degree of accuracy prescribed by the user. Tables of Chebyshev expansions of orders 48 and 50 for some basic mathematical functions are obtained as a result of applying this subroutine in conjunction with the recursive formulation of the Tau Method. A recently devised technique for the sharp determination of upper and lower error bounds for Tau Method approximations enables us to find the degree $n$ required to achieve a prescribed accuracy $ epsilon $ over a given interval $ [a, b] $. A number of practical illustrations are given.

keywords:
$cos (pi x)$; $erf (x) / x$; $exp (-x^2)$; $exp (x)$; $sin (pi x)$; $x exp (x^2) erfc(x)$; $z exp (z) Ei (-z)$; Arithmetic operations; Chebyshev expansions; Lower error bounds; Machine independent Fortran subroutine; Mathematical functions; Tau method; Upper error bounds

rawabstract:
We describe a machine independent Fortran subroutine which performs the four basic arithmetic operations with a degree of accuracy prescribed by the user. Tables of Chebyshev expansions of orders 48 and 50 for some basic mathematical functions are obtained as a result of applying this subroutine in conjunction with the recursive formulation of the Tau Method. A recently devised technique for the sharp determination of upper and lower error bounds for Tau Method approximations enables us to find the degree $n$ required to achieve a prescribed accuracy $ \epsilon $ over a given interval $ [a, b] $. A number of practical illustrations are given.

entry:
@Article{Khajah:1994:UHP,
  author =       "H. G. Khajah and E. L. Ortiz",
  title =        "Ultra-high precision computations",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "27",
  number =       "7",
  pages =        "41--57",
  month =        apr,
  year =         "1994",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(94)90148-1",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Mon Jun 13 22:03:39 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122194901481",
  abstract =     "We describe a machine independent Fortran subroutine
                 which performs the four basic arithmetic operations
                 with a degree of accuracy prescribed by the user.
                 Tables of Chebyshev expansions of orders 48 and 50 for
                 some basic mathematical functions are obtained as a
                 result of applying this subroutine in conjunction with
                 the recursive formulation of the Tau Method. A recently
                 devised technique for the sharp determination of upper
                 and lower error bounds for Tau Method approximations
                 enables us to find the degree $n$ required to achieve a
                 prescribed accuracy $ \epsilon $ over a given interval
                 $ [a, b] $. A number of practical illustrations are
                 given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Imperial Coll. of Sci., Technol. and
                 Med., London, UK",
  classification = "C6140D (High level languages); C7310 (Mathematics)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "$\cos(\pi x)$; $\erf(x) / x$; $\exp(-x^2)$; $\exp(x)$;
                 $\sin(\pi x)$; $x \exp(x^2) erfc(x)$; $z \exp(z)
                 \Ei(-z)$; Arithmetic operations; Chebyshev expansions;
                 Lower error bounds; Machine independent Fortran
                 subroutine; Mathematical functions; Tau method; Upper
                 error bounds",
  pubcountry =   "UK",
  thesaurus =    "FORTRAN; Mathematics computing",
}


bibtype: article
filename: elefunt.bib
label: Lewanowicz:1994:SAS
author: Stanislaw Lewanowicz
title: A simple approach to the summation of certain slowly convergent series
journal: j-MATH-COMPUT
volume: 63
number: 208
pages: 741--745
month: oct
monthnumber: 10
year: 1994
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65B10
MRnumber: 95a:65010
MRreviewer: Thomas A. Atchison
bibdate: Sat Jan 11 13:29:06 MST 1997
bibtimestamp: 1997.01.11 13:29:06 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Stanis{\l}aw Lewanowicz
rawtitle: A simple approach to the summation of certain slowly convergent series
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

entry:
@Article{Lewanowicz:1994:SAS,
  author =       "Stanis{\l}aw Lewanowicz",
  title =        "A simple approach to the summation of certain slowly
                 convergent series",
  journal =      j-MATH-COMPUT,
  volume =       "63",
  number =       "208",
  pages =        "741--745",
  month =        oct,
  year =         "1994",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65B10",
  MRnumber =     "95a:65010",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Litvinov:1994:ACR
author: Grigori L. Litvinov
title: Approximate construction of rational approximations and the effect of error autocorrection
journal: j-RUSS-J-MATH-PHYS
volume: 1
number: 3
pages: 313--352
year: 1994
CODEN: RJMPEL
ISSN: 1061-9208 (print), 1555-6638 (electronic) OR 10619208 (print), 15556638 (electronic)
ISSNL: 1061-9208 OR 10619208
bibdate: Tue Mar 24 20:54:11 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.24 20:54:11 ???
URL: http://arxiv.org/abs/math/0101042
fjournal: Russian Journal of Mathematical Physics
acknowledgement: ack-nhfb
rawauthor: Grigori L. Litvinov
rawtitle: Approximate construction of rational approximations and the effect of error autocorrection
abstract:
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Pade approximations, linear and nonlinear Pade Chebyshev approximations) where very significant errors in the coefficients do not affect the accuracy of the approximation. The matter of import is that the errors in the numerator and the denominator of a fractional rational approximant compensate each other. This effect is related to the fact that the errors in the coefficients of a rational approximant are not distributed in an arbitrary way but form the coefficients of a new approximant to the approximated function. Understanding of the error autocorrection mechanism allows to decrease this error by varying the approximation procedure depending on the form of the approximant. Some applications are described in the paper. In particular, a method of implementation of basic calculations on decimal computers that uses the technique of rational approximations is described in the Appendix.par To a considerable extent the paper is a survey and the exposition is as elementary as possible.

rawabstract:
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Pad{\'e} approximations, linear and nonlinear Pad{\'e} Chebyshev approximations) where very significant errors in the coefficients do not affect the accuracy of the approximation. The matter of import is that the errors in the numerator and the denominator of a fractional rational approximant compensate each other. This effect is related to the fact that the errors in the coefficients of a rational approximant are not distributed in an arbitrary way but form the coefficients of a new approximant to the approximated function. Understanding of the error autocorrection mechanism allows to decrease this error by varying the approximation procedure depending on the form of the approximant. Some applications are described in the paper. In particular, a method of implementation of basic calculations on decimal computers that uses the technique of rational approximations is described in the Appendix.\par To a considerable extent the paper is a survey and the exposition is as elementary as possible.

entry:
@Article{Litvinov:1994:ACR,
  author =       "Grigori L. Litvinov",
  title =        "Approximate construction of rational approximations
                 and the effect of error autocorrection",
  journal =      j-RUSS-J-MATH-PHYS,
  volume =       "1",
  number =       "3",
  pages =        "313--352",
  month =        "????",
  year =         "1994",
  CODEN =        "RJMPEL",
  ISSN =         "1061-9208 (print), 1555-6638 (electronic)",
  ISSN-L =       "1061-9208",
  bibdate =      "Tue Mar 24 20:54:11 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/math/0101042",
  abstract =     "Several construction methods for rational
                 approximations to functions of one real variable are
                 described in the present paper; the computational
                 results that characterize the comparative accuracy of
                 these methods are presented; an effect of error
                 autocorrection is considered. This effect occurs in
                 efficient methods of rational approximation (e.g.,
                 Pad{\'e} approximations, linear and nonlinear Pad{\'e}
                 Chebyshev approximations) where very significant errors
                 in the coefficients do not affect the accuracy of the
                 approximation. The matter of import is that the errors
                 in the numerator and the denominator of a fractional
                 rational approximant compensate each other. This effect
                 is related to the fact that the errors in the
                 coefficients of a rational approximant are not
                 distributed in an arbitrary way but form the
                 coefficients of a new approximant to the approximated
                 function. Understanding of the error autocorrection
                 mechanism allows to decrease this error by varying the
                 approximation procedure depending on the form of the
                 approximant. Some applications are described in the
                 paper. In particular, a method of implementation of
                 basic calculations on decimal computers that uses the
                 technique of rational approximations is described in
                 the Appendix.\par

                 To a considerable extent the paper is a survey and the
                 exposition is as elementary as possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "Russian Journal of Mathematical Physics",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1994:NESa
author: D. W. Lozier and F. W. J. Olver
title: Numerical evaluation of special functions
type: Report
number: NISTIR 5383
institution: Computing and Applied Mathematics Laboratory, U. S. Department of Commerce
address: Washington, DC, USA
pages: 47
month: mar
monthnumber: 3
year: 1994
MRclass: 65D20 (33-00)
bibdate: Thu Nov 16 07:52:34 2023
bibtimestamp: 2023.11.16 07:52:34 ???
URL: https://math.nist.gov/~DLozier/publications/nistir5383.pdf
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
rawauthor: D. W. Lozier and F. W. J. Olver
rawtitle: Numerical evaluation of special functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field.

TOC:
1. Introduction / 3 2. Mathematical Developments / 5 3. Packages, Libraries and Systems / 6 3.1. Software Packages / 6 3.2. Intermediate Libraries / 8 3.3. Comprehensive Libraries / 8 3.4. Interactive Systems / 12 4. Functions of One Variable / 15 4.1. Airy Functions / 15 4.2. Error Functions, Dawson's Integral, Fresnel Integrals, Goodwin--Staton Integral / 15 4.3. Exponential Integrals, Logarithmic Integral, Sine and Cosine Integrals / 16 4.4. Gamma, Psi, and Polygamma Functions / 16 4.5. Landau Density and Distribution Functions / 16 4.6. Polylogarithms, Clausen Integral / 16 4.7. Zeta Function / 17 4.8. Additional Functions of One Variable / 17 5. Functions of Two or More Variables / 17 5.1. Bessel Functions / 17 5.2. Coulomb Wave Functions / 18 5.3. Elliptic Integrals and Functions / 18 5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals / 19 5.5. Hypergeometric and Concuent Hypergeometric Functions / 19 5.6. Incomplete Bessel Functions, Incomplete Beta Function / 19 5.7. Incomplete Gamma Functions, Generalized Exponential Integrals / 20 5.8. Legendre Functions and Associated Legendre Functions / 20 5.9. Mathieu, Lame, and Spheroidal Wave Functions / 20 5.10. Orthogonal Polynomials / 21 5.11. Polylogarithms (Generalized) / 21 5.12. Struve and Anger--Weber Functions / 21 5.13. Weber Parabolic Cylinder Functions / 21 5.14. Zeta Function (Generalized) / 21 5.15. Additional Functions of Two or More Variables / 21 6. Testing and Library Construction / 22 7. Future Trends / 22 Acknowledgments / 23 A Note on the Reference Acronyms / 23 References / 23--47

rawabstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field.

rawTOC:
1. Introduction / 3 \\ 2. Mathematical Developments / 5 \\ 3. Packages, Libraries and Systems / 6 \\ 3.1. Software Packages / 6 \\ 3.2. Intermediate Libraries / 8 \\ 3.3. Comprehensive Libraries / 8 \\ 3.4. Interactive Systems / 12 \\ 4. Functions of One Variable / 15 \\ 4.1. Airy Functions / 15 \\ 4.2. Error Functions, Dawson's Integral, Fresnel Integrals, Goodwin--Staton Integral / 15 \\ 4.3. Exponential Integrals, Logarithmic Integral, Sine and Cosine Integrals / 16 \\ 4.4. Gamma, Psi, and Polygamma Functions / 16 \\ 4.5. Landau Density and Distribution Functions / 16 \\ 4.6. Polylogarithms, Clausen Integral / 16 \\ 4.7. Zeta Function / 17 \\ 4.8. Additional Functions of One Variable / 17 \\ 5. Functions of Two or More Variables / 17 \\ 5.1. Bessel Functions / 17 \\ 5.2. Coulomb Wave Functions / 18 \\ 5.3. Elliptic Integrals and Functions / 18 \\ 5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals / 19 \\ 5.5. Hypergeometric and Concuent Hypergeometric Functions / 19 \\ 5.6. Incomplete Bessel Functions, Incomplete Beta Function / 19 \\ 5.7. Incomplete Gamma Functions, Generalized Exponential Integrals / 20 \\ 5.8. Legendre Functions and Associated Legendre Functions / 20 \\ 5.9. Mathieu, Lam{\'e}, and Spheroidal Wave Functions / 20 \\ 5.10. Orthogonal Polynomials / 21 \\ 5.11. Polylogarithms (Generalized) / 21 \\ 5.12. Struve and Anger--Weber Functions / 21 \\ 5.13. Weber Parabolic Cylinder Functions / 21 \\ 5.14. Zeta Function (Generalized) / 21 \\ 5.15. Additional Functions of Two or More Variables / 21 \\ 6. Testing and Library Construction / 22 \\ 7. Future Trends / 22 \\ Acknowledgments / 23 \\ A Note on the Reference Acronyms / 23 \\ References / 23--47

entry:
@TechReport{Lozier:1994:NESa,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Numerical evaluation of special functions",
  type =         "Report",
  number =       "NISTIR 5383",
  institution =  "Computing and Applied Mathematics Laboratory, U. S.
                 Department of Commerce",
  address =      "Washington, DC, USA",
  pages =        "47",
  month =        mar,
  year =         "1994",
  MRclass =      "65D20 (33-00)",
  bibdate =      "Thu Nov 16 07:52:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://math.nist.gov/~DLozier/publications/nistir5383.pdf",
  abstract =     "Higher transcendental functions continue to play
                 varied and important roles in investigations by
                 engineers, mathematicians, scientists and
                 statisticians. The purpose of this paper is to assist
                 in locating useful approximations and software for the
                 numerical generation of these functions, and to offer
                 some suggestions for future developments in this
                 field.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  tableofcontents = "1. Introduction / 3 \\
                 2. Mathematical Developments / 5 \\
                 3. Packages, Libraries and Systems / 6 \\
                 3.1. Software Packages / 6 \\
                 3.2. Intermediate Libraries / 8 \\
                 3.3. Comprehensive Libraries / 8 \\
                 3.4. Interactive Systems / 12 \\
                 4. Functions of One Variable / 15 \\
                 4.1. Airy Functions / 15 \\
                 4.2. Error Functions, Dawson's Integral, Fresnel
                 Integrals, Goodwin--Staton Integral / 15 \\
                 4.3. Exponential Integrals, Logarithmic Integral, Sine
                 and Cosine Integrals / 16 \\
                 4.4. Gamma, Psi, and Polygamma Functions / 16 \\
                 4.5. Landau Density and Distribution Functions / 16 \\
                 4.6. Polylogarithms, Clausen Integral / 16 \\
                 4.7. Zeta Function / 17 \\
                 4.8. Additional Functions of One Variable / 17 \\
                 5. Functions of Two or More Variables / 17 \\
                 5.1. Bessel Functions / 17 \\
                 5.2. Coulomb Wave Functions / 18 \\
                 5.3. Elliptic Integrals and Functions / 18 \\
                 5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals
                 / 19 \\
                 5.5. Hypergeometric and Concuent Hypergeometric
                 Functions / 19 \\
                 5.6. Incomplete Bessel Functions, Incomplete Beta
                 Function / 19 \\
                 5.7. Incomplete Gamma Functions, Generalized
                 Exponential Integrals / 20 \\
                 5.8. Legendre Functions and Associated Legendre
                 Functions / 20 \\
                 5.9. Mathieu, Lam{\'e}, and Spheroidal Wave Functions /
                 20 \\
                 5.10. Orthogonal Polynomials / 21 \\
                 5.11. Polylogarithms (Generalized) / 21 \\
                 5.12. Struve and Anger--Weber Functions / 21 \\
                 5.13. Weber Parabolic Cylinder Functions / 21 \\
                 5.14. Zeta Function (Generalized) / 21 \\
                 5.15. Additional Functions of Two or More Variables /
                 21 \\
                 6. Testing and Library Construction / 22 \\
                 7. Future Trends / 22 \\
                 Acknowledgments / 23 \\
                 A Note on the Reference Acronyms / 23 \\
                 References / 23--47",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:1994:NESb
author: D. W. Lozier and F. W. J. Olver
title: Numerical evaluation of special functions
crossref: Gautschi:1994:MCH
volume: 48
pages: 79--125
year: 1994
DOI: https://doi.org/10.1090/psapm/048/1314844
MRclass: 65D20 (30-04 33-04 41-04)
MRnumber: 95m:65036 (1314844)
MRreviewer: John P. Coleman
bibdate: Fri Jul 9 05:44:10 2004
bibtimestamp: 2004.07.09 05:44:10 ???
series: Proc. Sympos. Appl. Math.
URL: http://math.nist.gov/mcsd/Reports/2001/nesf/
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
rawauthor: D. W. Lozier and F. W. J. Olver
rawtitle: Numerical evaluation of special functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

abstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists, and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in the field.

remark:
The references list contains about 400 entries which should ultimately be incorporated in this BibTeX bibliography collection.

rawabstract:
Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists, and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in the field.

entry:
@InProceedings{Lozier:1994:NESb,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Numerical evaluation of special functions",
  crossref =     "Gautschi:1994:MCH",
  volume =       "48",
  pages =        "79--125",
  year =         "1994",
  DOI =          "https://doi.org/10.1090/psapm/048/1314844",
  MRclass =      "65D20 (30-04 33-04 41-04)",
  MRnumber =     "95m:65036 (1314844)",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Fri Jul 9 05:44:10 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  series =       "Proc. Sympos. Appl. Math.",
  URL =          "http://math.nist.gov/mcsd/Reports/2001/nesf/",
  abstract =     "Higher transcendental functions continue to play
                 varied and important roles in investigations by
                 engineers, mathematicians, scientists, and
                 statisticians. The purpose of this paper is to assist
                 in locating useful approximations and software for the
                 numerical generation of these functions, and to offer
                 some suggestions for future developments in the
                 field.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  remark =       "The references list contains about 400 entries which
                 should ultimately be incorporated in this BibTeX
                 bibliography collection.",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1994:SNS
author: Daniel W. Lozier
title: Software Needs in Special Functions
type: Technical Report
number: NISTIR 5490
institution: pub-NIST
address: pub-NIST:adr
pages: 16
month: aug
monthnumber: 8
year: 1994
bibdate: Fri Jul 09 05:47:26 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 05:47:26 ???
note: Published in cite Lozier:1996:SNS.
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawnote: Published in \cite{Lozier:1996:SNS}.
rawtitle: Software Needs in Special Functions
entry:
@TechReport{Lozier:1994:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  type =         "Technical Report",
  number =       "NISTIR 5490",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "16",
  month =        aug,
  year =         "1994",
  bibdate =      "Fri Jul 09 05:47:26 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Lozier:1996:SNS}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: MacLeod:1994:CIA
author: Allan J. MacLeod
title: Computation of inhomogeneous Airy functions
journal: j-J-COMPUT-APPL-MATH
volume: 53
number: 1
pages: 109--116
day: 29
month: jul
monthnumber: 7
year: 1994
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:31 MST 2017
bibtimestamp: 2017.02.25 12:24:31 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794901961
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Allan J. MacLeod
rawtitle: Computation of inhomogeneous {Airy} functions
entry:
@Article{MacLeod:1994:CIA,
  author =       "Allan J. MacLeod",
  title =        "Computation of inhomogeneous {Airy} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "53",
  number =       "1",
  pages =        "109--116",
  day =          "29",
  month =        jul,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:31 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794901961",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: MacLeod:1994:TBT
author: Allan J. MacLeod
title: Table-based tests for Bessel function software
journal: j-ADV-COMPUT-MATH
volume: 2
number: 2
pages: 251--260
month: mar
monthnumber: 3
year: 1994
CODEN: ACMHEX
DOI: https://doi.org/10.1007/BF02521111
ISSN: 1019-7168 (print), 1572-9044 (electronic) OR 10197168 (print), 15729044 (electronic)
ISSNL: 1019-7168 OR 10197168
MRclass: 65-04 (33-04 33C10 65D20)
MRnumber: 1269384
bibdate: Sat Feb 3 18:21:41 MST 2018
bibtimestamp: 2018.02.03 18:21:41 MST
URL: http://link.springer.com/article/10.1007/BF02521111
fjournal: Advances in Computational Mathematics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10444
rawauthor: Allan J. MacLeod
rawtitle: Table-based tests for {Bessel} function software
bibsource:
https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{MacLeod:1994:TBT,
  author =       "Allan J. MacLeod",
  title =        "Table-based tests for {Bessel} function software",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "2",
  number =       "2",
  pages =        "251--260",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/BF02521111",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "65-04 (33-04 33C10 65D20)",
  MRnumber =     "1269384",
  bibdate =      "Sat Feb 3 18:21:41 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02521111",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
}


bibtype: inproceedings
filename: elefunt.bib
label: Magnus:1994:ASA
author: Alphonse P. Magnus
crossref: Cuyt:1994:NNM
pages: 173--185
year: 1994
bibdate: Mon Nov 24 21:30:41 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2008.11.24 21:30:41 ???
ZMnumber: 809.41015
acknowledgement: ack-nhfb
rawauthor: Alphonse P. Magnus
title:
Asymptotics and super asymptotics of best rational approximation error norms for the exponential function (the `$ 1 / 9 $' problem) by the Caratheodory--Fejer method

rawtitle:
Asymptotics and super asymptotics of best rational approximation error norms for the exponential function (the `$ 1 / 9 $' problem) by the {Carath{\'e}odory--Fej{\'e}r} method

entry:
@InProceedings{Magnus:1994:ASA,
  author =       "Alphonse P. Magnus",
  title =        "Asymptotics and super asymptotics of best rational
                 approximation error norms for the exponential function
                 (the `$ 1 / 9 $' problem) by the
                 {Carath{\'e}odory--Fej{\'e}r} method",
  crossref =     "Cuyt:1994:NNM",
  pages =        "173--185",
  year =         "1994",
  bibdate =      "Mon Nov 24 21:30:41 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "809.41015",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Marsaglia:1994:REI
author: George Marsaglia and Arif Zaman and John C. W. Marsaglia
title: Rapid evaluation of the inverse of the normal distribution function
journal: j-STAT-PROB-LETT
volume: 19
number: 4
pages: 259--266
day: 15
month: mar
monthnumber: 3
year: 1994
CODEN: SPLTDC
DOI: https://doi.org/10.1016/0167-7152(94)90174-0
ISSN: 0167-7152 (print), 1879-2103 (electronic) OR 01677152 (print), 18792103 (electronic)
ISSNL: 0167-7152 OR 01677152
MRclass: 65U05
MRnumber: 1 278 658
bibdate: Thu Dec 22 07:42:24 2011
bibtimestamp: 2011.12.22 07:42:24 ???
fjournal: Statistics & Probability Letters
ZMnumber: 0798.65132
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01677152
rawauthor: George Marsaglia and Arif Zaman and John C. W. Marsaglia
rawtitle: Rapid evaluation of the inverse of the normal distribution function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database

abstract:
This is an interesting article with direct application in generating normal random variable by computer programs. The suggested applications are related to Monte Carlo simulation based on massively parallel systems or supercomputers. The idea is to replace larger programs with complicated computations and with difficulties in accuracy controlling by simpler arithmetic programs that use tabled constants. These seem to be the normal evolution since memory becomes cheaper and cheaper.par The authors compute the inverse of the cPhi function $$ c P h i(x) = (2 / pi )^1 / 2 int ^infty _x exp ( - t^2 / 2) d t = u, $$ using a uniform random variable as input and the truncated Taylor series development of it. In order to increase the speed the coefficients of the truncated Taylor series $$ x(u_0 + h) = x(u_0) + x'(u_0) cdot h + 1 over 2 x''(u_0) cdot h^2 + 1 over 6 x'''(u_0) cdot h^3, $$ are predetermined for 1024 points. And here comes another bright idea: the 1024 points are chosen based on the representation of the uniform random variable in modern computers as floating point variable of the form: $ u = 2^-k ((1 / 2) + (j / 64)) + 2^-k cdot (m / 2^24) $ with $ 0 le k & l t; 32 $, $ 0 le j & l t; 32 $ and $ 0 le m & l t; 2^18 $ and considering 32 bit representation.par With this assumptions and the truncation to the third power of $h$ of the Taylor series, the authors show that the error does not exceed the limit of single precision accuracy. Furthermore the calculations are speeded up based on reducing multiplications. A number of FORTRAN programs are also presented in order to evaluate the complementary normal distribution function cPhi (several versions) with great accuracy, create the constant tables, and generate the normal distribution variable. These simple programs give the user the possibility to completely control the accuracy.

keywords:
cPhi function; FORTRAN programs; massive parallel systems; Monte Carlo simulation; normal distribution function; normal random variable; supercomputers; truncated Taylor series

ZMclass:
*65C99 Numerical simulation 65C05 Monte Carlo methods 60-04 Machine computation, programs (probability theory) 60E05 General theory of probability distributions 62E17 Approximations to statistical distributions (nonasymptotic)

rawabstract:
This is an interesting article with direct application in generating normal random variable by computer programs. The suggested applications are related to Monte Carlo simulation based on massively parallel systems or supercomputers. The idea is to replace larger programs with complicated computations and with difficulties in accuracy controlling by simpler arithmetic programs that use tabled constants. These seem to be the normal evolution since memory becomes cheaper and cheaper.\par The authors compute the inverse of the cPhi function $$ c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( - t^2 / 2) d t = u, $$ using a uniform random variable as input and the truncated Taylor series development of it. In order to increase the speed the coefficients of the truncated Taylor series $$ x(u_0 + h) = x(u_0) + x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1 \over 6} x'''(u_0) \cdot h^3, $$ are predetermined for 1024 points. And here comes another bright idea: the 1024 points are chosen based on the representation of the uniform random variable in modern computers as floating point variable of the form: $ u = 2^{-k} ((1 / 2) + (j / 64)) + 2^{-k} \cdot (m / 2^{24}) $ with $ 0 \le k & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m & l t; 2^{18} $ and considering 32 bit representation.\par With this assumptions and the truncation to the third power of $h$ of the Taylor series, the authors show that the error does not exceed the limit of single precision accuracy. Furthermore the calculations are speeded up based on reducing multiplications. A number of FORTRAN programs are also presented in order to evaluate the complementary normal distribution function cPhi (several versions) with great accuracy, create the constant tables, and generate the normal distribution variable. These simple programs give the user the possibility to completely control the accuracy.

entry:
@Article{Marsaglia:1994:REI,
  author =       "George Marsaglia and Arif Zaman and John C. W.
                 Marsaglia",
  title =        "Rapid evaluation of the inverse of the normal
                 distribution function",
  journal =      j-STAT-PROB-LETT,
  volume =       "19",
  number =       "4",
  pages =        "259--266",
  day =          "15",
  month =        mar,
  year =         "1994",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/0167-7152(94)90174-0",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "65U05",
  MRnumber =     "1 278 658",
  bibdate =      "Thu Dec 22 07:42:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  ZMnumber =     "0798.65132",
  abstract =     "This is an interesting article with direct application
                 in generating normal random variable by computer
                 programs. The suggested applications are related to
                 Monte Carlo simulation based on massively parallel
                 systems or supercomputers. The idea is to replace
                 larger programs with complicated computations and with
                 difficulties in accuracy controlling by simpler
                 arithmetic programs that use tabled constants. These
                 seem to be the normal evolution since memory becomes
                 cheaper and cheaper.\par

                 The authors compute the inverse of the cPhi function $$
                 c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( -
                 t^2 / 2) d t = u, $$ using a uniform random variable as
                 input and the truncated Taylor series development of
                 it. In order to increase the speed the coefficients of
                 the truncated Taylor series $$ x(u_0 + h) = x(u_0) +
                 x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1
                 \over 6} x'''(u_0) \cdot h^3, $$ are predetermined for
                 1024 points. And here comes another bright idea: the
                 1024 points are chosen based on the representation of
                 the uniform random variable in modern computers as
                 floating point variable of the form: $ u = 2^{-k} ((1 /
                 2) + (j / 64)) + 2^{-k} \cdot (m / 2^{24}) $ with $ 0
                 \le k & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m
                 & l t; 2^{18} $ and considering 32 bit
                 representation.\par

                 With this assumptions and the truncation to the third
                 power of $h$ of the Taylor series, the authors show
                 that the error does not exceed the limit of single
                 precision accuracy. Furthermore the calculations are
                 speeded up based on reducing multiplications. A number
                 of FORTRAN programs are also presented in order to
                 evaluate the complementary normal distribution function
                 cPhi (several versions) with great accuracy, create the
                 constant tables, and generate the normal distribution
                 variable. These simple programs give the user the
                 possibility to completely control the accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "cPhi function; FORTRAN programs; massive parallel
                 systems; Monte Carlo simulation; normal distribution
                 function; normal random variable; supercomputers;
                 truncated Taylor series",
  ZMclass =      "*65C99 Numerical simulation 65C05 Monte Carlo methods
                 60-04 Machine computation, programs (probability
                 theory) 60E05 General theory of probability
                 distributions 62E17 Approximations to statistical
                 distributions (nonasymptotic)",
  ZMreviewer =   "A. Pasculescu (Bucuresti)",
}


bibtype: article
filename: elefunt.bib
label: Merrheim:1994:CEF
author: X. Merrheim
title: The computation of elementary functions in radix $ 2^p $
journal: j-COMPUTING
volume: 53
number: 3--4
pages: 219--232
year: 1994
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 68M07
MRnumber: 95j:68028
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Computing
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: X. Merrheim
rawtitle: The computation of elementary functions in radix $ 2^p $
note:
International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993).

rawnote:
International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993).

entry:
@Article{Merrheim:1994:CEF,
  author =       "X. Merrheim",
  title =        "The computation of elementary functions in radix $ 2^p
                 $",
  journal =      j-COMPUTING,
  volume =       "53",
  number =       "3--4",
  pages =        "219--232",
  year =         "1994",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68M07",
  MRnumber =     "95j:68028",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "International Symposium on Scientific Computing,
                 Computer Arithmetic and Validated Numerics (Vienna,
                 1993).",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: article
filename: elefunt.bib
label: Narayanaswami:1994:AE
author: Chandrasekhar Narayanaswami and William Luken
title: Approximating $ x^n $ efficiently
journal: j-INFO-PROC-LETT
volume: 50
number: 4
pages: 205--210
day: 25
month: may
monthnumber: 5
year: 1994
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 65D20 (41-04 65B99)
MRnumber: 95b:65031
bibdate: Wed Nov 11 12:16:26 MST 1998
bibtimestamp: 1998.11.11 12:16:26 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
affiliation: IBM Advanced Workstations and Systems Div
affiliationaddress: Austin, TX, USA
corpsource: IBM Adv. Workstations and Syst. Div., Austin, TX, USA
journalURL: http://www.sciencedirect.com/science/journal/00200190
journalabr: Inf Process Lett
treatment: T Theoretical or Mathematical
rawauthor: Chandrasekhar Narayanaswami and William Luken
rawtitle: Approximating $ x^n $ efficiently
bibsource:
Compendex database; http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
$x^n$ approximation; approximation theory; Approximation theory; Color computer graphics; Computational complexity; Computational methods; computer graphics; elementary functions; floating-point arithmetic; Function evaluation; graphics modeling; Image quality; Light intensity computation; look-up tables; performance requirements; Polynomial evaluation; Polynomials; polynomials; power function; scientific applications; Semiconducting silicon; Table lookup

entry:
@Article{Narayanaswami:1994:AE,
  author =       "Chandrasekhar Narayanaswami and William Luken",
  title =        "Approximating $ x^n $ efficiently",
  journal =      j-INFO-PROC-LETT,
  volume =       "50",
  number =       "4",
  pages =        "205--210",
  day =          "25",
  month =        may,
  year =         "1994",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "65D20 (41-04 65B99)",
  MRnumber =     "95b:65031",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Advanced Workstations and Systems Div",
  affiliationaddress = "Austin, TX, USA",
  classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F
                 (Interpolation and function approximation); C4130
                 (Interpolation and function approximation); C6130B
                 (Graphics techniques)",
  corpsource =   "IBM Adv. Workstations and Syst. Div., Austin, TX,
                 USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "$x^n$ approximation; approximation theory;
                 Approximation theory; Color computer graphics;
                 Computational complexity; Computational methods;
                 computer graphics; elementary functions; floating-point
                 arithmetic; Function evaluation; graphics modeling;
                 Image quality; Light intensity computation; look-up
                 tables; performance requirements; Polynomial
                 evaluation; Polynomials; polynomials; power function;
                 scientific applications; Semiconducting silicon; Table
                 lookup",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Nishioka:1994:EFB
author: Keiji Nishioka
title: Elementary functions based on elliptic curves
journal: j-TOKYO-J-MATH
volume: 17
number: 2
pages: 439--446
year: 1994
ISSN: 0387-3870 OR 03873870
MRclass: 12H05
MRnumber: 96b:12011
MRreviewer: Alexandru Buium
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Tokyo journal of mathematics
acknowledgement: ack-nhfb
rawauthor: Keiji Nishioka
rawtitle: Elementary functions based on elliptic curves
entry:
@Article{Nishioka:1994:EFB,
  author =       "Keiji Nishioka",
  title =        "Elementary functions based on elliptic curves",
  journal =      j-TOKYO-J-MATH,
  volume =       "17",
  number =       "2",
  pages =        "439--446",
  year =         "1994",
  ISSN =         "0387-3870",
  MRclass =      "12H05",
  MRnumber =     "96b:12011",
  MRreviewer =   "Alexandru Buium",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tokyo journal of mathematics",
}


bibtype: article
filename: elefunt.bib
label: Ohta:1994:INP
author: Shigemi Ohta and Eiichi Goto and Weng Fai Wong and Nobuaki Yoshida
title: Improvement and new proposal on fast evaluation of elementary functions. (Japanese)
journal: j-TRANS-INFO-PROCESSING-SOC-JAPAN
volume: 35
number: 5
pages: 926--933
month: may
monthnumber: 5
year: 1994
CODEN: JSGRD5
ISSN: 0387-5806 OR 03875806
ISSNL: 0387-5806 OR 03875806
MRclass: 65D20
MRnumber: 95f:65045
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Transactions of the Information Processing Society of Japan
language: Japanese
acknowledgement: ack-nhfb
affiliation: RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan
thesaurus: Digital arithmetic; Function evaluation; Random number generation; Table lookup
rawauthor: Shigemi Ohta and Eiichi Goto and Weng Fai Wong and Nobuaki Yoshida
rawtitle: Improvement and new proposal on fast evaluation of elementary functions. ({Japanese})
abstract:
Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp. 1570-1579, 1993) introduced fast methods for numerical evaluation of elementary functions based on table lookup. They are called ATA (add/table-lookup/add) and ATA-M (add/table-lookup/add and multiply) methods for single- and double-precision calculations respectively. In this paper, an improvement to these methods that shrinks the size of the table by a factor of about 3/16 is presented. Another method called the `split parallel multiplication method', which is characterized by simpler table lookup than ATA-M and by split and parallel use of double-precision floating point circuitry, is also introduced, These new methods fit on to integrated circuits of a size comparable with commercially available floating-point accelerators. Methods for accelerating double-precision division, generating uniform pseudo-random numbers in double-precision, and accelerating the multiplication of single-precision complex numbers using the same circuitry are proposed.

keywords:
Add/table-lookup/add method; Add/table-lookup/add/multiply method; ATA method; ATA-M method; Double-precision calculations; Double-precision division; Double-precision floating point circuitry; Elementary functions evaluation; Floating-point accelerators; Integrated circuits; Numerical evaluation; Single-precision calculations; Single-precision complex number multiplication; Split parallel multiplication method; Table size; Uniform pseudo-random number generation

rawabstract:
Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp. 1570-1579, 1993) introduced fast methods for numerical evaluation of elementary functions based on table lookup. They are called ATA (add/table-lookup/add) and ATA-M (add/table-lookup/add and multiply) methods for single- and double-precision calculations respectively. In this paper, an improvement to these methods that shrinks the size of the table by a factor of about 3/16 is presented. Another method called the `split parallel multiplication method', which is characterized by simpler table lookup than ATA-M and by split and parallel use of double-precision floating point circuitry, is also introduced, These new methods fit on to integrated circuits of a size comparable with commercially available floating-point accelerators. Methods for accelerating double-precision division, generating uniform pseudo-random numbers in double-precision, and accelerating the multiplication of single-precision complex numbers using the same circuitry are proposed.

entry:
@Article{Ohta:1994:INP,
  author =       "Shigemi Ohta and Eiichi Goto and Weng Fai Wong and
                 Nobuaki Yoshida",
  title =        "Improvement and new proposal on fast evaluation of
                 elementary functions. ({Japanese})",
  journal =      j-TRANS-INFO-PROCESSING-SOC-JAPAN,
  volume =       "35",
  number =       "5",
  pages =        "926--933",
  month =        may,
  year =         "1994",
  CODEN =        "JSGRD5",
  ISSN =         "0387-5806",
  ISSN-L =       "0387-5806",
  MRclass =      "65D20",
  MRnumber =     "95f:65045",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp.
                 1570-1579, 1993) introduced fast methods for numerical
                 evaluation of elementary functions based on table
                 lookup. They are called ATA (add/table-lookup/add) and
                 ATA-M (add/table-lookup/add and multiply) methods for
                 single- and double-precision calculations respectively.
                 In this paper, an improvement to these methods that
                 shrinks the size of the table by a factor of about 3/16
                 is presented. Another method called the `split parallel
                 multiplication method', which is characterized by
                 simpler table lookup than ATA-M and by split and
                 parallel use of double-precision floating point
                 circuitry, is also introduced, These new methods fit on
                 to integrated circuits of a size comparable with
                 commercially available floating-point accelerators.
                 Methods for accelerating double-precision division,
                 generating uniform pseudo-random numbers in
                 double-precision, and accelerating the multiplication
                 of single-precision complex numbers using the same
                 circuitry are proposed.",
  acknowledgement = ack-nhfb,
  affiliation =  "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods); C6130 (Data handling techniques)",
  fjournal =     "Transactions of the Information Processing Society of
                 Japan",
  keywords =     "Add/table-lookup/add method;
                 Add/table-lookup/add/multiply method; ATA method; ATA-M
                 method; Double-precision calculations; Double-precision
                 division; Double-precision floating point circuitry;
                 Elementary functions evaluation; Floating-point
                 accelerators; Integrated circuits; Numerical
                 evaluation; Single-precision calculations;
                 Single-precision complex number multiplication; Split
                 parallel multiplication method; Table size; Uniform
                 pseudo-random number generation",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Digital arithmetic; Function evaluation; Random number
                 generation; Table lookup",
}


bibtype: inproceedings
filename: elefunt.bib
label: Olver:1994:GEI
author: F. W. J. Olver
title: The generalized exponential integral
crossref: Zahar:1994:ACF
pages: 497--510
year: 1994
MRclass: 33B20 (34E05 41A60)
MRnumber: 1333639
MRreviewer: Richard B. Paris
bibdate: Sat Feb 18 15:02:52 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:02:52 ???
series: International Series of Numerical Mathematics
acknowledgement: ack-nhfb
rawauthor: F. W. J. Olver
rawtitle: The generalized exponential integral
entry:
@InProceedings{Olver:1994:GEI,
  author =       "F. W. J. Olver",
  title =        "The generalized exponential integral",
  crossref =     "Zahar:1994:ACF",
  pages =        "497--510",
  year =         "1994",
  MRclass =      "33B20 (34E05 41A60)",
  MRnumber =     "1333639",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Sat Feb 18 15:02:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "International Series of Numerical Mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Osada:1994:CAM
author: Naoki Osada
title: Convergence acceleration methods
journal: Surikaisekikenkyusho Kokyuroku
volume: 880
pages: 28--43
year: 1994
MRclass: 65B05
MRnumber: 1366233
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
note: The state of the art of scientific computing and its prospects (Japanese) (Kyoto, 1993)
fjournal: Surikaisekikenkyusho Kokyuroku
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Naoki Osada
rawnote: The state of the art of scientific computing and its prospects (Japanese) (Kyoto, 1993)
rawtitle: Convergence acceleration methods
entry:
@Article{Osada:1994:CAM,
  author =       "Naoki Osada",
  title =        "Convergence acceleration methods",
  journal =      "S\=urikaisekikenky\=usho K\=oky\=uroku",
  volume =       "880",
  number =       "??",
  pages =        "28--43",
  month =        "????",
  year =         "1994",
  MRclass =      "65B05",
  MRnumber =     "1366233",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "The state of the art of scientific computing and its
                 prospects (Japanese) (Kyoto, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "S\=urikaisekikenky\=usho K\=oky\=uroku",
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Rappoport:1994:TMC
author: Juri M. Rappoport
title: The Tau-Method and the Computation of the Bessel Functions of the Complex Order
crossref: Brown:1994:PCL
pages: 353--355
year: 1994
bibdate: Sat Jun 11 17:22:09 2011
bibtimestamp: 2011.06.11 17:22:09 ???
acknowledgement: ack-nhfb
rawauthor: Juri M. Rappoport
rawtitle: The {Tau-Method} and the Computation of the {Bessel} Functions of the Complex Order
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database

entry:
@InProceedings{Rappoport:1994:TMC,
  author =       "Juri M. Rappoport",
  title =        "The {Tau-Method} and the Computation of the {Bessel}
                 Functions of the Complex Order",
  crossref =     "Brown:1994:PCL",
  pages =        "353--355",
  year =         "1994",
  bibdate =      "Sat Jun 11 17:22:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Schulte:1994:HDE
author: M. J. Schulte and E. E. Swartzlander, Jr.
title: Hardware Design for Exactly Rounded Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 8
pages: 964--973
month: aug
monthnumber: 8
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.295858
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:29:07 MST
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Dept. of Electr. and Comput. Eng., Texas Univ., Austin, TX, USA
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. J. Schulte and E. E. {Swartzlander, Jr.}
rawtitle: Hardware Design for Exactly Rounded Elementary Functions
abstract:
This paper presents hardware designs that produce exactly rounded results for the functions of reciprocal, square-root, 2/sup x/, and log/sub 2/(x). These designs use polynomial approximation in which the terms in the approximation are generated in parallel, and then summed by using a multi-operand adder. To reduce the number of terms in the approximation, the input interval is partitioned into subintervals of equal size, and different coefficients are used for each subinterval. The coefficients used in the approximation are initially determined based on the Chebyshev series approximation. They are then adjusted to obtain exactly rounded results for all inputs. Hardware designs are presented, and delay and area comparisons are made based on the degree of the approximating polynomial and the accuracy of the final result. For single-precision floating point numbers, a design that produces exactly rounded results for all four functions has an estimated delay of 80 ns and a total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS technology. Allowing the results to have a maximum error of one unit in the last place reduces the computational delay by 5% to 30% and the area requirements by 33% to 77%.

keywords:
1 Micron; 1.0-Micron CMOS technology; Argument reduction; Chebyshev series approximation; Chip area; Computational delay; Computer arithmetic; Exact rounding; Exactly rounded elementary functions; Hardware designs; Multi-operand adder; Parallel multiplier; Polynomial approximation; Reciprocal; Single-precision floating point numbers; Special-purpose hardware; Square-root

thesaurus:
Approximation theory; Chebyshev approximation; CMOS integrated circuits; Digital arithmetic; Multiplying circuits; Polynomials; Summing circuits

rawabstract:
This paper presents hardware designs that produce exactly rounded results for the functions of reciprocal, square-root, 2/sup x/, and log/sub 2/(x). These designs use polynomial approximation in which the terms in the approximation are generated in parallel, and then summed by using a multi-operand adder. To reduce the number of terms in the approximation, the input interval is partitioned into subintervals of equal size, and different coefficients are used for each subinterval. The coefficients used in the approximation are initially determined based on the Chebyshev series approximation. They are then adjusted to obtain exactly rounded results for all inputs. Hardware designs are presented, and delay and area comparisons are made based on the degree of the approximating polynomial and the accuracy of the final result. For single-precision floating point numbers, a design that produces exactly rounded results for all four functions has an estimated delay of 80 ns and a total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS technology. Allowing the results to have a maximum error of one unit in the last place reduces the computational delay by 5\% to 30\% and the area requirements by 33\% to 77\%.

entry:
@Article{Schulte:1994:HDE,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Hardware Design for Exactly Rounded Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "964--973",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295858",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This paper presents hardware designs that produce
                 exactly rounded results for the functions of
                 reciprocal, square-root, 2/sup x/, and log/sub 2/(x).
                 These designs use polynomial approximation in which the
                 terms in the approximation are generated in parallel,
                 and then summed by using a multi-operand adder. To
                 reduce the number of terms in the approximation, the
                 input interval is partitioned into subintervals of
                 equal size, and different coefficients are used for
                 each subinterval. The coefficients used in the
                 approximation are initially determined based on the
                 Chebyshev series approximation. They are then adjusted
                 to obtain exactly rounded results for all inputs.
                 Hardware designs are presented, and delay and area
                 comparisons are made based on the degree of the
                 approximating polynomial and the accuracy of the final
                 result. For single-precision floating point numbers, a
                 design that produces exactly rounded results for all
                 four functions has an estimated delay of 80 ns and a
                 total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS
                 technology. Allowing the results to have a maximum
                 error of one unit in the last place reduces the
                 computational delay by 5\% to 30\% and the area
                 requirements by 33\% to 77\%.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Dept. of Electr. and Comput. Eng., Texas Univ.,
                 Austin, TX, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "B0290F (Interpolation and function approximation);
                 B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C4130 (Interpolation and function
                 approximation); C5120 (Logic and switching circuits);
                 C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "1 Micron; 1.0-Micron CMOS technology; Argument
                 reduction; Chebyshev series approximation; Chip area;
                 Computational delay; Computer arithmetic; Exact
                 rounding; Exactly rounded elementary functions;
                 Hardware designs; Multi-operand adder; Parallel
                 multiplier; Polynomial approximation; Reciprocal;
                 Single-precision floating point numbers;
                 Special-purpose hardware; Square-root",
  numericalindex = "Size 1.0E-06 m",
  pubcountry =   "USA",
  thesaurus =    "Approximation theory; Chebyshev approximation; CMOS
                 integrated circuits; Digital arithmetic; Multiplying
                 circuits; Polynomials; Summing circuits",
}


bibtype: inproceedings
filename: elefunt.bib
label: Skaf:1994:LHI
author: Ali Skaf and Jean-Michel Muller and Alain Guyot
editor: Anonymous
title: On-Line Hardware Implementation for Complex Exponential and Logarithm
publisher: Editions Frontieres
address: B. P. 33. 91192 Gif-sur-Yvette Cedex, France
pages: 252--255
year: 1994
ISBN: 2-86332-160-9 OR 2863321609
ISBN13: 978-2-86332-160-7 OR 9782863321607
bibdate: Fri Sep 29 10:32:36 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.09.29 10:32:36 ???
acknowledgement: ack-nhfb
rawauthor: Ali Skaf and Jean-Michel Muller and Alain Guyot
raweditor: Anonymous
rawtitle: On-Line Hardware Implementation for Complex Exponential and Logarithm
booktitle:
ESSCIRC '94: Twentieth European Solid-State Circuits Conference. Ulm, Germany. September 20--22, 1994

rawbooktitle:
{ESSCIRC '94: Twentieth European Solid-State Circuits Conference. Ulm, Germany. September 20--22, 1994}

entry:
@InProceedings{Skaf:1994:LHI,
  author =       "Ali Skaf and Jean-Michel Muller and Alain Guyot",
  editor =       "Anonymous",
  booktitle =    "{ESSCIRC '94: Twentieth European Solid-State Circuits
                 Conference. Ulm, Germany. September 20--22, 1994}",
  title =        "On-Line Hardware Implementation for Complex
                 Exponential and Logarithm",
  publisher =    "{\'E}ditions Fronti{\`e}res",
  address =      "B. P. 33. 91192 Gif-sur-Yvette Cedex, France",
  pages =        "252--255",
  year =         "1994",
  ISBN =         "2-86332-160-9",
  ISBN-13 =      "978-2-86332-160-7",
  bibdate =      "Fri Sep 29 10:32:36 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Sorenson:1994:TFG
author: J. Sorenson
title: Two Fast GCD Algorithms
journal: j-J-ALG
volume: 16
number: 1
pages: 110--144
month: jan
monthnumber: 1
year: 1994
CODEN: JOALDV
DOI: https://doi.org/10.1006/jagm.1994.1006
ISSN: 0196-6774 (print), 1090-2678 (electronic) OR 01966774 (print), 10902678 (electronic)
ISSNL: 0196-6774 OR 01966774
bibdate: Tue Dec 11 09:15:38 MST 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib
bibtimestamp: 2012.12.11 09:15:38 MST
URL: http://www.sciencedirect.com/science/article/pii/S0196677484710066
fjournal: Journal of Algorithms
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01966774
rawauthor: J. Sorenson
rawtitle: Two Fast {GCD} Algorithms
entry:
@Article{Sorenson:1994:TFG,
  author =       "J. Sorenson",
  title =        "Two Fast {GCD} Algorithms",
  journal =      j-J-ALG,
  volume =       "16",
  number =       "1",
  pages =        "110--144",
  month =        jan,
  year =         "1994",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1006/jagm.1994.1006",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:15:38 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0196677484710066",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}


bibtype: article
filename: elefunt.bib
label: Spouge:1994:CGD
author: John L. Spouge
title: Computation of the Gamma, Digamma, and Trigamma Functions
journal: j-SIAM-J-NUMER-ANAL
volume: 31
number: 3
pages: 931--944
month: jun
monthnumber: 6
year: 1994
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 33B15 (30E10 33-04 40-04 65D20)
MRnumber: 95g:33002
MRreviewer: E. Kaucher
bibdate: Mon Jan 20 15:27:00 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.20 15:27:00 MST
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: John L. Spouge
rawtitle: Computation of the Gamma, Digamma, and Trigamma Functions
entry:
@Article{Spouge:1994:CGD,
  author =       "John L. Spouge",
  title =        "Computation of the Gamma, Digamma, and Trigamma
                 Functions",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "31",
  number =       "3",
  pages =        "931--944",
  month =        jun,
  year =         "1994",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "33B15 (30E10 33-04 40-04 65D20)",
  MRnumber =     "95g:33002",
  MRreviewer =   "E. Kaucher",
  bibdate =      "Mon Jan 20 15:27:00 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: inproceedings
filename: elefunt.bib
label: Temme:1994:CAI
author: N. M. Temme
title: Computational aspects of incomplete gamma functions with large complex parameters
crossref: Zahar:1994:ACF
pages: 551--562
year: 1994
bibdate: Sat Feb 18 15:02:52 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:02:52 ???
series: International Series of Numerical Mathematics
acknowledgement: ack-nhfb
rawauthor: N. M. Temme
rawtitle: Computational aspects of incomplete gamma functions with large complex parameters
entry:
@InProceedings{Temme:1994:CAI,
  author =       "N. M. Temme",
  title =        "Computational aspects of incomplete gamma functions
                 with large complex parameters",
  crossref =     "Zahar:1994:ACF",
  pages =        "551--562",
  year =         "1994",
  bibdate =      "Sat Feb 18 15:02:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "International Series of Numerical Mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Temme:1994:SAI
author: N. M. Temme
title: A Set of Algorithms for the Incomplete Gamma Functions
journal: j-PROBAB-ENGRG-INFORM-SCI
volume: 8
number: 2
pages: 291--307
month: apr
monthnumber: 4
year: 1994
DOI: https://doi.org/10.1017/S0269964800003417
ISSN: 0269-9648 (print), 1469-8951 (electronic) OR 02699648 (print), 14698951 (electronic)
ISSNL: 0269-9648 OR 02699648
bibdate: Thu Aug 24 08:18:58 MDT 2017
bibtimestamp: 2017.08.24 08:18:58 MDT
URL: https://www.cambridge.org/core/product/F5677268895A0805A0BDF31E4B20A106
fjournal: Probability in the Engineering and Informational Sciences
acknowledgement: ack-nhfb
ajournal: Probab. Engrg. Inform. Sci.
journalURL: http://www.journals.cambridge.org/jid_PES
onlinedate: 01 July 2009
rawauthor: N. M. Temme
rawtitle: A Set of Algorithms for the Incomplete Gamma Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/probab-engrg-inform-sci.bib

entry:
@Article{Temme:1994:SAI,
  author =       "N. M. Temme",
  title =        "A Set of Algorithms for the Incomplete Gamma
                 Functions",
  journal =      j-PROBAB-ENGRG-INFORM-SCI,
  volume =       "8",
  number =       "2",
  pages =        "291--307",
  month =        apr,
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1017/S0269964800003417",
  ISSN =         "0269-9648 (print), 1469-8951 (electronic)",
  ISSN-L =       "0269-9648",
  bibdate =      "Thu Aug 24 08:18:58 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/probab-engrg-inform-sci.bib",
  URL =          "https://www.cambridge.org/core/product/F5677268895A0805A0BDF31E4B20A106",
  acknowledgement = ack-nhfb,
  ajournal =     "Probab. Engrg. Inform. Sci.",
  fjournal =     "Probability in the Engineering and Informational
                 Sciences",
  journal-URL =  "http://www.journals.cambridge.org/jid_PES",
  onlinedate =   "01 July 2009",
}


bibtype: article
filename: elefunt.bib
label: Timmermann:1994:CFV
author: D. Timmermann and B. Rix and H. Hahn and B. J. Hosticka
title: A CMOS floating-point vector-arithmetic unit
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 29
number: 5
pages: 634--639
month: may
monthnumber: 5
year: 1994
CODEN: IJSCBC
DOI: https://doi.org/10.1109/4.284719
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:29:07 MST
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
affiliation: Fraunhofer Inst. of Microelectron. Circuits and Syst., Duisburg, Germany
rawauthor: D. Timmermann and B. Rix and H. Hahn and B. J. Hosticka
rawtitle: A {CMOS} floating-point vector-arithmetic unit
abstract:
This work describes a floating-point arithmetic unit based on the CORDIC algorithm. The unit computes a full set of high level arithmetic and elementary functions: multiplication, division, (co)sine, hyperbolic (co)sine, square root, natural logarithm, inverse (hyperbolic) tangent, vector norm, and phase. The chip has been integrated in 1.6 mu m double-metal n-well CMOS technology and achieves a normalized peak performance of 220 MFLOPS.

keywords:
1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine; Division; Double-metal n-well CMOS technology; Floating-point vector-arithmetic unit; Hyperbolic sine; Inverse tangent; Multiplication; Natural logarithm; Phase; Sine; Square root; Vector norm

thesaurus:
CMOS integrated circuits; Digital arithmetic; Integrated logic circuits; Parallel architectures; Pipeline processing; Vector processor systems

rawabstract:
This work describes a floating-point arithmetic unit based on the CORDIC algorithm. The unit computes a full set of high level arithmetic and elementary functions: multiplication, division, (co)sine, hyperbolic (co)sine, square root, natural logarithm, inverse (hyperbolic) tangent, vector norm, and phase. The chip has been integrated in 1.6 mu m double-metal n-well CMOS technology and achieves a normalized peak performance of 220 MFLOPS.

entry:
@Article{Timmermann:1994:CFV,
  author =       "D. Timmermann and B. Rix and H. Hahn and B. J.
                 Hosticka",
  title =        "A {CMOS} floating-point vector-arithmetic unit",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "29",
  number =       "5",
  pages =        "634--639",
  month =        may,
  year =         "1994",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.284719",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This work describes a floating-point arithmetic unit
                 based on the CORDIC algorithm. The unit computes a full
                 set of high level arithmetic and elementary functions:
                 multiplication, division, (co)sine, hyperbolic
                 (co)sine, square root, natural logarithm, inverse
                 (hyperbolic) tangent, vector norm, and phase. The chip
                 has been integrated in 1.6 mu m double-metal n-well
                 CMOS technology and achieves a normalized peak
                 performance of 220 MFLOPS.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fraunhofer Inst. of Microelectron. Circuits and Syst.,
                 Duisburg, Germany",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5120 (Logic and switching circuits); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine;
                 Division; Double-metal n-well CMOS technology;
                 Floating-point vector-arithmetic unit; Hyperbolic sine;
                 Inverse tangent; Multiplication; Natural logarithm;
                 Phase; Sine; Square root; Vector norm",
  numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS",
  pubcountry =   "USA",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Integrated logic circuits; Parallel architectures;
                 Pipeline processing; Vector processor systems",
}


bibtype: article
filename: elefunt.bib
label: Turner:1994:SRM
author: Stephen M. Turner
title: Square roots mod $p$
journal: j-AMER-MATH-MONTHLY
volume: 101
number: 5
pages: 443--449
month: may
monthnumber: 5
year: 1994
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 11A07
MRnumber: 95c:11004
MRreviewer: David Lee Hilliker
bibdate: Wed Dec 3 17:17:33 MST 1997
bibtimestamp: 1997.12.03 17:17:33 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Stephen M. Turner
rawtitle: Square roots mod $p$
entry:
@Article{Turner:1994:SRM,
  author =       "Stephen M. Turner",
  title =        "Square roots mod $p$",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "5",
  pages =        "443--449",
  month =        may,
  year =         "1994",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11A07",
  MRnumber =     "95c:11004",
  MRreviewer =   "David Lee Hilliker",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: book
filename: elefunt.bib
label: Watanabe:1994:MSP
author: T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu Oguni
title: Mathematical Software for the P.C. and Work Stations: a Collection of Fortran 77 Programs
publisher: pub-NORTH-HOLLAND
address: pub-NORTH-HOLLAND:adr
pages: xiv + 387
month: jun
monthnumber: 6
year: 1994
ISBN: 0-444-82000-0 OR 0444820000
ISBN13: 978-0-444-82000-6 OR 9780444820006
LCCN: QA 76.73 F25 F6813 1994
bibdate: Sun Sep 28 10:42:07 MDT 1997
bibtimestamp: 1997.09.28 10:42:07 MDT
note: Translation of: FORTRAN 77 ni yoru suchi keisan sofutowea.
URL: http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000
acknowledgement: ack-nhfb
rawauthor: T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu Oguni
rawnote: Translation of: FORTRAN 77 ni yoru suchi keisan sofutowea.
rawtitle: Mathematical Software for the {P.C.} and Work Stations: a Collection of {Fortran 77} Programs
bibsource:
http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/; http://www.cbooks.com/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
Fortran 77 (computer program language); Numerical analysis --- Use of --- Computers; Fortran 77 (Computer program language)

entry:
@Book{Watanabe:1994:MSP,
  author =       "T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu
                 Oguni",
  title =        "Mathematical Software for the {P.C.} and Work
                 Stations: a Collection of {Fortran 77} Programs",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xiv + 387",
  month =        jun,
  year =         "1994",
  ISBN =         "0-444-82000-0",
  ISBN-13 =      "978-0-444-82000-6",
  LCCN =         "QA 76.73 F25 F6813 1994",
  bibdate =      "Sun Sep 28 10:42:07 MDT 1997",
  bibsource =    "http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/;
                 http://www.cbooks.com/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translation of: FORTRAN 77 ni yoru suchi keisan
                 sofutowea.",
  price =        "US\$178.50",
  URL =          "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000",
  acknowledgement = ack-nhfb,
  alttitle =     "{Fortran 77} ni yoru suchi keisan sofutowea.
                 English.",
  keywords =     "Fortran 77 (computer program language); Numerical
                 analysis --- Use of --- Computers; {Fortran 77}
                 (Computer program language)",
}


bibtype: inproceedings
filename: elefunt.bib
label: Wong:1994:FEE
author: W. F. Wong and E. Goto
title: Fast evaluation of the elementary functions in double precision
crossref: Mudge:1994:PTS
pages: 349--358
year: 1994
bibdate: Tue Dec 12 09:29:07 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:29:07 MST
acknowledgement: ack-nhfb
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore
bookpages: xi + 621
thesaurus: Digital arithmetic; Polynomials; Table lookup
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast evaluation of the elementary functions in double precision
abstract:
One of the most spectacular development in computer technology is the growth in memory density and speed. It is with this development in mind that we intend to tackle the old problem of computing the elementary functions. Since the dawn of computing, the fast and accurate computation of the elementary functions has been a constant concern of numerical computing. It now seems possible to use tables of sizes in the range of megabits to aid in such computation. To this end, in this paper, we propose a method called ATA-M (Add-Table Lookup-Add with Multiplication) for evaluating polynomials with the aid of tables. When applied to the elementary functions, we obtained a set of algorithms which computes the reciprocal, square root, exponential, sine, cosine, logarithm, are tangent and the hyperbolic functions in about 3 to 4 double precision floating point multiplication time and utilizing about 2 Mbyte of tables.

keywords:
Add-Table Lookup-Add with Multiplication; ATA-M; Double precision; Elementary functions; Floating point multiplication time; Hyperbolic functions; Memory density; Memory speed; Numerical computing; Polynomials

rawabstract:
One of the most spectacular development in computer technology is the growth in memory density and speed. It is with this development in mind that we intend to tackle the old problem of computing the elementary functions. Since the dawn of computing, the fast and accurate computation of the elementary functions has been a constant concern of numerical computing. It now seems possible to use tables of sizes in the range of megabits to aid in such computation. To this end, in this paper, we propose a method called ATA-M (Add-Table Lookup-Add with Multiplication) for evaluating polynomials with the aid of tables. When applied to the elementary functions, we obtained a set of algorithms which computes the reciprocal, square root, exponential, sine, cosine, logarithm, are tangent and the hyperbolic functions in about 3 to 4 double precision floating point multiplication time and utilizing about 2 Mbyte of tables.

entry:
@InProceedings{Wong:1994:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in double
                 precision",
  crossref =     "Mudge:1994:PTS",
  bookpages =    "xi + 621",
  pages =        "349--358",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "One of the most spectacular development in computer
                 technology is the growth in memory density and speed.
                 It is with this development in mind that we intend to
                 tackle the old problem of computing the elementary
                 functions. Since the dawn of computing, the fast and
                 accurate computation of the elementary functions has
                 been a constant concern of numerical computing. It now
                 seems possible to use tables of sizes in the range of
                 megabits to aid in such computation. To this end, in
                 this paper, we propose a method called ATA-M (Add-Table
                 Lookup-Add with Multiplication) for evaluating
                 polynomials with the aid of tables. When applied to the
                 elementary functions, we obtained a set of algorithms
                 which computes the reciprocal, square root,
                 exponential, sine, cosine, logarithm, are tangent and
                 the hyperbolic functions in about 3 to 4 double
                 precision floating point multiplication time and
                 utilizing about 2 Mbyte of tables.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  confdate =     "4-7 Jan. 1994",
  conflocation = "Wailea, HI, USA",
  confsponsor =  "IEEE; ACM; Univ. Hawaii; Univ. Hawaii Coll. Bus.
                 Admin",
  keywords =     "Add-Table Lookup-Add with Multiplication; ATA-M;
                 Double precision; Elementary functions; Floating point
                 multiplication time; Hyperbolic functions; Memory
                 density; Memory speed; Numerical computing;
                 Polynomials",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Polynomials; Table lookup",
}


bibtype: article
filename: elefunt.bib
label: Wong:1994:FHB
author: W. F. Wong and E. Goto
title: Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 3
pages: 278--294
month: mar
monthnumber: 3
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.272429
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:13:54 MDT 2011
bibtimestamp: 2011.07.07 07:13:54 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Error analysis
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

abstract:
As the name suggests, elementary functions play a vital role in scientific computations. Yet due to their inherent nature, they are a considerable computing task by themselves. Not surprisingly, since the dawn of computing, the goal of speeding up elementary function computation has been pursued. This paper describes new hardware based algorithms for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine. These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis. The contribution of this work lies in the fact that these algorithms are very fast and yet are accurate. If we let the time to perform an IEEE Standard 754 double precision floating point multiplication be $ tau _times $, our algorithms to achieve roughly $ 3.68 tau _times $, $ 4.56 tau _times $, $ 5.25 tau _times $, $ 3.69 tau _times $, $ 7.06 tau _times $, and $ 6.5 tau _times $, for division, logarithm, square root, exponential, are tangent and complex exponential (sine and cosine) respectively. The trade-off is the need for tables and some specialized hardware. The total amount of tables required, however, is less than 128 Kbytes. We discuss the hardware, algorithmic and accuracy aspects of these algorithms.

keywords:
Arc tangent; Common elementary functions; Cosine; Elementary function computations; Floating point multiplication; Hardware-based algorithms; Microscopic parallelism; Reciprocal square root; Rectangular multipliers; Scientific computations; Sine

rawabstract:
As the name suggests, elementary functions play a vital role in scientific computations. Yet due to their inherent nature, they are a considerable computing task by themselves. Not surprisingly, since the dawn of computing, the goal of speeding up elementary function computation has been pursued. This paper describes new hardware based algorithms for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine. These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis. The contribution of this work lies in the fact that these algorithms are very fast and yet are accurate. If we let the time to perform an IEEE Standard 754 double precision floating point multiplication be $ \tau_\times $, our algorithms to achieve roughly $ 3.68 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $ 6.5 \tau_\times $, for division, logarithm, square root, exponential, are tangent and complex exponential (sine and cosine) respectively. The trade-off is the need for tables and some specialized hardware. The total amount of tables required, however, is less than 128 Kbytes. We discuss the hardware, algorithmic and accuracy aspects of these algorithms.

entry:
@Article{Wong:1994:FHB,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-Based Algorithms for Elementary Function
                 Computations Using Rectangular Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "3",
  pages =        "278--294",
  month =        mar,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.272429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:54 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
  abstract =     "As the name suggests, elementary functions play a
                 vital role in scientific computations. Yet due to their
                 inherent nature, they are a considerable computing task
                 by themselves. Not surprisingly, since the dawn of
                 computing, the goal of speeding up elementary function
                 computation has been pursued. This paper describes new
                 hardware based algorithms for the computation of the
                 common elementary functions, namely division,
                 logarithm, reciprocal square root, arc tangent, sine
                 and cosine. These algorithms exploit microscopic
                 parallelism using specialized hardware with heavy use
                 of truncation based on detailed accuracy analysis. The
                 contribution of this work lies in the fact that these
                 algorithms are very fast and yet are accurate. If we
                 let the time to perform an IEEE Standard 754 double
                 precision floating point multiplication be $
                 \tau_\times $, our algorithms to achieve roughly $ 3.68
                 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times
                 $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $
                 6.5 \tau_\times $, for division, logarithm, square
                 root, exponential, are tangent and complex exponential
                 (sine and cosine) respectively. The trade-off is the
                 need for tables and some specialized hardware. The
                 total amount of tables required, however, is less than
                 128 Kbytes. We discuss the hardware, algorithmic and
                 accuracy aspects of these algorithms.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arc tangent; Common elementary functions; Cosine;
                 Elementary function computations; Floating point
                 multiplication; Hardware-based algorithms; Microscopic
                 parallelism; Reciprocal square root; Rectangular
                 multipliers; Scientific computations; Sine",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Error analysis",
}


bibtype: article
filename: elefunt.bib
label: Xu:1994:VPC
author: Guo Liang Xu and Jia Kai Li
title: Variable precision computation of elementary functions. (Chinese)
journal: j-J-NUMER-METHODS-COMPUT-APPL
volume: 15
number: 3
pages: 161--171
year: 1994
ISSN: 1000-3266 OR 10003266
MRclass: 65D20 (65Y20)
MRnumber: MR1357336 (96i:65013)
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Journal on Numerical Methods and Computer Applications. Shuzhi Jisuan yu Jisuanji Yingyong
acknowledgement: ack-nhfb
rawauthor: Guo Liang Xu and Jia Kai Li
rawtitle: Variable precision computation of elementary functions. ({Chinese})
entry:
@Article{Xu:1994:VPC,
  author =       "Guo Liang Xu and Jia Kai Li",
  title =        "Variable precision computation of elementary
                 functions. ({Chinese})",
  journal =      j-J-NUMER-METHODS-COMPUT-APPL,
  volume =       "15",
  number =       "3",
  pages =        "161--171",
  year =         "1994",
  ISSN =         "1000-3266",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "MR1357336 (96i:65013)",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal on Numerical Methods and Computer
                 Applications. Shuzhi Jisuan yu Jisuanji Yingyong",
}


bibtype: article
filename: elefunt.bib
label: Abad:1995:CRC
author: Julio Abad and Javier Sesma
title: Computation of the Regular Confluent Hypergeometric Function
journal: j-MATHEMATICA-J
volume: 5
number: 4
pages: ??--??
month: Fall
year: 1995
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:34:06 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v5i4/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.11.06 13:34:06 MDT
URL: http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: Julio Abad and Javier Sesma
rawtitle: Computation of the Regular Confluent Hypergeometric Function
entry:
@Article{Abad:1995:CRC,
  author =       "Julio Abad and Javier Sesma",
  title =        "Computation of the Regular Confluent Hypergeometric
                 Function",
  journal =      j-MATHEMATICA-J,
  volume =       "5",
  number =       "4",
  pages =        "??--??",
  month =        "Fall",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:06 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v5i4/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: elefunt.bib
label: Amos:1995:RAP
author: D. E. Amos
journal: j-TOMS
volume: 21
number: 4
pages: 388--393
month: dec
monthnumber: 12
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/212066.212078
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:24:54 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1999.03.09 10:24:54 ???
note: See cite Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA.
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: D. E. Amos
rawnote: See \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.
title:
A Remark on Algorithm 644: a Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order

keywords:
complex Airy Functions; complex Bessel functions; derivatives of Airy functions; H, I, J, K, and Y Bessel functions; log gamma function

subject:
G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.m [Numerical Analysis]: Miscellaneous; G.m [Mathematics of Computing]: Miscellaneous

rawtitle:
A Remark on {Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order

entry:
@Article{Amos:1995:RAP,
  author =       "D. E. Amos",
  title =        "A Remark on {Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "388--393",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212078",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:24:54 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex Airy Functions; complex Bessel functions;
                 derivatives of Airy functions; H, I, J, K, and Y Bessel
                 functions; log gamma function",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.m [Numerical Analysis]: Miscellaneous;
                 G.m [Mathematics of Computing]: Miscellaneous",
}


bibtype: article
filename: elefunt.bib
label: Bagby:1995:CNP
author: Richard J. Bagby
title: Calculating normal probabilities
journal: j-AMER-MATH-MONTHLY
volume: 102
number: 1
pages: 46--48
month: jan
monthnumber: 1
year: 1995
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 65D20
MRnumber: 96f:65021
bibdate: Wed Dec 3 17:17:33 MST 1997
bibtimestamp: 1997.12.03 17:17:33 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Richard J. Bagby
rawtitle: Calculating normal probabilities
bibsource:
http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Bagby:1995:CNP,
  author =       "Richard J. Bagby",
  title =        "Calculating normal probabilities",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "1",
  pages =        "46--48",
  month =        jan,
  year =         "1995",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65D20",
  MRnumber =     "96f:65021",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: Baratchart:1995:RIE
author: L. Baratchart and E. B. Saff and F. Wielonsky
title: Rational interpolation of the exponential function
journal: j-CAN-J-MATH
volume: 47
pages: 1121--1147
year: 1995
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1995-058-6
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
bibdate: Sat Sep 10 15:39:05 MDT 2011
bibtimestamp: 2011.09.10 15:39:05 MDT
fjournal: Canadian Journal of Mathematics = Journal canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cjm/
rawauthor: L. Baratchart and E. B. Saff and F. Wielonsky
rawtitle: Rational interpolation of the exponential function
bibsource:
http://cms.math.ca/cjm/v47/; https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Baratchart:1995:RIE,
  author =       "L. Baratchart and E. B. Saff and F. Wielonsky",
  title =        "Rational interpolation of the exponential function",
  journal =      j-CAN-J-MATH,
  volume =       "47",
  number =       "??",
  pages =        "1121--1147",
  month =        "????",
  year =         "1995",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1995-058-6",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:39:05 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v47/;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
}


bibtype: techreport
filename: elefunt.bib
label: Borwein:1995:EARa
author: Peter Borwein
title: An Efficient Algorithm for the Riemann Zeta Function
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 9
day: 20
month: jan
monthnumber: 1
year: 1995
bibdate: Thu Sep 01 18:09:22 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.09.01 18:09:22 ???
URL: http://docserver.carma.newcastle.edu.au/107
acknowledgement: ack-nhfb
authordates: 10 May 1953--23 August 2020
rawauthor: Peter Borwein
rawtitle: An Efficient Algorithm for the {Riemann} Zeta Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed. These algorithms out perform the standard methods based on Euler--Maclaurin summation, are easier to implement and are easier to analyse.

rawabstract:
A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed. These algorithms out perform the standard methods based on Euler--Maclaurin summation, are easier to implement and are easier to analyse.

entry:
@TechReport{Borwein:1995:EARa,
  author =       "Peter Borwein",
  title =        "An Efficient Algorithm for the {Riemann} Zeta
                 Function",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "9",
  day =          "20",
  month =        jan,
  year =         "1995",
  bibdate =      "Thu Sep 01 18:09:22 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/107",
  abstract =     "A very simple class of algorithms for the computation
                 of the Riemann-zeta function to arbitrary precision in
                 arbitrary domains is proposed. These algorithms out
                 perform the standard methods based on Euler--Maclaurin
                 summation, are easier to implement and are easier to
                 analyse.",
  acknowledgement = ack-nhfb,
  author-dates = "10 May 1953--23 August 2020",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: elefunt.bib
label: Borwein:1995:EARb
author: P. Borwein
booktitle: CMS Conference Proceedings
title: An efficient algorithm for the Riemann zeta function
volume: 27
publisher: Canadian Mathematical Society
address: 616 Cooper Street, Ottawa, ON, K1R 5J2, Canada
pages: 29--34
month: jan
monthnumber: 1
year: 1995
bibdate: Wed Jun 28 08:27:14 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.06.28 08:27:14 ???
URL: https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
acknowledgement: ack-nhfb
rawauthor: P. Borwein
rawbooktitle: {CMS} Conference Proceedings
rawtitle: An efficient algorithm for the {Riemann} zeta function
entry:
@InProceedings{Borwein:1995:EARb,
  author =       "P. Borwein",
  editor =       "????",
  booktitle =    "{CMS} Conference Proceedings",
  title =        "An efficient algorithm for the {Riemann} zeta
                 function",
  volume =       "27",
  publisher =    "Canadian Mathematical Society",
  address =      "616 Cooper Street, Ottawa, ON, K1R 5J2, Canada",
  pages =        "29--34",
  month =        jan,
  year =         "1995",
  bibdate =      "Wed Jun 28 08:27:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
  acknowledgement = ack-nhfb,
  xxURL =        "http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1995:NCR
author: B. C. Carlson
title: Numerical computation of real or complex elliptic integrals
journal: j-NUMER-ALGORITHMS
volume: 10
number: 1--2
pages: 13--26
month: jul
monthnumber: 7
year: 1995
CODEN: NUALEG
DOI: https://doi.org/10.1007/BF02198293
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 33Exx (33-04 65D20)
MRnumber: 1 345 407
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
note: Special functions (Torino, 1993)
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Ames Lab., Iowa State Univ., Ames, IA, USA
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawnote: Special functions (Torino, 1993)
rawtitle: Numerical computation of real or complex elliptic integrals
abstract:
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

keywords:
Bulirsch's integrals; complex elliptic integrals; complex values; consistency checks; elliptic equations; integral equations; Legendre's integrals; numerical analysis; numerical check values; numerical computation algorithms; real elliptic integrals

rawabstract:
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

entry:
@Article{Carlson:1995:NCR,
  author =       "B. C. Carlson",
  title =        "Numerical computation of real or complex elliptic
                 integrals",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "1--2",
  pages =        "13--26",
  month =        jul,
  year =         "1995",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/BF02198293",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "33Exx (33-04 65D20)",
  MRnumber =     "1 345 407",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Special functions (Torino, 1993)",
  abstract =     "Algorithms for numerical computation of symmetric
                 elliptic integrals of all three kinds are improved in
                 several ways and extended to complex values of the
                 variables (with some restrictions in the case of the
                 integral of the third kind). Numerical check values,
                 consistency checks, and relations to Legendre's
                 integrals and Bulirsch's integrals are included.",
  acknowledgement = ack-nhfb,
  classification = "B0290R (Integral equations); C4180 (Integral
                 equations)",
  conflocation = "Torino, Italy; 14-15 Oct. 1993",
  conftitle =    "International Joint Symposium on Special Functions and
                 Artificial Intelligence",
  corpsource =   "Ames Lab., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Bulirsch's integrals; complex elliptic integrals;
                 complex values; consistency checks; elliptic equations;
                 integral equations; Legendre's integrals; numerical
                 analysis; numerical check values; numerical computation
                 algorithms; real elliptic integrals",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:1995:DGI
author: M. Aslam Chaudhry and S. M. Zubair
journal: j-J-COMPUT-APPL-MATH
volume: 59
number: 3
pages: 253--284
day: 30
month: may
monthnumber: 5
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:37 MST 2017
bibtimestamp: 2017.02.25 12:24:37 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279400026W
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Aslam Chaudhry and S. M. Zubair
title:
On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms

rawtitle:
On the decomposition of generalized incomplete gamma functions with applications to {Fourier} transforms

entry:
@Article{Chaudhry:1995:DGI,
  author =       "M. Aslam Chaudhry and S. M. Zubair",
  title =        "On the decomposition of generalized incomplete gamma
                 functions with applications to {Fourier} transforms",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "59",
  number =       "3",
  pages =        "253--284",
  day =          "30",
  month =        may,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279400026W",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chen:1995:UCA
author: San-Gee Chen and Chieh-Chih Li
booktitle: IEEE Signal Processing Society Workshop on VLSI Signal Processing, VIII, 1995
title: A unified cellular array for multiplication, division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 533--541
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: San-Gee Chen and Chieh-Chih Li
rawbooktitle: {IEEE} Signal Processing Society Workshop on {VLSI} Signal Processing, {VIII, 1995}
rawtitle: A unified cellular array for multiplication, division and square root
entry:
@InProceedings{Chen:1995:UCA,
  author =       "San-Gee Chen and Chieh-Chih Li",
  booktitle =    "{IEEE} Signal Processing Society Workshop on {VLSI}
                 Signal Processing, {VIII, 1995}",
  title =        "A unified cellular array for multiplication, division
                 and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--541",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A unified fast, small-area processor capable of
                 executing multiplication, division and square-root
                 operations, all starting from MSD is proposed. Unlike
                 the existing designs which require both addition and
                 subtraction operations, and complicated \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Das:1995:IFC
author: D. Das and K. Mukhopadhyaya and B. P. Sinha
title: Implementation of four common functions on an LNS co-processor
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 1
pages: 155--161
month: jan
monthnumber: 1
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.367997
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Das and K. Mukhopadhyaya and B. P. Sinha
rawtitle: Implementation of four common functions on an {LNS} co-processor
entry:
@Article{Das:1995:IFC,
  author =       "D. Das and K. Mukhopadhyaya and B. P. Sinha",
  title =        "Implementation of four common functions on an {LNS}
                 co-processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "155--161",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.367997",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We propose a scheme for evaluating four commonly used
                 functions namely, (1) inverse trigonometric functions,
                 (2) trigonometric functions, (3) the exponential
                 function, and (4) the logarithmic function with the
                 help of a logarithmic number system (\ldots{}).",
}


bibtype: article
filename: elefunt.bib
label: Daumas:1995:MRR
author: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
journal: j-J-UCS
volume: 1
number: 3
pages: 162--175 (electronic)
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
MRclass: 68M07 (68Q20)
MRnumber: 1 390 003
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
title:
Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions

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

entry:
@Article{Daumas:1995:MRR,
  author =       "Marc Daumas and Christophe Mazenc and Xavier Merrheim
                 and Jean-Michel Muller",
  title =        "Modular range reduction: a new algorithm for fast and
                 accurate computation of the elementary functions",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "162--175 (electronic)",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (68Q20)",
  MRnumber =     "1 390 003",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


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

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

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


bibtype: article
filename: elefunt.bib
label: Driver:1995:NQH
author: Kathy Driver
title: Nondiagonal quadratic Hermite--Pade approximation to the exponential function
journal: j-J-COMPUT-APPL-MATH
volume: 65
number: 1--3
pages: 125--134
day: 29
month: dec
monthnumber: 12
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:25 MST 2017
bibtimestamp: 2017.02.25 13:02:25 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795001069
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Kathy Driver
rawtitle: Nondiagonal quadratic {Hermite--Pad{\'e}} approximation to the exponential function
entry:
@Article{Driver:1995:NQH,
  author =       "Kathy Driver",
  title =        "Nondiagonal quadratic {Hermite--Pad{\'e}}
                 approximation to the exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "65",
  number =       "1--3",
  pages =        "125--134",
  day =          "29",
  month =        dec,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001069",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Goano:1995:ACC
author: Michele Goano
title: Algorithm 745: Computation of the Complete and Incomplete Fermi--Dirac Integral
journal: j-TOMS
volume: 21
number: 3
pages: 221--232
month: sep
monthnumber: 9
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/210089.210090
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:19:43 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.03.09 10:19:43 ???
note: See remark cite Goano:1997:RA7
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Michele Goano
rawnote: See remark \cite{Goano:1997:RA7}
rawtitle: {Algorithm 745}: Computation of the Complete and Incomplete {Fermi--Dirac} Integral
keywords:
asymptotic expansions; confluent hypergeometric functions; convergence acceleration; e[k] transforms; epsilon algorithm; Euler transformation; Fermi--Dirac integral; incomplete Fermi--Dirac integral; incomplete gamma function; Levin's u transform; Riemann's zeta function

subject:
G.1.2 [Mathematics of Computing]: Approximation; G.4 [Mathematics of Computing]: Mathematical Software; J.2 [Computer Applications]: Physical Sciences and Engineering

entry:
@Article{Goano:1995:ACC,
  author =       "Michele Goano",
  title =        "{Algorithm 745}: Computation of the Complete and
                 Incomplete {Fermi--Dirac} Integral",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210090",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:19:43 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Goano:1997:RA7}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "asymptotic expansions; confluent hypergeometric
                 functions; convergence acceleration; e[k] transforms;
                 epsilon algorithm; Euler transformation; Fermi--Dirac
                 integral; incomplete Fermi--Dirac integral; incomplete
                 gamma function; Levin's u transform; Riemann's zeta
                 function",
  subject =      "G.1.2 [Mathematics of Computing]: Approximation; G.4
                 [Mathematics of Computing]: Mathematical Software; J.2
                 [Computer Applications]: Physical Sciences and
                 Engineering",
}


bibtype: article
filename: elefunt.bib
label: Hobson:1995:EMR
author: R. F. Hobson and M. W. Fraser
title: An efficient maximum-redundancy radix-$8$ SRT division and square-root method
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 30
number: 1
pages: 29--38
month: jan
monthnumber: 1
year: 1995
CODEN: IJSCBC
DOI: https://doi.org/10.1109/4.350197
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
affiliation: Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC, Canada
rawauthor: R. F. Hobson and M. W. Fraser
rawtitle: An efficient maximum-redundancy radix-$8$ {SRT} division and square-root method
abstract:
A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.

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

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

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

entry:
@Article{Hobson:1995:EMR,
  author =       "R. F. Hobson and M. W. Fraser",
  title =        "An efficient maximum-redundancy radix-$8$ {SRT}
                 division and square-root method",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "1",
  pages =        "29--38",
  month =        jan,
  year =         "1995",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.350197",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the next quotient or
                 square-root digit by the divisor or square-root value.
                 A separate (parallel) full precision iterative
                 multiplier is used for partial remainder production.
                 Strategic details of a radix-8 implementation are
                 discussed. It is shown that a maximally redundant digit
                 set is a viable choice for high performance in this
                 case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC,
                 Canada",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
                 floating point algorithm; Integrated control path;
                 Maximally redundant digit set; Maximum-redundancy
                 radix-8 SRT algorithm; Multiplication; Parallel
                 iterative multiplier; Partial remainder production;
                 Redundant partial-remainder; Square-root method; Table
                 lookup",
  numericalindex = "Size 1.2E-06 m",
  pubcountry =   "USA",
  summary =      "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the \ldots{}",
  thesaurus =    "Adders; CMOS digital integrated circuits; Digital
                 arithmetic; Dividing circuits; Floating point
                 arithmetic; Multiplying circuits",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ito:1995:EIA
author: M. Ito and N. Takagi and S. Yajima
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2--9
month: jul
monthnumber: 7
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-sfo
rawauthor: M. Ito and N. Takagi and S. Yajima
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
entry:
@InProceedings{Ito:1995:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Efficient Initial Approximation and Fast Converging
                 Methods for Division and Square Root",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2--9",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Efficient initial approximations and fast converging
                 algorithms are important to achieve the desired
                 precision faster at lower hardware cost in
                 multiplicative division and square root. In this paper,
                 a new initial approximation method for division,
                 \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Jeffrey:1995:HMF
author: Alan Jeffrey
title: Handbook of Mathematical Formulas and Integrals
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xxiv + 410
year: 1995
LCCN: QA47 .J38 1995
bibdate: Wed Jun 12 14:33:38 MDT 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.06.12 14:33:38 MDT
URL: http://www.sciencedirect.com/science/book/9780123825803
subject: Mathematics; Tables; Formulae; Mathematiques; Formules; formulas (algorithms); Mathematics.
acknowledgement: ack-nhfb
rawauthor: Alan Jeffrey
rawtitle: Handbook of Mathematical Formulas and Integrals
ISBN:
0-08-052301-3, 0-12-382580-6 (e-book), 1-4832-9514-1 (e-book) OR 0080523013, 0123825806 (ebook), 1483295141 (ebook)

ISBN13:
978-0-08-052301-9, 978-0-12-382580-3 (e-book), 978-1-4832-9514-5 (e-book) OR 9780080523019, 9780123825803 (ebook), 9781483295145 (ebook)

abstract:
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's booktitle Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.

TOC:
0: Quick Reference List of Frequently Used Data 0.1: Useful Identities / 1 0.2: Complex Relationships / 2 0.3: Constants / 2 0.4: Derivatives of Elementary Functions / 3 0.5: Rules of Differentiation and Integration / 3 0.6: Standard Integrals / 4 0.7: Standard Series / 11 0.8: Geometry / 13 1: Numerical, Algebraic, and Analytical Results for Series and Calculus 1.1: Algebraic Results Involving Real and Complex Numbers / 25 1.2: Finite Sums / 29 1.3: Bernoulli and Euler Numbers and Polynomials 37 1.4: Determinants / 47 1.5: Matrices / 55 1.6: Permutations and Combinations / 62 1.7: Partial Fraction Decomposition / 63 1.8: Convergence of Series / 66 1.9: Infinite Products / 71 1.10: Functional Series / 73 1.11: Power Series / 74 1.12: Taylor Series / 79 1.13: Fourier Series / 81 1.14: Asymptotic Expansions / 85 1.15: Basic Results from the Calculus / 86 2: Functions and Identities 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 2.2: Logarithms and Exponentials / 112 2.3: The Exponential Function / 114 2.4: Trigonometric Identities / 115 2.5: Hyperbolic Identities / 121 2.6: The Logarithm / 126 2.7: Inverse Trigonometric and Hyperbolic Functions / 128 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 3: Derivatives of Elementary Functions 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 3.2: Derivatives of Trigonometric Functions / 140 3.3: Derivatives of Inverse Trigonometric Functions / 140 3.4: Derivatives of Hyperbolic Functions / 141 3.5: Derivatives of Inverse Hyperbolic Functions 142 4: Indefinite Integrals of Algebraic Functions 4.1: Algebraic and Transcendental Functions / 145 4.2: Indefinite Integrals of Rational Functions 146 4.3: Nonrational Algebraic Functions / 158 5: Indefinite Integrals of Exponential Functions 5.1: Basic Results / 167 6: Indefinite Integrals of Logarithmic Functions 6.1: Combinations of Logarithms and Polynomials 173 7: Indefinite Integrals of Hyperbolic Functions 7.1: Basic Results / 179 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 7.9: Integrands Involving tanh kx and coth kx 188 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 8: Indefinite Integrals Involving Inverse Hyperbolic Functions 8.1: Basic Results / 191 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) 194 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 9: Indefinite Integrals of Trigonometric Functions 9.1: Basic Results / 197 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 9.3: Integrands Involving tan x and/or cot x 205 9.4: Integrands Involving sin x and cos x / 207 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 10: Indefinite Integrals of Inverse Trigonometric Functions 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions / 215 11: The Gamma, Beta, Pi, and Psi Functions 11.1: The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 12: Elliptic Integrals and Functions 12.1: Elliptic Integrals / 229 12.2: Jacobian Elliptic Functions / 235 12.3: Derivatives and Integrals / 237 12.4: Inverse Jacobian Elliptic Functions / 237 13: Probability Integrals and the Error Function 13.1: Normal Distribution / 239 13.2: The Error Function / 242 14: Fresnel Integrals, Sine and Cosine Integrals 14.1: Definitions, Series Representations, and Values at Infinity / 245 14.2: Definitions, Series Representations, and Values at Infinity / 247 15: Definite Integrals 15.1: Integrands Involving Powers of x / 249 15.2: Integrands Involving Trigonometric Functions 251 15.3: Integrands Involving the Exponential Function / 254 15.4: Integrands Involving the Hyperbolic Function 256 15.5: Integrands Involving the Logarithmic Function / 256 16: Different Forms of Fourier Series 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L 259 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L 260 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 16.10: Representative Examples of Fourier Series 261 16.11: Fourier Series and Discontinuous Functions 265 17: Bessel Functions 17.1: Bessel's Differential Equation / 269 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 17.3: Bessel Functions of Fractional Order / 272 17.4: Asymptotic Representations for Bessel Functions / 273 17.5: Zeros of Bessel Functions / 273 17.6: Bessel's Modified Equation / 274 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 17.8: Modified Bessel Functions of Fractional Order / 277 17.9: Asymptotic Representations of Modified Bessel Functions / 278 17.10: Relationships between Bessel Functions 278 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 17.12: Indefinite Integrals of Bessel Functions 281 17.13: Definite Integrals Involving Bessel Functions / 282 17.14: Spherical Bessel Functions / 283 18: Orthogonal Polynomials 18.2: Legendre Polynomials P[subscript n](x) 286 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 18.4: Laguerre Polynomials L[subscript n](x) 294 18.5: Hermite Polynomials H[subscript n](x) / 296 19: Laplace Transformation 20: Fourier Transforms 21: Numerical Integration 21.1: Classical Methods / 315 22: Solutions of Standard Ordinary Differential Equations 22.2: Separation of Variables / 323 22.3: Linear First-Order Equations / 323 22.4: Bernoulli's Equation / 324 22.5: Exact Equations / 325 22.6: Homogeneous Equations / 325 22.7: Linear Differential Equations / 326 22.8: Constant Coefficient Linear Differential Equations Homogeneous Case / 327 22.9: Linear Homogeneous Second-Order Equation 330 22.10: Constant Coefficient Linear Differential Equations Inhomogeneous Case / 331 22.11: Linear Inhomogeneous Second-Order Equation 333 22.12: Determination of Particular Integrals by the Method of Undetermined Coefficients / 334 22.13: The Cauchy-Euler Equation / 336 22.14: Legendre's Equation / 337 22.15: Bessel's Equations / 337 22.16: Power Series and Frobenius Methods / 339 22.17: The Hypergeometric Equation / 344 22.18: Numerical Methods / 345 23: Vector Analysis 23.1: Scalars and Vectors / 353 23.2: Scalar Products / 358 23.3: Vector Products / 359 23.4: Triple Products / 360 23.5: Products of Four Vectors / 361 23.6: Derivatives of Vector Functions of a Scalar t / 361 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 23.9: Line Integrals / 364 23.10: Vector Integral Theorems / 366 23.11: A Vector Rate of Change Theorem / 368 23.12: Useful Vector Identities and Results / 368 24: Systems of Orthogonal Coordinates 24.1: Curvilinear Coordinates / 369 24.2: Vector Operators in Orthogonal Coordinates 371 24.3: Systems of Orthogonal Coordinates / 371 25: Partial Differential Equations and Special Functions 25.1: Fundamental Ideas / 381 25.2: Method of Separation of Variables / 385 25.3: The Sturm--Liouville Problem and Special Functions / 387 25.4: A First-Order System and the Wave Equation 390 25.5: Conservation Equations (Laws) / 391 25.6: The Method of Characteristics / 392 25.7: Discontinuous Solutions (Shocks) / 396 25.8: Similarity Solutions / 398 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 26: The z-Transform 26.1: The z-Transform and Transform Pairs / 403 27: Numerical Approximation 27.2: Economization of Series / 411 27.3: Pade Approximation / 413 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

rawabstract:
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's \booktitle{Handbook of Mathematical Formulas and Integrals}. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.

rawTOC:
0: Quick Reference List of Frequently Used Data \\ 0.1: Useful Identities / 1 \\ 0.2: Complex Relationships / 2 \\ 0.3: Constants / 2 \\ 0.4: Derivatives of Elementary Functions / 3 \\ 0.5: Rules of Differentiation and Integration / 3 \\ 0.6: Standard Integrals / 4 \\ 0.7: Standard Series / 11 \\ 0.8: Geometry / 13 \\ 1: Numerical, Algebraic, and Analytical Results for Series and Calculus \\ 1.1: Algebraic Results Involving Real and Complex Numbers / 25 \\ 1.2: Finite Sums / 29 \\ 1.3: Bernoulli and Euler Numbers and Polynomials 37 \\ 1.4: Determinants / 47 \\ 1.5: Matrices / 55 \\ 1.6: Permutations and Combinations / 62 \\ 1.7: Partial Fraction Decomposition / 63 \\ 1.8: Convergence of Series / 66 \\ 1.9: Infinite Products / 71 \\ 1.10: Functional Series / 73 \\ 1.11: Power Series / 74 \\ 1.12: Taylor Series / 79 \\ 1.13: Fourier Series / 81 \\ 1.14: Asymptotic Expansions / 85 \\ 1.15: Basic Results from the Calculus / 86 \\ 2: Functions and Identities \\ 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 \\ 2.2: Logarithms and Exponentials / 112 \\ 2.3: The Exponential Function / 114 \\ 2.4: Trigonometric Identities / 115 \\ 2.5: Hyperbolic Identities / 121 \\ 2.6: The Logarithm / 126 \\ 2.7: Inverse Trigonometric and Hyperbolic Functions / 128 \\ 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 \\ 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 \\ 3: Derivatives of Elementary Functions \\ 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 \\ 3.2: Derivatives of Trigonometric Functions / 140 \\ 3.3: Derivatives of Inverse Trigonometric Functions / 140 \\ 3.4: Derivatives of Hyperbolic Functions / 141 \\ 3.5: Derivatives of Inverse Hyperbolic Functions 142 \\ 4: Indefinite Integrals of Algebraic Functions \\ 4.1: Algebraic and Transcendental Functions / 145 \\ 4.2: Indefinite Integrals of Rational Functions 146 \\ 4.3: Nonrational Algebraic Functions / 158 \\ 5: Indefinite Integrals of Exponential Functions \\ 5.1: Basic Results / 167 \\ 6: Indefinite Integrals of Logarithmic Functions \\ 6.1: Combinations of Logarithms and Polynomials 173 \\ 7: Indefinite Integrals of Hyperbolic Functions \\ 7.1: Basic Results / 179 \\ 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 \\ 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 \\ 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 \\ 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 \\ 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 \\ 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 \\ 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 \\ 7.9: Integrands Involving tanh kx and coth kx 188 \\ 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 \\ 8: Indefinite Integrals Involving Inverse Hyperbolic Functions \\ 8.1: Basic Results / 191 \\ 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 \\ 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) 194 \\ 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 \\ 9: Indefinite Integrals of Trigonometric Functions \\ 9.1: Basic Results / 197 \\ 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 \\ 9.3: Integrands Involving tan x and/or cot x 205 \\ 9.4: Integrands Involving sin x and cos x / 207 \\ 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 \\ 10: Indefinite Integrals of Inverse Trigonometric Functions \\ 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions / 215 \\ 11: The Gamma, Beta, Pi, and Psi Functions \\ 11.1: The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 \\ 12: Elliptic Integrals and Functions \\ 12.1: Elliptic Integrals / 229 \\ 12.2: Jacobian Elliptic Functions / 235 \\ 12.3: Derivatives and Integrals / 237 \\ 12.4: Inverse Jacobian Elliptic Functions / 237 \\ 13: Probability Integrals and the Error Function \\ 13.1: Normal Distribution / 239 \\ 13.2: The Error Function / 242 \\ 14: Fresnel Integrals, Sine and Cosine Integrals \\ 14.1: Definitions, Series Representations, and Values at Infinity / 245 \\ 14.2: Definitions, Series Representations, and Values at Infinity / 247 \\ 15: Definite Integrals \\ 15.1: Integrands Involving Powers of x / 249 \\ 15.2: Integrands Involving Trigonometric Functions 251 \\ 15.3: Integrands Involving the Exponential Function / 254 \\ 15.4: Integrands Involving the Hyperbolic Function 256 \\ 15.5: Integrands Involving the Logarithmic Function / 256 \\ 16: Different Forms of Fourier Series \\ 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 \\ 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 \\ 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 \\ 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 \\ 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L 259 \\ 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 \\ 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L 260 \\ 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 \\ 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 \\ 16.10: Representative Examples of Fourier Series 261 \\ 16.11: Fourier Series and Discontinuous Functions 265 \\ 17: Bessel Functions \\ 17.1: Bessel's Differential Equation / 269 \\ 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 \\ 17.3: Bessel Functions of Fractional Order / 272 \\ 17.4: Asymptotic Representations for Bessel Functions / 273 \\ 17.5: Zeros of Bessel Functions / 273 \\ 17.6: Bessel's Modified Equation / 274 \\ 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 \\ 17.8: Modified Bessel Functions of Fractional Order / 277 \\ 17.9: Asymptotic Representations of Modified Bessel Functions / 278 \\ 17.10: Relationships between Bessel Functions 278 \\ 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 \\ 17.12: Indefinite Integrals of Bessel Functions 281 \\ 17.13: Definite Integrals Involving Bessel Functions / 282 \\ 17.14: Spherical Bessel Functions / 283 \\ 18: Orthogonal Polynomials \\ 18.2: Legendre Polynomials P[subscript n](x) 286 \\ 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 \\ 18.4: Laguerre Polynomials L[subscript n](x) 294 \\ 18.5: Hermite Polynomials H[subscript n](x) / 296 \\ 19: Laplace Transformation \\ 20: Fourier Transforms \\ 21: Numerical Integration \\ 21.1: Classical Methods / 315 \\ 22: Solutions of Standard Ordinary Differential Equations \\ 22.2: Separation of Variables / 323 \\ 22.3: Linear First-Order Equations / 323 \\ 22.4: Bernoulli's Equation / 324 \\ 22.5: Exact Equations / 325 \\ 22.6: Homogeneous Equations / 325 \\ 22.7: Linear Differential Equations / 326 \\ 22.8: Constant Coefficient Linear Differential Equations \\ Homogeneous Case / 327 \\ 22.9: Linear Homogeneous Second-Order Equation 330 \\ 22.10: Constant Coefficient Linear Differential Equations \\ Inhomogeneous Case / 331 \\ 22.11: Linear Inhomogeneous Second-Order Equation 333 \\ 22.12: Determination of Particular Integrals by the Method of Undetermined Coefficients / 334 \\ 22.13: The Cauchy-Euler Equation / 336 \\ 22.14: Legendre's Equation / 337 \\ 22.15: Bessel's Equations / 337 \\ 22.16: Power Series and Frobenius Methods / 339 \\ 22.17: The Hypergeometric Equation / 344 \\ 22.18: Numerical Methods / 345 \\ 23: Vector Analysis \\ 23.1: Scalars and Vectors / 353 \\ 23.2: Scalar Products / 358 \\ 23.3: Vector Products / 359 \\ 23.4: Triple Products / 360 \\ 23.5: Products of Four Vectors / 361 \\ 23.6: Derivatives of Vector Functions of a Scalar t / 361 \\ 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 \\ 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 \\ 23.9: Line Integrals / 364 \\ 23.10: Vector Integral Theorems / 366 \\ 23.11: A Vector Rate of Change Theorem / 368 \\ 23.12: Useful Vector Identities and Results / 368 \\ 24: Systems of Orthogonal Coordinates \\ 24.1: Curvilinear Coordinates / 369 \\ 24.2: Vector Operators in Orthogonal Coordinates 371 \\ 24.3: Systems of Orthogonal Coordinates / 371 \\ 25: Partial Differential Equations and Special Functions \\ 25.1: Fundamental Ideas / 381 \\ 25.2: Method of Separation of Variables / 385 \\ 25.3: The Sturm--Liouville Problem and Special Functions / 387 \\ 25.4: A First-Order System and the Wave Equation 390 \\ 25.5: Conservation Equations (Laws) / 391 \\ 25.6: The Method of Characteristics / 392 \\ 25.7: Discontinuous Solutions (Shocks) / 396 \\ 25.8: Similarity Solutions / 398 \\ 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 \\ 26: The z-Transform \\ 26.1: The z-Transform and Transform Pairs / 403 \\ 27: Numerical Approximation \\ 27.2: Economization of Series / 411 \\ 27.3: Pade Approximation / 413 \\ 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

entry:
@Book{Jeffrey:1995:HMF,
  author =       "Alan Jeffrey",
  title =        "Handbook of Mathematical Formulas and Integrals",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xxiv + 410",
  year =         "1995",
  ISBN =         "0-08-052301-3, 0-12-382580-6 (e-book), 1-4832-9514-1
                 (e-book)",
  ISBN-13 =      "978-0-08-052301-9, 978-0-12-382580-3 (e-book),
                 978-1-4832-9514-5 (e-book)",
  LCCN =         "QA47 .J38 1995",
  bibdate =      "Wed Jun 12 14:33:38 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/book/9780123825803",
  abstract =     "If there is a formula to solve a given problem in
                 mathematics, you will find it in Alan Jeffrey's
                 \booktitle{Handbook of Mathematical Formulas and
                 Integrals}. Thanks to its unique thumb-tab indexing
                 feature, answers are easy to find based upon the type
                 of problem they solve. The Handbook covers important
                 formulas, functions, relations, and methods from
                 algebra, trigonometric and exponential functions,
                 combinatorics, probability, matrix theory, calculus and
                 vector calculus, both ordinary and partial differential
                 equations, Fourier series, orthogonal polynomials, and
                 Laplace transforms. Based on Gradshteyn and Ryzhik's
                 Table of Integrals, Series, and Products, Fifth Edition
                 (edited by Jeffrey), but far more accessible and
                 written with particular attention to the needs of
                 students and practicing scientists and engineers, this
                 book is an essential resource. Affordable and
                 authoritative, it is the first place to look for help
                 and a rewarding place to browse.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Tables; Formulae; Math{\'e}matiques;
                 Formules; formulas (algorithms); Mathematics.",
  tableofcontents = "0: Quick Reference List of Frequently Used Data \\
                 0.1: Useful Identities / 1 \\
                 0.2: Complex Relationships / 2 \\
                 0.3: Constants / 2 \\
                 0.4: Derivatives of Elementary Functions / 3 \\
                 0.5: Rules of Differentiation and Integration / 3 \\
                 0.6: Standard Integrals / 4 \\
                 0.7: Standard Series / 11 \\
                 0.8: Geometry / 13 \\
                 1: Numerical, Algebraic, and Analytical Results for
                 Series and Calculus \\
                 1.1: Algebraic Results Involving Real and Complex
                 Numbers / 25 \\
                 1.2: Finite Sums / 29 \\
                 1.3: Bernoulli and Euler Numbers and Polynomials 37 \\
                 1.4: Determinants / 47 \\
                 1.5: Matrices / 55 \\
                 1.6: Permutations and Combinations / 62 \\
                 1.7: Partial Fraction Decomposition / 63 \\
                 1.8: Convergence of Series / 66 \\
                 1.9: Infinite Products / 71 \\
                 1.10: Functional Series / 73 \\
                 1.11: Power Series / 74 \\
                 1.12: Taylor Series / 79 \\
                 1.13: Fourier Series / 81 \\
                 1.14: Asymptotic Expansions / 85 \\
                 1.15: Basic Results from the Calculus / 86 \\
                 2: Functions and Identities \\
                 2.1: Complex Numbers and Trigonometric and Hyperbolic
                 Functions / 101 \\
                 2.2: Logarithms and Exponentials / 112 \\
                 2.3: The Exponential Function / 114 \\
                 2.4: Trigonometric Identities / 115 \\
                 2.5: Hyperbolic Identities / 121 \\
                 2.6: The Logarithm / 126 \\
                 2.7: Inverse Trigonometric and Hyperbolic Functions /
                 128 \\
                 2.8: Series Representations of Trigonometric and
                 Hyperbolic Functions / 133 \\
                 2.9: Useful Limiting Values and Inequalities Involving
                 Elementary Functions / 136 \\
                 3: Derivatives of Elementary Functions \\
                 3.1: Derivatives of Algebraic, Logarithmic, and
                 Exponential Functions / 139 \\
                 3.2: Derivatives of Trigonometric Functions / 140 \\
                 3.3: Derivatives of Inverse Trigonometric Functions /
                 140 \\
                 3.4: Derivatives of Hyperbolic Functions / 141 \\
                 3.5: Derivatives of Inverse Hyperbolic Functions 142
                 \\
                 4: Indefinite Integrals of Algebraic Functions \\
                 4.1: Algebraic and Transcendental Functions / 145 \\
                 4.2: Indefinite Integrals of Rational Functions 146 \\
                 4.3: Nonrational Algebraic Functions / 158 \\
                 5: Indefinite Integrals of Exponential Functions \\
                 5.1: Basic Results / 167 \\
                 6: Indefinite Integrals of Logarithmic Functions \\
                 6.1: Combinations of Logarithms and Polynomials 173 \\
                 7: Indefinite Integrals of Hyperbolic Functions \\
                 7.1: Basic Results / 179 \\
                 7.2: Integrands Involving Powers of sinh(bx) or
                 cosh(bx) / 180 \\
                 7.3: Integrands Involving (a [plus or minus]
                 bx)[superscript m] sinh(cx) or (a + bx)[superscript m]
                 cosh(cx) / 181 \\
                 7.4: Integrands Involving x[superscript m]
                 sinh[superscript n] x or x[superscript m]
                 cosh[superscript n] x / 183 \\
                 7.5: Integrands Involving x[superscript m]
                 sinh[superscript -n] x or x[superscript m]
                 cosh[superscript -n] x / 183 \\
                 7.6: Integrands Involving (1 [plus or minus] cosh
                 x)[superscript -m] / 185 \\
                 7.7: Integrands Involving sinh(ax)cosh[superscript -n]
                 x or cosh(ax)sinh[superscript -n] x / 185 \\
                 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d)
                 / 186 \\
                 7.9: Integrands Involving tanh kx and coth kx 188 \\
                 7.10: Integrands Involving (a + bx)[superscript m] sinh
                 kx or (a + bx)[superscript m] cosh kx / 189 \\
                 8: Indefinite Integrals Involving Inverse Hyperbolic
                 Functions \\
                 8.1: Basic Results / 191 \\
                 8.2: Integrands Involving x[superscript -n]
                 arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 \\
                 8.3: Integrands Involving x[superscript n] arctanh(x/a)
                 or x[superscript n] arccoth(x/a) 194 \\
                 8.4: Integrands Involving x[superscript -n]
                 arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195
                 \\
                 9: Indefinite Integrals of Trigonometric Functions \\
                 9.1: Basic Results / 197 \\
                 9.2: Integrands Involving Powers of x and Powers of sin
                 x or cos x / 197 \\
                 9.3: Integrands Involving tan x and/or cot x 205 \\
                 9.4: Integrands Involving sin x and cos x / 207 \\
                 9.5: Integrands Involving Sines and Cosines with Linear
                 Arguments and Powers of x / 211 \\
                 10: Indefinite Integrals of Inverse Trigonometric
                 Functions \\
                 10.1: Integrands Involving Powers of x and Powers of
                 Inverse Trigonometric Functions / 215 \\
                 11: The Gamma, Beta, Pi, and Psi Functions \\
                 11.1: The Euler Integral and Limit and Infinite Product
                 Representations for [Gamma] (x) / 221 \\
                 12: Elliptic Integrals and Functions \\
                 12.1: Elliptic Integrals / 229 \\
                 12.2: Jacobian Elliptic Functions / 235 \\
                 12.3: Derivatives and Integrals / 237 \\
                 12.4: Inverse Jacobian Elliptic Functions / 237 \\
                 13: Probability Integrals and the Error Function \\
                 13.1: Normal Distribution / 239 \\
                 13.2: The Error Function / 242 \\
                 14: Fresnel Integrals, Sine and Cosine Integrals \\
                 14.1: Definitions, Series Representations, and Values
                 at Infinity / 245 \\
                 14.2: Definitions, Series Representations, and Values
                 at Infinity / 247 \\
                 15: Definite Integrals \\
                 15.1: Integrands Involving Powers of x / 249 \\
                 15.2: Integrands Involving Trigonometric Functions 251
                 \\
                 15.3: Integrands Involving the Exponential Function /
                 254 \\
                 15.4: Integrands Involving the Hyperbolic Function 256
                 \\
                 15.5: Integrands Involving the Logarithmic Function /
                 256 \\
                 16: Different Forms of Fourier Series \\
                 16.1: Fourier Series for f(x) on -[pi] [less than or
                 equal] x [less than or equal] [pi] / 257 \\
                 16.2: Fourier Series for f(x) on -L [less than or
                 equal] x [less than or equal] L / 258 \\
                 16.3: Fourier Series for f(x) on a [less than or equal]
                 x [less than or equal] b / 258 \\
                 16.4: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 259
                 \\
                 16.5: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L 259 \\
                 16.6: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 260
                 \\
                 16.7: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L 260 \\
                 16.8: Complex (Exponential) Fourier Series for f(x) on
                 -[pi] [less than or equal] x [less than or equal] [pi]
                 / 260 \\
                 16.9: Complex (Exponential) Fourier Series for f(x) on
                 -L [less than or equal] x [less than or equal] L 261
                 \\
                 16.10: Representative Examples of Fourier Series 261
                 \\
                 16.11: Fourier Series and Discontinuous Functions 265
                 \\
                 17: Bessel Functions \\
                 17.1: Bessel's Differential Equation / 269 \\
                 17.2: Series Expansions for J[subscript v](x) and
                 Y[subscript v](x) / 270 \\
                 17.3: Bessel Functions of Fractional Order / 272 \\
                 17.4: Asymptotic Representations for Bessel Functions /
                 273 \\
                 17.5: Zeros of Bessel Functions / 273 \\
                 17.6: Bessel's Modified Equation / 274 \\
                 17.7: Series Expansions for I[subscript v](x) and
                 K[subscript v](x) / 276 \\
                 17.8: Modified Bessel Functions of Fractional Order /
                 277 \\
                 17.9: Asymptotic Representations of Modified Bessel
                 Functions / 278 \\
                 17.10: Relationships between Bessel Functions 278 \\
                 17.11: Integral Representations of J[subscript n](x),
                 I[subscript n](x), and K[subscript n](x) / 281 \\
                 17.12: Indefinite Integrals of Bessel Functions 281 \\
                 17.13: Definite Integrals Involving Bessel Functions /
                 282 \\
                 17.14: Spherical Bessel Functions / 283 \\
                 18: Orthogonal Polynomials \\
                 18.2: Legendre Polynomials P[subscript n](x) 286 \\
                 18.3: Chebyshev Polynomials T[subscript n](x) and
                 U[subscript n](x) / 290 \\
                 18.4: Laguerre Polynomials L[subscript n](x) 294 \\
                 18.5: Hermite Polynomials H[subscript n](x) / 296 \\
                 19: Laplace Transformation \\
                 20: Fourier Transforms \\
                 21: Numerical Integration \\
                 21.1: Classical Methods / 315 \\
                 22: Solutions of Standard Ordinary Differential
                 Equations \\
                 22.2: Separation of Variables / 323 \\
                 22.3: Linear First-Order Equations / 323 \\
                 22.4: Bernoulli's Equation / 324 \\
                 22.5: Exact Equations / 325 \\
                 22.6: Homogeneous Equations / 325 \\
                 22.7: Linear Differential Equations / 326 \\
                 22.8: Constant Coefficient Linear Differential
                 Equations \\
                 Homogeneous Case / 327 \\
                 22.9: Linear Homogeneous Second-Order Equation 330 \\
                 22.10: Constant Coefficient Linear Differential
                 Equations \\
                 Inhomogeneous Case / 331 \\
                 22.11: Linear Inhomogeneous Second-Order Equation 333
                 \\
                 22.12: Determination of Particular Integrals by the
                 Method of Undetermined Coefficients / 334 \\
                 22.13: The Cauchy-Euler Equation / 336 \\
                 22.14: Legendre's Equation / 337 \\
                 22.15: Bessel's Equations / 337 \\
                 22.16: Power Series and Frobenius Methods / 339 \\
                 22.17: The Hypergeometric Equation / 344 \\
                 22.18: Numerical Methods / 345 \\
                 23: Vector Analysis \\
                 23.1: Scalars and Vectors / 353 \\
                 23.2: Scalar Products / 358 \\
                 23.3: Vector Products / 359 \\
                 23.4: Triple Products / 360 \\
                 23.5: Products of Four Vectors / 361 \\
                 23.6: Derivatives of Vector Functions of a Scalar t /
                 361 \\
                 23.7: Derivatives of Vector Functions of Several Scalar
                 Variables / 362 \\
                 23.8: Integrals of Vector Functions of a Scalar
                 Variable t / 363 \\
                 23.9: Line Integrals / 364 \\
                 23.10: Vector Integral Theorems / 366 \\
                 23.11: A Vector Rate of Change Theorem / 368 \\
                 23.12: Useful Vector Identities and Results / 368 \\
                 24: Systems of Orthogonal Coordinates \\
                 24.1: Curvilinear Coordinates / 369 \\
                 24.2: Vector Operators in Orthogonal Coordinates 371
                 \\
                 24.3: Systems of Orthogonal Coordinates / 371 \\
                 25: Partial Differential Equations and Special
                 Functions \\
                 25.1: Fundamental Ideas / 381 \\
                 25.2: Method of Separation of Variables / 385 \\
                 25.3: The Sturm--Liouville Problem and Special
                 Functions / 387 \\
                 25.4: A First-Order System and the Wave Equation 390
                 \\
                 25.5: Conservation Equations (Laws) / 391 \\
                 25.6: The Method of Characteristics / 392 \\
                 25.7: Discontinuous Solutions (Shocks) / 396 \\
                 25.8: Similarity Solutions / 398 \\
                 25.9: Burgers's Equation, the KdV Equation, and the
                 KdVB Equation / 400 \\
                 26: The z-Transform \\
                 26.1: The z-Transform and Transform Pairs / 403 \\
                 27: Numerical Approximation \\
                 27.2: Economization of Series / 411 \\
                 27.3: Pade Approximation / 413 \\
                 27.4: Finite Difference Approximations to Ordinary and
                 Partial Derivatives / 415",
}


bibtype: article
filename: elefunt.bib
label: Krattenthaler:1995:HHM
author: C. Krattenthaler
journal: j-J-SYMBOLIC-COMP
volume: 20
number: 5--6
pages: 737--744
month: nov
monthnumber: 11
year: 1995
CODEN: JSYCEH
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 05Axx (11Bxx 33-04 33Cxx 33Dxx)
MRnumber: 1 395 424
bibdate: Sat May 10 15:54:09 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.10 15:54:09 MDT
note: Symbolic computation in combinatorics $ Delta _1 $ (Ithaca, NY, 1993).
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics computing); C1100 (Mathematical techniques)
corpsource: Inst. fur Math., Wien Univ., Austria
journalURL: http://www.sciencedirect.com/science/journal/07477171
treatment: T Theoretical or Mathematical
rawauthor: C. Krattenthaler
rawnote: Symbolic computation in combinatorics $ \Delta_1 $ (Ithaca, NY, 1993).
title:
HYP and HYPQ: Mathematica packages for the manipulation of binomial sums and hypergeometric series, respectively $q$-binomial sums and basic hypergeometric series

keywords:
basic hypergeometric; binomial sums; HYP; hypergeometric series; HYPQ; Mathematica packages; mathematics computing; packages; q-binomial sums; series; series (mathematics); software; symbol manipulation

rawtitle:
{HYP} and {HYPQ}: {Mathematica} packages for the manipulation of binomial sums and hypergeometric series, respectively $q$-binomial sums and basic hypergeometric series

entry:
@Article{Krattenthaler:1995:HHM,
  author =       "C. Krattenthaler",
  title =        "{HYP} and {HYPQ}: {Mathematica} packages for the
                 manipulation of binomial sums and hypergeometric
                 series, respectively $q$-binomial sums and basic
                 hypergeometric series",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "20",
  number =       "5--6",
  pages =        "737--744",
  month =        nov # "--" # dec,
  year =         "1995",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "05Axx (11Bxx 33-04 33Cxx 33Dxx)",
  MRnumber =     "1 395 424",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Symbolic computation in combinatorics $ \Delta_1 $
                 (Ithaca, NY, 1993).",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics computing); C1100 (Mathematical
                 techniques)",
  corpsource =   "Inst. fur Math., Wien Univ., Austria",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "basic hypergeometric; binomial sums; HYP;
                 hypergeometric series; HYPQ; Mathematica packages;
                 mathematics computing; packages; q-binomial sums;
                 series; series (mathematics); software; symbol
                 manipulation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kwan:1995:CII
author: H. Kwan and R. L. Nelson, Jr. and E. E. Swartzlander, Jr.
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: Cascaded Implementation of an Iterative Inverse-Square-Root Algorithm, with Overflow Lookahead
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 115--122
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: H. Kwan and R. L. {Nelson, Jr.} and E. E. {Swartzlander, Jr.}
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: Cascaded Implementation of an Iterative Inverse-Square-Root Algorithm, with Overflow Lookahead
entry:
@InProceedings{Kwan:1995:CII,
  author =       "H. Kwan and R. L. {Nelson, Jr.} and E. E.
                 {Swartzlander, Jr.}",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Cascaded Implementation of an Iterative
                 Inverse-Square-Root Algorithm, with Overflow
                 Lookahead",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "115--122",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "We present an unconventional method of computing the
                 inverse of the square root. It implements the
                 equivalent of two iterations of a well-known
                 multiplicative method to obtain 24-bit mantissa
                 accuracy. We implement each ``iteration'' as a
                 \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lang:1995:VHR
author: T. Lang and P. Montuschi
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: Very-High Radix Combined Division and Square Root with Prescaling and Selection by Rounding
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 124--131
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: T. Lang and P. Montuschi
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: Very-High Radix Combined Division and Square Root with Prescaling and Selection by Rounding
entry:
@InProceedings{Lang:1995:VHR,
  author =       "T. Lang and P. Montuschi",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Very-High Radix Combined Division and Square Root with
                 Prescaling and Selection by Rounding",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "124--131",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "An algorithm for square root with prescaling is
                 developed and combined with a similar scheme for
                 division. An implementation is described, evaluated and
                 compared with other combined div/sqrt \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Lau:1995:NLC
author: H. T. (Hang Tong) Lau
title: A Numerical Library in C for Scientists and Engineers
publisher: pub-CRC
address: pub-CRC:adr
pages: xvii + 795
year: 1995
ISBN: 0-8493-7376-X OR 084937376X
ISBN13: 978-0-8493-7376-3 OR 9780849373763
LCCN: QA76.73.C15 L38 1995
bibdate: Fri Sep 26 14:29:10 MDT 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2008.09.26 14:29:10 MDT
URL: http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html
subject: C (Computer program language)
acknowledgement: ack-nhfb
rawauthor: H. T. (Hang Tong) Lau
rawtitle: A Numerical Library in {C} for Scientists and Engineers
TOC:
1. Elementary Procedures 1.1. Real vector and matrix Initialization 1.2. Real vector and matrix Duplication 1.3. Real vector and matrix Multiplication 1.4. Real vector vector products 1.5. Real matrix vector products 1.6. Real matrix matrix products 1.7. Real vector and matrix Elimination 1.8. Real vector and matrix Interchanging 1.9. Real vector and matrix Rotation 1.10. Real vector and matrix Norms 1.11. Real vector and matrix Scaling 1.12. Complex vector and matrix Multiplication 1.13. Complex vector and matrix Scalar products 1.14. Complex vector and matrix Elimination 1.15. Complex vector and matrix Rotation 1.16. Complex vector and matrix Norms 1.17. Complex vector and matrix Scaling 1.18. Complex monadic operations 1.19. Complex dyadic operations 1.20. Long integer arithmetic 2. Algebraic Evaluations 2.1. Evaluation of polynomials in Grunert form 2.2. Evaluation of general orthogonal polynomials 2.3. Evaluation of Chebyshev polynomials 2.4. Evaluation of Fourier series 2.5. Evaluation of continued fractions 2.6. Transformation of polynomial representation 2.7. Operations on orthogonal polynomials 3. Linear Algebra 3.1. Full real general matrices 3.2. Real Symmetric positive definite matrices 3.3. General real symmetric matrices 3.4. Real full rank overdetermined systems 3.5. Other real matrix problems 3.6. Real sparse non-symmetric band matrices 3.7. Real sparse non-symmetric tridiagonal matrices 3.8. Sparse symmetric positive definite band matrices 3.9. Symmetric positive definite tridiagonal matrices 3.10. Sparse real matrices Iterative methods 3.11. Similarity transformation 3.12. Other transformations 3.13. The (ordinary) eigenvalue problem 3.14. The generalized eigenvalue problem 3.15. Singular values 3.16. Zeros of polynomials 4. Analytic Evaluations 4.1. Evaluation of an infinite series 4.2. Quadrature 4.3. Numerical differentiation 5. Analytic Problems 5.1. Non-linear equations 5.2. Unconstrained optimization 5.3. Overdetermined nonlinear systems 5.4. Differential equations Initial value problems 5.5. Two point boundary value problems 5.6. Two-dimensional boundary value problems 5.7. Parameter estimation in differential equations 6. Special Functions 6.1. Elementary functions 6.2. Exponential integral 6.3. Gamma function 6.4. Error function 6.5. Bessel functions of integer order 6.6. Bessel functions of real order 7. Interpolation and Approximation 7.1. Real data in one dimension Appendix B: Prototype Declarations Appendix C: Procedure Descriptions Appendix D: Memory Management Utilities

shortTOC:
Introduction 1 Elementary Procedures 2 Algebraic Evaluations 3 Linear Algebra 4 Analytic Evaluations 5 Analytic Problems 6 Special Functions 7 Interpolation and Approximation

rawshortTOC:
Introduction \\ 1 Elementary Procedures \\ 2 Algebraic Evaluations \\ 3 Linear Algebra \\ 4 Analytic Evaluations \\ 5 Analytic Problems \\ 6 Special Functions \\ 7 Interpolation and Approximation

rawTOC:
1. Elementary Procedures \\ 1.1. Real vector and matrix Initialization \\ 1.2. Real vector and matrix Duplication \\ 1.3. Real vector and matrix Multiplication \\ 1.4. Real vector vector products \\ 1.5. Real matrix vector products \\ 1.6. Real matrix matrix products \\ 1.7. Real vector and matrix Elimination \\ 1.8. Real vector and matrix Interchanging \\ 1.9. Real vector and matrix Rotation \\ 1.10. Real vector and matrix Norms \\ 1.11. Real vector and matrix Scaling \\ 1.12. Complex vector and matrix Multiplication \\ 1.13. Complex vector and matrix Scalar products \\ 1.14. Complex vector and matrix Elimination \\ 1.15. Complex vector and matrix Rotation \\ 1.16. Complex vector and matrix Norms \\ 1.17. Complex vector and matrix Scaling \\ 1.18. Complex monadic operations \\ 1.19. Complex dyadic operations \\ 1.20. Long integer arithmetic \\ 2. Algebraic Evaluations \\ 2.1. Evaluation of polynomials in Grunert form \\ 2.2. Evaluation of general orthogonal polynomials \\ 2.3. Evaluation of Chebyshev polynomials \\ 2.4. Evaluation of Fourier series \\ 2.5. Evaluation of continued fractions \\ 2.6. Transformation of polynomial representation \\ 2.7. Operations on orthogonal polynomials \\ 3. Linear Algebra \\ 3.1. Full real general matrices \\ 3.2. Real Symmetric positive definite matrices \\ 3.3. General real symmetric matrices \\ 3.4. Real full rank overdetermined systems \\ 3.5. Other real matrix problems \\ 3.6. Real sparse non-symmetric band matrices \\ 3.7. Real sparse non-symmetric tridiagonal matrices \\ 3.8. Sparse symmetric positive definite band matrices \\ 3.9. Symmetric positive definite tridiagonal matrices \\ 3.10. Sparse real matrices \\ Iterative methods \\ 3.11. Similarity transformation \\ 3.12. Other transformations \\ 3.13. The (ordinary) eigenvalue problem \\ 3.14. The generalized eigenvalue problem \\ 3.15. Singular values \\ 3.16. Zeros of polynomials \\ 4. Analytic Evaluations \\ 4.1. Evaluation of an infinite series \\ 4.2. Quadrature \\ 4.3. Numerical differentiation \\ 5. Analytic Problems \\ 5.1. Non-linear equations \\ 5.2. Unconstrained optimization \\ 5.3. Overdetermined nonlinear systems \\ 5.4. Differential equations \\ Initial value problems \\ 5.5. Two point boundary value problems \\ 5.6. Two-dimensional boundary value problems \\ 5.7. Parameter estimation in differential equations \\ 6. Special Functions \\ 6.1. Elementary functions \\ 6.2. Exponential integral \\ 6.3. Gamma function \\ 6.4. Error function \\ 6.5. Bessel functions of integer order \\ 6.6. Bessel functions of real order \\ 7. Interpolation and Approximation \\ 7.1. Real data in one dimension \\ Appendix B: Prototype Declarations \\ Appendix C: Procedure Descriptions \\ Appendix D: Memory Management Utilities

entry:
@Book{Lau:1995:NLC,
  author =       "H. T. (Hang Tong) Lau",
  title =        "A Numerical Library in {C} for Scientists and
                 Engineers",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "xvii + 795",
  year =         "1995",
  ISBN =         "0-8493-7376-X",
  ISBN-13 =      "978-0-8493-7376-3",
  LCCN =         "QA76.73.C15 L38 1995",
  bibdate =      "Fri Sep 26 14:29:10 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Introduction \\
                 1 Elementary Procedures \\
                 2 Algebraic Evaluations \\
                 3 Linear Algebra \\
                 4 Analytic Evaluations \\
                 5 Analytic Problems \\
                 6 Special Functions \\
                 7 Interpolation and Approximation",
  subject =      "C (Computer program language)",
  tableofcontents = "1. Elementary Procedures \\
                 1.1. Real vector and matrix Initialization \\
                 1.2. Real vector and matrix Duplication \\
                 1.3. Real vector and matrix Multiplication \\
                 1.4. Real vector vector products \\
                 1.5. Real matrix vector products \\
                 1.6. Real matrix matrix products \\
                 1.7. Real vector and matrix Elimination \\
                 1.8. Real vector and matrix Interchanging \\
                 1.9. Real vector and matrix Rotation \\
                 1.10. Real vector and matrix Norms \\
                 1.11. Real vector and matrix Scaling \\
                 1.12. Complex vector and matrix Multiplication \\
                 1.13. Complex vector and matrix Scalar products \\
                 1.14. Complex vector and matrix Elimination \\
                 1.15. Complex vector and matrix Rotation \\
                 1.16. Complex vector and matrix Norms \\
                 1.17. Complex vector and matrix Scaling \\
                 1.18. Complex monadic operations \\
                 1.19. Complex dyadic operations \\
                 1.20. Long integer arithmetic \\
                 2. Algebraic Evaluations \\
                 2.1. Evaluation of polynomials in Grunert form \\
                 2.2. Evaluation of general orthogonal polynomials \\
                 2.3. Evaluation of Chebyshev polynomials \\
                 2.4. Evaluation of Fourier series \\
                 2.5. Evaluation of continued fractions \\
                 2.6. Transformation of polynomial representation \\
                 2.7. Operations on orthogonal polynomials \\
                 3. Linear Algebra \\
                 3.1. Full real general matrices \\
                 3.2. Real Symmetric positive definite matrices \\
                 3.3. General real symmetric matrices \\
                 3.4. Real full rank overdetermined systems \\
                 3.5. Other real matrix problems \\
                 3.6. Real sparse non-symmetric band matrices \\
                 3.7. Real sparse non-symmetric tridiagonal matrices \\
                 3.8. Sparse symmetric positive definite band matrices
                 \\
                 3.9. Symmetric positive definite tridiagonal matrices
                 \\
                 3.10. Sparse real matrices \\
                 Iterative methods \\
                 3.11. Similarity transformation \\
                 3.12. Other transformations \\
                 3.13. The (ordinary) eigenvalue problem \\
                 3.14. The generalized eigenvalue problem \\
                 3.15. Singular values \\
                 3.16. Zeros of polynomials \\
                 4. Analytic Evaluations \\
                 4.1. Evaluation of an infinite series \\
                 4.2. Quadrature \\
                 4.3. Numerical differentiation \\
                 5. Analytic Problems \\
                 5.1. Non-linear equations \\
                 5.2. Unconstrained optimization \\
                 5.3. Overdetermined nonlinear systems \\
                 5.4. Differential equations \\
                 Initial value problems \\
                 5.5. Two point boundary value problems \\
                 5.6. Two-dimensional boundary value problems \\
                 5.7. Parameter estimation in differential equations \\
                 6. Special Functions \\
                 6.1. Elementary functions \\
                 6.2. Exponential integral \\
                 6.3. Gamma function \\
                 6.4. Error function \\
                 6.5. Bessel functions of integer order \\
                 6.6. Bessel functions of real order \\
                 7. Interpolation and Approximation \\
                 7.1. Real data in one dimension \\
                 Appendix B: Prototype Declarations \\
                 Appendix C: Procedure Descriptions \\
                 Appendix D: Memory Management Utilities",
}


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

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

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


bibtype: article
filename: elefunt.bib
label: Lether:1995:MAZ
author: F. G. Lether and P. R. Wenston
title: Minimax approximations to the zeros of $ P_n(x) $ and Gauss--Legendre quadrature
journal: j-J-COMPUT-APPL-MATH
volume: 59
number: 2
pages: 245--252
day: 19
month: may
monthnumber: 5
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:37 MST 2017
bibtimestamp: 2017.02.25 12:24:37 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794000305
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: F. G. Lether and P. R. Wenston
rawtitle: Minimax approximations to the zeros of {$ P_n(x) $} and {Gauss--Legendre} quadrature
entry:
@Article{Lether:1995:MAZ,
  author =       "F. G. Lether and P. R. Wenston",
  title =        "Minimax approximations to the zeros of {$ P_n(x) $}
                 and {Gauss--Legendre} quadrature",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "59",
  number =       "2",
  pages =        "245--252",
  day =          "19",
  month =        may,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794000305",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lewanowicz:1995:AMC
author: Stanislaw Lewanowicz and Stefan Paszkowski
title: An analytic method for convergence acceleration of certain hypergeometric series
journal: j-MATH-COMPUT
volume: 64
number: 210
pages: 691--713
month: apr
monthnumber: 4
year: 1995
CODEN: MCMPAF
DOI: https://doi.org/10.2307/2153446
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33C45 (65B10 65D20)
MRnumber: 1277769 (95h:33006)
MRreviewer: Anton Hut'a
bibdate: Thu Dec 1 17:36:45 2011
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
affiliation: Inst. of Comput. Sci., Wroclaw Univ., Poland
classcodes: B0290 (Numerical analysis); C4100 (Numerical analysis)
corpsource: Inst. of Comput. Sci., Wroclaw Univ., Poland
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Stanis{\l}aw Lewanowicz and Stefan Paszkowski
rawtitle: An analytic method for convergence acceleration of certain hypergeometric series
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

keywords:
analytic method; convergence acceleration; convergence of numerical methods; fast converging expansions; hypergeometric; iterated transformation; mathematical constants; series; series (mathematics)

entry:
@Article{Lewanowicz:1995:AMC,
  author =       "Stanis{\l}aw Lewanowicz and Stefan Paszkowski",
  title =        "An analytic method for convergence acceleration of
                 certain hypergeometric series",
  journal =      j-MATH-COMPUT,
  volume =       "64",
  number =       "210",
  pages =        "691--713",
  month =        apr,
  year =         "1995",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2153446",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C45 (65B10 65D20)",
  MRnumber =     "1277769 (95h:33006)",
  MRreviewer =   "Anton Hut'a",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  classcodes =   "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analytic method; convergence acceleration; convergence
                 of numerical methods; fast converging expansions;
                 hypergeometric; iterated transformation; mathematical
                 constants; series; series (mathematics)",
  treatment =    "T Theoretical or Mathematical",
}


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

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


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

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

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

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


bibtype: article
filename: elefunt.bib
label: Lucas:1995:EII
author: S. K. Lucas and H. A. Stone
title: Evaluating infinite integrals involving Bessel functions of arbitrary order
journal: j-J-COMPUT-APPL-MATH
volume: 64
number: 3
pages: 217--231
year: 1995
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(95)00142-5
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Thu Jul 8 13:22:49 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.07.08 13:22:49 ???
URL: http://www.sciencedirect.com/science/article/B6TYH-4002HHC-J/2/54f1e67d9bea3e951acc3c39556ab452
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: S. K. Lucas and H. A. Stone
rawtitle: Evaluating infinite integrals involving {Bessel} functions of arbitrary order
keywords:
$varepsilon $-algorithm; Bessel functions; Bessel zeros; infinite integration; mW transform; quadrature

remark:
This paper examines several methods for accurately integrating oscillatory functions, such as products of $ f(x) $ with a trigonometric function or a Bessel function. It also discusses finding zeros of Bessel functions, and sequence acceleration techniques.

entry:
@Article{Lucas:1995:EII,
  author =       "S. K. Lucas and H. A. Stone",
  title =        "Evaluating infinite integrals involving {Bessel}
                 functions of arbitrary order",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "64",
  number =       "3",
  pages =        "217--231",
  year =         "1995",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(95)00142-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Jul 8 13:22:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/B6TYH-4002HHC-J/2/54f1e67d9bea3e951acc3c39556ab452",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "$\varepsilon$-algorithm; Bessel functions; Bessel
                 zeros; infinite integration; mW transform; quadrature",
  remark =       "This paper examines several methods for accurately
                 integrating oscillatory functions, such as products of
                 $ f(x) $ with a trigonometric function or a Bessel
                 function. It also discusses finding zeros of Bessel
                 functions, and sequence acceleration techniques.",
}


bibtype: article
filename: elefunt.bib
label: Luther:1995:HAT
author: Wolfram Luther
title: Highly accurate tables for elementary functions
journal: j-BIT-NUM-MATH
volume: 35
number: 3
pages: 352--360
month: sep
monthnumber: 9
year: 1995
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01732609
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D20 (68U05)
MRnumber: 97h:65024
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
keywords: elementary functions
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Wolfram Luther
rawtitle: Highly accurate tables for elementary functions
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.mai.liu.se/BIT/contents/bit35.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352

entry:
@Article{Luther:1995:HAT,
  author =       "Wolfram Luther",
  title =        "Highly accurate tables for elementary functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "35",
  number =       "3",
  pages =        "352--360",
  month =        sep,
  year =         "1995",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01732609",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D20 (68U05)",
  MRnumber =     "97h:65024",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit35.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lynch:1995:KTF
author: T. Lynch and A. Ahmed and M. Schulte and T. Callaway
title: The K5 Transcendental Functions
crossref: Knowles:1995:PSC
pages: 163--171
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf
acknowledgement: ack-nhfb
rawauthor: T. Lynch and A. Ahmed and M. Schulte and T. Callaway
rawtitle: The {K5} Transcendental Functions
entry:
@InProceedings{Lynch:1995:KTF,
  author =       "T. Lynch and A. Ahmed and M. Schulte and T. Callaway",
  title =        "The {K5} Transcendental Functions",
  crossref =     "Knowles:1995:PSC",
  pages =        "163--171",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Maroni:1995:IRB
author: P. Maroni
title: An integral representation for the Bessel form
journal: j-J-COMPUT-APPL-MATH
volume: 57
number: 1--2
pages: 251--260
day: 20
month: feb
monthnumber: 2
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:35 MST 2017
bibtimestamp: 2017.02.25 12:24:35 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042793E0249L
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: P. Maroni
rawtitle: An integral representation for the {Bessel} form
entry:
@Article{Maroni:1995:IRB,
  author =       "P. Maroni",
  title =        "An integral representation for the {Bessel} form",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "57",
  number =       "1--2",
  pages =        "251--260",
  day =          "20",
  month =        feb,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042793E0249L",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Matsubara:1995:NBS
author: G. Matsubara and N. Ide and H. Tago and S. Suzuki and N. Goto
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: 30-ns 55-b Shared Radix $2$ Division and Square Root Using a Self-Timed Circuit
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 98--105
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: G. Matsubara and N. Ide and H. Tago and S. Suzuki and N. Goto
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: 30-ns 55-b Shared Radix $2$ Division and Square Root Using a Self-Timed Circuit
entry:
@InProceedings{Matsubara:1995:NBS,
  author =       "G. Matsubara and N. Ide and H. Tago and S. Suzuki and
                 N. Goto",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "30-ns 55-b Shared Radix $2$ Division and Square Root
                 Using a Self-Timed Circuit",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "98--105",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "A shared radix 2 division and square root
                 implementation using a self-timed circuit is presented.
                 The same execution time for division and square root is
                 achieved by using an on-the-fly digit decoding and a
                 root multiple generation technique. Most \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Miller:1995:RCF
author: A. R. Miller and I. S. Moskowitz
title: Reduction of a class of Fox--Wright psi functions for certain rational parameters
journal: j-COMPUT-MATH-APPL
volume: 30
number: 11
pages: 73--82
month: dec
monthnumber: 12
year: 1995
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:19 MST 2017
bibtimestamp: 2017.03.01 21:48:19 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219500165U
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: A. R. Miller and I. S. Moskowitz
rawtitle: Reduction of a class of {Fox--Wright} psi functions for certain rational parameters
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
From the abstract: ``The Fox--Wright Psi function is a special case of Fox's $H$-function and a generalization of the generalized hypergeometric function. In the present paper, we show that the Psi function reduces to a single generalized hypergeometric function when certain of its parameters are integers and to a finite sum of generalized hypergeometric functions when these parameters are rational numbers.''

entry:
@Article{Miller:1995:RCF,
  author =       "A. R. Miller and I. S. Moskowitz",
  title =        "Reduction of a class of {Fox--Wright} psi functions
                 for certain rational parameters",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "11",
  pages =        "73--82",
  month =        dec,
  year =         "1995",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500165U",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``The Fox--Wright Psi function is a
                 special case of Fox's $H$-function and a generalization
                 of the generalized hypergeometric function. In the
                 present paper, we show that the Psi function reduces to
                 a single generalized hypergeometric function when
                 certain of its parameters are integers and to a finite
                 sum of generalized hypergeometric functions when these
                 parameters are rational numbers.''",
}


bibtype: article
filename: elefunt.bib
label: Montuschi:1995:RRI
author: P. Montuschi and L. Ciminiera
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 1
pages: 144--146
month: jan
monthnumber: 1
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.368000
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
note: See cite Montuschi:1993:RIT.
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and L. Ciminiera
rawnote: See \cite{Montuschi:1993:RIT}.
title:
A remark on ``Reducing iteration time when result digit is zero for radix-$2$ SRT division and square root with redundant remainders''

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

entry:
@Article{Montuschi:1995:RRI,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "A remark on {``Reducing iteration time when result
                 digit is zero for radix-$2$ SRT division and square
                 root with redundant remainders''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "144--146",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.368000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Montuschi:1993:RIT}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "In a previous paper by P. Montuschi and L. Ciminiera
                 (ibid., vol. 42, no.2 p239-246, Feb 1993), an
                 architecture for shared radix 2 division and square
                 root has been presented whose main characteristic is
                 the ability to avoid any addition/subtraction,
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Muldoon:1995:EZB
author: Martin E. Muldoon
title: Electrostatics and zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 65
number: 1--3
pages: 299--308
day: 29
month: dec
monthnumber: 12
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:25 MST 2017
bibtimestamp: 2017.02.25 13:02:25 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795001182
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Martin E. Muldoon
rawtitle: Electrostatics and zeros of {Bessel} functions
entry:
@Article{Muldoon:1995:EZB,
  author =       "Martin E. Muldoon",
  title =        "Electrostatics and zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "65",
  number =       "1--3",
  pages =        "299--308",
  day =          "29",
  month =        dec,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001182",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


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


bibtype: article
filename: elefunt.bib
label: Paszkowski:1995:QHS
author: S. Paszkowski
title: Quasipower and hypergeometric series---construction and evaluation
journal: j-NUMER-ALGORITHMS
volume: 10
number: 3--4
pages: 337--361
month: oct
monthnumber: 10
year: 1995
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 41A58 (33-04 65B99)
MRnumber: 96k:41042
MRreviewer: Walter Schempp
bibdate: Fri Nov 6 18:06:29 MST 1998
bibtimestamp: 1998.11.06 18:06:29 MST
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Inst. for Low Temp. and Structure Res., Polish Acad. of Sci., Wroclaw, Poland
journalURL: http://link.springer.com/journal/11075
treatment: P Practical; T Theoretical or Mathematical
rawauthor: S. Paszkowski
rawtitle: Quasipower and hypergeometric series---construction and evaluation
bibsource:
http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

keywords:
approximation theory; Euler's dilogarithm; Hermite-Pade approximation; hypergeometric series; Levin's transforms; Pade approximants; power series; quasipower; recurrence relations; series (mathematics); transforms

entry:
@Article{Paszkowski:1995:QHS,
  author =       "S. Paszkowski",
  title =        "Quasipower and hypergeometric series---construction
                 and evaluation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "3--4",
  pages =        "337--361",
  month =        oct,
  year =         "1995",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "41A58 (33-04 65B99)",
  MRnumber =     "96k:41042",
  MRreviewer =   "Walter Schempp",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290Z (Other numerical methods); C4130 (Interpolation
                 and function approximation); C4190 (Other numerical
                 methods)",
  corpsource =   "Inst. for Low Temp. and Structure Res., Polish Acad.
                 of Sci., Wroclaw, Poland",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "approximation theory; Euler's dilogarithm;
                 Hermite-Pade approximation; hypergeometric series;
                 Levin's transforms; Pade approximants; power series;
                 quasipower; recurrence relations; series (mathematics);
                 transforms",
  pubcountry =   "Switzerland",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Prabhu:1995:MRD
author: J. A. Prabhu and G. B. Zyner
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: 167 MHz Radix-$8$ Divide and Square Root Using Overlapped Radix-$2$ Stages
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 155--162
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: J. A. Prabhu and G. B. Zyner
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: {167 MHz} Radix-$8$ Divide and Square Root Using Overlapped Radix-$2$ Stages
entry:
@InProceedings{Prabhu:1995:MRD,
  author =       "J. A. Prabhu and G. B. Zyner",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "{167 MHz} Radix-$8$ Divide and Square Root Using
                 Overlapped Radix-$2$ Stages",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "155--162",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "UltraSPARC's IEEE-754 compliant floating point divide
                 and square root implementation is presented. Three
                 overlapping stages of SRT radix-$2$ quotient selection
                 logic enable an effective radix-$8$ calculation at 167
                 MHz while only a single radix-$2$ \ldots{}",
}


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


bibtype: article
filename: elefunt.bib
label: Sidhu:1995:EIF
author: Satinder S. Sidhu
title: Elliptic Integrals and Functions
journal: j-COMPUT-PHYS
volume: 9
number: 3
pages: 268--276
month: may
monthnumber: 5
year: 1995
CODEN: CPHYE2
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Thu Feb 02 18:05:53 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2012.02.02 18:05:53 ???
fjournal: Computers in Physics
acknowledgement: ack-nhfb
rawauthor: Satinder S. Sidhu
rawtitle: Elliptic Integrals and Functions
entry:
@Article{Sidhu:1995:EIF,
  author =       "Satinder S. Sidhu",
  title =        "Elliptic Integrals and Functions",
  journal =      j-COMPUT-PHYS,
  volume =       "9",
  number =       "3",
  pages =        "268--276",
  month =        may # "\slash " # jun,
  year =         "1995",
  CODEN =        "CPHYE2",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Thu Feb 02 18:05:53 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers in Physics",
}


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

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

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

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


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

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database

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

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


bibtype: book
filename: elefunt.bib
label: Varchenko:1995:MHF
author: A. N. (Aleksandr Nikolaevich) Varchenko
volume: 21
publisher: pub-WORLD-SCI
address: pub-WORLD-SCI:adr
pages: ix + 371
year: 1995
ISBN: 981-02-1880-X OR 981021880X
ISBN13: 978-981-02-1880-5 OR 9789810218805
LCCN: QA353.H9 V37 1995
bibdate: Sat Oct 30 21:12:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:12:24 MDT
series: Advanced series in mathematical physics
acknowledgement: ack-nhfb
rawauthor: A. N. (Aleksandr Nikolaevich) Varchenko
title:
Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups

subject:
Hypergeometric functions; Kac-Moody algebras; Representations of Lie algebras; Representations of quantum groups

TOC:
1. Introduction 2. Construction of complexes calculating homology of the complement of a configuration 3. Construction of homology complexes for discriminantal configuration 4. Algebraic interpretation of chain complexes of a discriminantal configuration 5. Quasiisomorphism of two-sided Hochschild complexes to suitable one-sided Hochschild complexes 6. Bundle properties of a discriminantal configuration 7. R-matrix for the two-sided Hochschild complexes 8. Monodromy 9. R-matrix operator as the canonical element, quantum doubles 10. Hypergeometric integrals 11. Kac--Moody Lie algebras without Serre's relations and their doubles 12. Hypergeometric integrals of a discriminantal configuration 13. Resonances at infinity 14. Degenerations of discriminantal configurations 15. Remarks on homology groups of a configuration with coefficients in local systems more general than complex one-dimensional

rawtitle:
Multidimensional Hypergeometric Functions and Representation Theory of {Lie} Algebras and Quantum Groups

rawTOC:
1. Introduction \\ 2. Construction of complexes calculating homology of the complement of a configuration \\ 3. Construction of homology complexes for discriminantal configuration \\ 4. Algebraic interpretation of chain complexes of a discriminantal configuration \\ 5. Quasiisomorphism of two-sided Hochschild complexes to suitable one-sided Hochschild complexes \\ 6. Bundle properties of a discriminantal configuration \\ 7. R-matrix for the two-sided Hochschild complexes \\ 8. Monodromy \\ 9. R-matrix operator as the canonical element, quantum doubles \\ 10. Hypergeometric integrals \\ 11. Kac--Moody Lie algebras without Serre's relations and their doubles \\ 12. Hypergeometric integrals of a discriminantal configuration \\ 13. Resonances at infinity \\ 14. Degenerations of discriminantal configurations \\ 15. Remarks on homology groups of a configuration with coefficients in local systems more general than complex one-dimensional

entry:
@Book{Varchenko:1995:MHF,
  author =       "A. N. (Aleksandr Nikolaevich) Varchenko",
  title =        "Multidimensional Hypergeometric Functions and
                 Representation Theory of {Lie} Algebras and Quantum
                 Groups",
  volume =       "21",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "ix + 371",
  year =         "1995",
  ISBN =         "981-02-1880-X",
  ISBN-13 =      "978-981-02-1880-5",
  LCCN =         "QA353.H9 V37 1995",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Advanced series in mathematical physics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Kac-Moody algebras;
                 Representations of Lie algebras; Representations of
                 quantum groups",
  tableofcontents = "1. Introduction \\
                 2. Construction of complexes calculating homology of
                 the complement of a configuration \\
                 3. Construction of homology complexes for
                 discriminantal configuration \\
                 4. Algebraic interpretation of chain complexes of a
                 discriminantal configuration \\
                 5. Quasiisomorphism of two-sided Hochschild complexes
                 to suitable one-sided Hochschild complexes \\
                 6. Bundle properties of a discriminantal configuration
                 \\
                 7. R-matrix for the two-sided Hochschild complexes \\
                 8. Monodromy \\
                 9. R-matrix operator as the canonical element, quantum
                 doubles \\
                 10. Hypergeometric integrals \\
                 11. Kac--Moody Lie algebras without Serre's relations
                 and their doubles \\
                 12. Hypergeometric integrals of a discriminantal
                 configuration \\
                 13. Resonances at infinity \\
                 14. Degenerations of discriminantal configurations \\
                 15. Remarks on homology groups of a configuration with
                 coefficients in local systems more general than complex
                 one-dimensional",
}


bibtype: book
filename: elefunt.bib
label: Vilenkin:1995:RLG
author: N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii Ulsianovich) Klimyk
title: Representation of Lie Groups and Special Functions: Recent Advances
volume: 316
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: xvi + 497
year: 1995
ISBN: 0-7923-3210-5 OR 0792332105
ISBN13: 978-0-7923-3210-7 OR 9780792332107
LCCN: QA176 .V55 1995
bibdate: Sat Oct 30 16:43:03 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 16:43:03 MDT
series: Mathematics and its applications
remark: Translated to English from Russian by V. A. Groza and A. A. Groza.
subject: Representations of Lie groups; Functions, Special; Integral transforms
acknowledgement: ack-nhfb
rawauthor: N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii Ulsianovich) Klimyk
rawtitle: Representation of {Lie} Groups and Special Functions: Recent Advances
URL:
http://www.loc.gov/catdir/enhancements/fy0823/95108075-d.html; http://www.loc.gov/catdir/enhancements/fy0823/95108075-t.html

TOC:
Preface / xiii 1. $h$-Harmonic Polynomials, $h$-Hankel Transform, and Coxeter Groups / 1 2. Symmetric Polynomials and Symmetric Functions / 67 3. Hypergeometric Functions Related to Jack Polynomials / 185 4. Clebsch--Gordan Coefficients and Racah Coefficients of Finite Dimensional Representations / 265 5. Clebsch--Gordan Coefficients of the Group $U(n)$ and Related Generalizations of Hypergeometric Functions / 317 6. Gel'fand Hypergeometric Functions / 393 Bibliography / 463 Supplementary Bibliography / 484 Bibliography Notes / 488 Subject Index / 494

rawTOC:
Preface / xiii \\ 1. $h$-Harmonic Polynomials, $h$-Hankel Transform, and Coxeter Groups / 1 \\ 2. Symmetric Polynomials and Symmetric Functions / 67 \\ 3. Hypergeometric Functions Related to Jack Polynomials / 185 \\ 4. Clebsch--Gordan Coefficients and Racah Coefficients of Finite Dimensional Representations / 265 \\ 5. Clebsch--Gordan Coefficients of the Group $U(n)$ and Related Generalizations of Hypergeometric Functions / 317 \\ 6. Gel'fand Hypergeometric Functions / 393 \\ Bibliography / 463 \\ Supplementary Bibliography / 484 \\ Bibliography Notes / 488 \\ Subject Index / 494

entry:
@Book{Vilenkin:1995:RLG,
  author =       "N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii
                 Ulsianovich) Klimyk",
  title =        "Representation of {Lie} Groups and Special Functions:
                 Recent Advances",
  volume =       "316",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xvi + 497",
  year =         "1995",
  ISBN =         "0-7923-3210-5",
  ISBN-13 =      "978-0-7923-3210-7",
  LCCN =         "QA176 .V55 1995",
  bibdate =      "Sat Oct 30 16:43:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematics and its applications",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0823/95108075-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0823/95108075-t.html",
  acknowledgement = ack-nhfb,
  remark =       "Translated to English from Russian by V. A. Groza and
                 A. A. Groza.",
  subject =      "Representations of Lie groups; Functions, Special;
                 Integral transforms",
  tableofcontents = "Preface / xiii \\
                 1. $h$-Harmonic Polynomials, $h$-Hankel Transform, and
                 Coxeter Groups / 1 \\
                 2. Symmetric Polynomials and Symmetric Functions / 67
                 \\
                 3. Hypergeometric Functions Related to Jack Polynomials
                 / 185 \\
                 4. Clebsch--Gordan Coefficients and Racah Coefficients
                 of Finite Dimensional Representations / 265 \\
                 5. Clebsch--Gordan Coefficients of the Group $U(n)$ and
                 Related Generalizations of Hypergeometric Functions /
                 317 \\
                 6. Gel'fand Hypergeometric Functions / 393 \\
                 Bibliography / 463 \\
                 Supplementary Bibliography / 484 \\
                 Bibliography Notes / 488 \\
                 Subject Index / 494",
}


bibtype: article
filename: elefunt.bib
label: Vrahatis:1995:RPP
author: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
journal: j-COMP-PHYS-COMM
volume: 92
number: 2--3
pages: 252--266
month: dec
monthnumber: 12
year: 1995
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(95)00115-9
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:01 MST 2012
bibtimestamp: 2012.02.13 21:30:01 MST
note: See erratum cite Vrahatis:1999:ESP.
URL: http://www.sciencedirect.com/science/article/pii/0010465595001159
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
rawnote: See erratum \cite{Vrahatis:1999:ESP}.
title:
RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions

rawtitle:
{RFSFNS}: a portable package for the numerical determination of the number and the calculation of roots of {Bessel} functions

entry:
@Article{Vrahatis:1995:RPP,
  author =       "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
                 Zafiropoulos and T. N. Grapsa",
  title =        "{RFSFNS}: a portable package for the numerical
                 determination of the number and the calculation of
                 roots of {Bessel} functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "92",
  number =       "2--3",
  pages =        "252--266",
  month =        dec,
  year =         "1995",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(95)00115-9",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:01 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Vrahatis:1999:ESP}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465595001159",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Watson:1995:TTB
author: G. N. (George Neville) Watson
title: A Treatise on the Theory of Bessel Functions
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
edition: Second
pages: vi + 804
year: 1995
LCCN: QA408 .W2 1995
bibdate: Sat Apr 19 09:15:26 MDT 2008
bibtimestamp: 2008.04.19 09:15:26 MDT
series: Cambridge mathematical library
remark: First published 1922. Second edition 1944. Reprinted 1966.
subject: Bessel functions
acknowledgement: ack-nhfb
rawauthor: G. N. (George Neville) Watson
rawtitle: A Treatise on the Theory of {Bessel} Functions
ISBN:
0-521-48391-3 (paperback), 0-521-06743-X (hardcover) OR 0521483913 (paperback), 052106743X (hardcover)

ISBN13:
978-0-521-48391-9 (paperback), 978-0-521-06743-0 (hardcover) OR 9780521483919 (paperback), 9780521067430 (hardcover)

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

URL:
http://www.loc.gov/catdir/description/cam028/96139881.html; http://www.loc.gov/catdir/toc/cam029/96139881.html

TOC:
1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices

rawTOC:
1. Bessel functions before 1826 \\ 2. The Bessel coefficients \\ 3. Bessel functions \\ 4. Differential equations \\ 5. Miscellaneous properties of Bessel functions \\ 6. Integral representations of Bessel functions \\ 7. Asymptotic expansions of Bessel functions \\ 8. Bessel functions of large order \\ 9. Polynomials associated with Bessel functions \\ 10. Functions associated with Bessel functions \\ 11. Addition theorems \\ 12. Definite integrals \\ 13. Infinitive integrals \\ 14. Multiple integrals \\ 15. The zeros of Bessel functions \\ 16. Neumann series and Lommel's functions of two variables \\ 17. Kapteyn series \\ 18. Series of Fourier-Bessel and Dini \\ 19. Schl{\"o}mlich series \\ 20. The tabulation of Bessel functions \\ Tables of Bessel functions \\ Bibliography \\ Indices

entry:
@Book{Watson:1995:TTB,
  author =       "G. N. (George Neville) Watson",
  title =        "A Treatise on the Theory of {Bessel} Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "vi + 804",
  year =         "1995",
  ISBN =         "0-521-48391-3 (paperback), 0-521-06743-X (hardcover)",
  ISBN-13 =      "978-0-521-48391-9 (paperback), 978-0-521-06743-0
                 (hardcover)",
  LCCN =         "QA408 .W2 1995",
  bibdate =      "Sat Apr 19 09:15:26 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge mathematical library",
  URL =          "http://www.loc.gov/catdir/description/cam028/96139881.html;
                 http://www.loc.gov/catdir/toc/cam029/96139881.html",
  acknowledgement = ack-nhfb,
  remark =       "First published 1922. Second edition 1944. Reprinted
                 1966.",
  subject =      "Bessel functions",
  tableofcontents = "1. Bessel functions before 1826 \\
                 2. The Bessel coefficients \\
                 3. Bessel functions \\
                 4. Differential equations \\
                 5. Miscellaneous properties of Bessel functions \\
                 6. Integral representations of Bessel functions \\
                 7. Asymptotic expansions of Bessel functions \\
                 8. Bessel functions of large order \\
                 9. Polynomials associated with Bessel functions \\
                 10. Functions associated with Bessel functions \\
                 11. Addition theorems \\
                 12. Definite integrals \\
                 13. Infinitive integrals \\
                 14. Multiple integrals \\
                 15. The zeros of Bessel functions \\
                 16. Neumann series and Lommel's functions of two
                 variables \\
                 17. Kapteyn series \\
                 18. Series of Fourier-Bessel and Dini \\
                 19. Schl{\"o}mlich series \\
                 20. The tabulation of Bessel functions \\
                 Tables of Bessel functions \\
                 Bibliography \\
                 Indices",
  xxauthor =     "G. N. Watson",
}


bibtype: article
filename: elefunt.bib
label: Wong:1995:EHS
author: W. F. Wong and Yoshio Oyanagi and Eiichi Goto
title: Evaluation of the Hitachi S-3800 Supercomputer Using Six Benchmarks
journal: j-IJSAHPC
volume: 9
number: 1
pages: 58--70
month: Spring
year: 1995
CODEN: IJSAE9
ISSN: 0890-2720 OR 08902720
bibdate: Tue Feb 18 09:07:32 MST 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.02.18 09:07:32 MST
fjournal: International Journal of Supercomputer Applications and High Performance Computing
acknowledgement: ack-nhfb
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore
affiliationaddress: Singapore
journalURL: http://hpc.sagepub.com/content/by/year
journalabr: Int J Supercomput Appl High Perform Comput
rawauthor: W. F. Wong and Yoshio Oyanagi and Eiichi Goto
rawtitle: Evaluation of the {Hitachi S-3800} Supercomputer Using Six Benchmarks
abstract:
The S-3000 series is the third generation of Hitachi's supercomputers. It is claimed to be currently the fastest single processor supercomputer. In this paper, we introduce the S-3000 and, using six benchmarks we designed, evaluate a member of this series of supercomputer, the top of the range S-3800, against its predecessor, the Hitachi HITAC S-820. Our purpose is to determine in what areas the S-3800 is an improvement over its predecessor. The suite of benchmarks include kernels for random number generation, elementary function computation, FFT, dense matrix operations, SOR, and list vector (scatter / gather) operations. The use of small-to medium-sized kernels, as opposed to large application benchmarks, help to better understand the behavior of the machine. Our findings support the claim that the S-3000 series is at least twice as fast as the previous generation of Hitachi supercomputers.

keywords:
Benchmarks; Computer selection and evaluation; Computer testing; Fast Fourier transforms; Fastest single processor; Hitachi supercomputer; Matrix algebra; Medium sized kernels; Performance; Random number generation; Supercomputers; Vectors

rawabstract:
The S-3000 series is the third generation of Hitachi's supercomputers. It is claimed to be currently the fastest single processor supercomputer. In this paper, we introduce the S-3000 and, using six benchmarks we designed, evaluate a member of this series of supercomputer, the top of the range S-3800, against its predecessor, the Hitachi HITAC S-820. Our purpose is to determine in what areas the S-3800 is an improvement over its predecessor. The suite of benchmarks include kernels for random number generation, elementary function computation, FFT, dense matrix operations, SOR, and list vector (scatter\slash gather) operations. The use of small-to medium-sized kernels, as opposed to large application benchmarks, help to better understand the behavior of the machine. Our findings support the claim that the S-3000 series is at least twice as fast as the previous generation of Hitachi supercomputers.

entry:
@Article{Wong:1995:EHS,
  author =       "W. F. Wong and Yoshio Oyanagi and Eiichi Goto",
  title =        "Evaluation of the {Hitachi S-3800} Supercomputer Using
                 Six Benchmarks",
  journal =      j-IJSAHPC,
  volume =       "9",
  number =       "1",
  pages =        "58--70",
  month =        "Spring",
  year =         "1995",
  CODEN =        "IJSAE9",
  ISSN =         "0890-2720",
  bibdate =      "Tue Feb 18 09:07:32 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The S-3000 series is the third generation of Hitachi's
                 supercomputers. It is claimed to be currently the
                 fastest single processor supercomputer. In this paper,
                 we introduce the S-3000 and, using six benchmarks we
                 designed, evaluate a member of this series of
                 supercomputer, the top of the range S-3800, against its
                 predecessor, the Hitachi HITAC S-820. Our purpose is to
                 determine in what areas the S-3800 is an improvement
                 over its predecessor. The suite of benchmarks include
                 kernels for random number generation, elementary
                 function computation, FFT, dense matrix operations,
                 SOR, and list vector (scatter\slash gather) operations.
                 The use of small-to medium-sized kernels, as opposed to
                 large application benchmarks, help to better understand
                 the behavior of the machine. Our findings support the
                 claim that the S-3000 series is at least twice as fast
                 as the previous generation of Hitachi supercomputers.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore",
  affiliationaddress = "Singapore",
  classification = "722.4; 921.3; 921.6; 922.2",
  fjournal =     "International Journal of Supercomputer Applications
                 and High Performance Computing",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
  journalabr =   "Int J Supercomput Appl High Perform Comput",
  keywords =     "Benchmarks; Computer selection and evaluation;
                 Computer testing; Fast Fourier transforms; Fastest
                 single processor; Hitachi supercomputer; Matrix
                 algebra; Medium sized kernels; Performance; Random
                 number generation; Supercomputers; Vectors",
}


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

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

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

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


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

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

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

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

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


bibtype: article
filename: elefunt.bib
label: Zhang:1995:TMAa
author: J. Zhang and J. A. Belward
title: Tau-method approximations for the Bessel function $ Y_0 (z) $
journal: j-COMPUT-MATH-APPL
volume: 30
number: 7
pages: 5--14
month: oct
monthnumber: 10
year: 1995
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(95)00120-N
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sun Jun 12 08:33:42 2011
bibtimestamp: 2011.06.12 08:33:42 ???
URL: http://www.sciencedirect.com/science/article/pii/089812219500120N
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. Zhang and J. A. Belward
rawtitle: Tau-method approximations for the {Bessel} function {$ Y_0 (z) $}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Zhang:1995:TMAa,
  author =       "J. Zhang and J. A. Belward",
  title =        "Tau-method approximations for the {Bessel} function {$
                 Y_0 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "7",
  pages =        "5--14",
  month =        oct,
  year =         "1995",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(95)00120-N",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 08:33:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500120N",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1995:TMAb
author: J. Zhang
title: Tau-method approximations for the Bessel function $ Y_1 (z) $
journal: j-COMPUT-MATH-APPL
volume: 30
number: 7
pages: 15--19
month: oct
monthnumber: 10
year: 1995
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(95)00121-E
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sun Jun 12 09:26:01 2011
bibtimestamp: 2011.06.12 09:26:01 ???
URL: http://www.sciencedirect.com/science/article/pii/089812219500121E
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. Zhang
rawtitle: Tau-method approximations for the {Bessel} function {$ Y_1 (z) $}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
From p. 18 (conclusions section), ``We may use this method to approximate the Bessel functions of other integer orders. ldots It is therefore advisable to use the recurrence relations of the Bessel functions to compute function values for $ n > 1 $ ldots ''. [This is a similar limitation as with Chebyshev and minimax polynomial approximations: they are valid only for a single order the Bessel function.]

entry:
@Article{Zhang:1995:TMAb,
  author =       "J. Zhang",
  title =        "Tau-method approximations for the {Bessel} function {$
                 Y_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "7",
  pages =        "15--19",
  month =        oct,
  year =         "1995",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(95)00121-E",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 09:26:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500121E",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From p. 18 (conclusions section), ``We may use this
                 method to approximate the Bessel functions of other
                 integer orders. \ldots{} It is therefore advisable to
                 use the recurrence relations of the Bessel functions to
                 compute function values for $ n > 1 $ \ldots''. [This
                 is a similar limitation as with Chebyshev and minimax
                 polynomial approximations: they are valid only for a
                 single order the Bessel function.]",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ahrendt:1996:FHC
author: Timm Ahrendt
title: Fast High-Precision Computations of Complex Square Roots
crossref: LakshmanYN:1996:IPI
pages: 142--149
year: 1996
bibdate: Thu Mar 12 08:43:16 MST 1998
bibtimestamp: 1998.03.12 08:43:16 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/
keywords: algebraic computation; algorithms; ISSAC; measurement; SIGNUM; SIGSAM; symbolic computation
acknowledgement: ack-nhfb
rawauthor: Timm Ahrendt
rawtitle: Fast High-Precision Computations of Complex Square Roots
bibsource:
http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

subject:
bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf F.1.1 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Models of Computation, Bounded-action devices. bf G.1.5 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. bf G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.

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


bibtype: article
filename: elefunt.bib
label: Balla:1996:SCB
author: K. Balla and V. H. Linh
title: The simultaneous computation of Bessel functions of first and second kind
journal: j-COMPUT-MATH-APPL
volume: 31
number: 4--5
pages: 87--97
month: feb
monthnumber: 2
year: 1996
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:26 MST 2017
bibtimestamp: 2017.03.01 21:48:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122195002200
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: K. Balla and V. H. Linh
rawtitle: The simultaneous computation of {Bessel} functions of first and second kind
entry:
@Article{Balla:1996:SCB,
  author =       "K. Balla and V. H. Linh",
  title =        "The simultaneous computation of {Bessel} functions of
                 first and second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "31",
  number =       "4--5",
  pages =        "87--97",
  month =        feb # "\slash " # mar,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:26 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122195002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


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


bibtype: article
filename: elefunt.bib
label: Chaudhry:1996:ACF
author: M. A. Chaudhry and N. M. Temme and E. J. M. Veling
title: Asymptotics and closed form of a generalized incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 67
number: 2
pages: 371--379
day: 29
month: mar
monthnumber: 3
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795000186
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. A. Chaudhry and N. M. Temme and E. J. M. Veling
rawtitle: Asymptotics and closed form of a generalized incomplete gamma function
entry:
@Article{Chaudhry:1996:ACF,
  author =       "M. A. Chaudhry and N. M. Temme and E. J. M. Veling",
  title =        "Asymptotics and closed form of a generalized
                 incomplete gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "2",
  pages =        "371--379",
  day =          "29",
  month =        mar,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795000186",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


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


bibtype: article
filename: elefunt.bib
label: Heinrich:1996:AAF
author: Peter Heinrich
title: Algorithm Alley: a Fast Integer Square Root
journal: j-DDJ
volume: 21
number: 4
pages: 113--114, 130
month: apr
monthnumber: 4
year: 1996
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Peter Heinrich
rawtitle: Algorithm Alley: a Fast Integer Square Root
bibsource:
http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Heinrich:1996:AAF,
  author =       "Peter Heinrich",
  title =        "Algorithm Alley: a Fast Integer Square Root",
  journal =      j-DDJ,
  volume =       "21",
  number =       "4",
  pages =        "113--114, 130",
  month =        apr,
  year =         "1996",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: techreport
filename: elefunt.bib
label: Hickey:1996:FSP
author: Timothy J. Hickey and Qun Ju
title: Fast, Sound, and Precise Narrowing of the Exponential Function
type: Technical report
institution: Computer Science Department, Brandeis University
address: Waltham, MA, USA 02254
pages: 113--114, 130
month: mar
monthnumber: 3
year: 1996
bibdate: Sat Nov 05 15:42:23 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.11.05 15:42:23 ???
URL: http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz
acknowledgement: ack-nhfb
rawauthor: Timothy J. Hickey and Qun Ju
rawtitle: Fast, Sound, and Precise Narrowing of the Exponential Function
entry:
@TechReport{Hickey:1996:FSP,
  author =       "Timothy J. Hickey and Qun Ju",
  title =        "Fast, Sound, and Precise Narrowing of the Exponential
                 Function",
  type =         "Technical report",
  institution =  "Computer Science Department, Brandeis University",
  address =      "Waltham, MA, USA 02254",
  month =        mar,
  year =         "1996",
  bibdate =      "Sat Nov 05 15:42:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Homeier:1996:CAI
author: H. H. H. Homeier
title: On Convergence Acceleration for the Iterative Solution of the Inverse Dyson Equation
journal: j-J-MOL-STRUCT-THEOCHEM
volume: 368
pages: 81--91
year: 1996
CODEN: THEODJ
ISSN: 0166-1280 (print), 1872-7999 (electronic) OR 01661280 (print), 18727999 (electronic)
ISSNL: 0166-1280 OR 01661280
note: Proceedings of the 2nd Electronic Computational Chemistry Conference.
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954
fjournal: Journal of molecular structure. Theochem
keywords: convergence acceleration
journalURL: http://www.sciencedirect.com/science/journal/01661280
rawauthor: H. H. H. Homeier
rawnote: Proceedings of the 2nd {Electronic Computational Chemistry Conference}.
rawtitle: On Convergence Acceleration for the Iterative Solution of the Inverse {Dyson} Equation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Homeier:1996:CAI,
  author =       "H. H. H. Homeier",
  title =        "On Convergence Acceleration for the Iterative Solution
                 of the Inverse {Dyson} Equation",
  journal =      j-J-MOL-STRUCT-THEOCHEM,
  volume =       "368",
  pages =        "81--91",
  year =         "1996",
  CODEN =        "THEODJ",
  ISSN =         "0166-1280 (print), 1872-7999 (electronic)",
  ISSN-L =       "0166-1280",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 2nd {Electronic Computational
                 Chemistry Conference}.",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954",
  fjournal =     "Journal of molecular structure. Theochem",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01661280",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-QM-95-4, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1995",
}


bibtype: techreport
filename: elefunt.bib
label: Homeier:1996:KMP
author: H. H. H. Homeier
number: Homeier:1996:KMP
institution: inst-IPTC
address: inst-IPTC:adr
pages: 81--91
year: 1996
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962
keywords: convergence acceleration
rawauthor: H. H. H. Homeier
title:
Zur Konvergenzverbesserung der Moller--Plesset Storungsreihe (English: On Convergence Acceleration of the Moller--Plesset Perturbation Series)

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

note:
Poster CP 14.77, Fruhjahrstagung des Arbeitskreises Festkorperphysik bei der DPG, Regensburg 1996. Abstract: Verhandl. DPG (VI) 31, 2165-2166 (1996).

rawnote:
Poster CP 14.77, {Fr{\"u}hjahrstagung des Arbeitskreises Festk{\"o}rperphysik bei der DPG, Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31, 2165-2166 (1996).

rawtitle:
{Zur Konvergenzverbesserung der M{\o}ller--Plesset St{\"o}rungsreihe} ({English}: {On} Convergence Acceleration of the {M{\o}ller--Plesset} Perturbation Series)

entry:
@TechReport{Homeier:1996:KMP,
  author =       "H. H. H. Homeier",
  title =        "{Zur Konvergenzverbesserung der M{\o}ller--Plesset
                 St{\"o}rungsreihe} ({English}: {On} Convergence
                 Acceleration of the {M{\o}ller--Plesset} Perturbation
                 Series)",
  number =       "Homeier:1996:KMP",
  institution =  inst-IPTC,
  address =      inst-IPTC:adr,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Poster CP 14.77, {Fr{\"u}hjahrstagung des
                 Arbeitskreises Festk{\"o}rperphysik bei der DPG,
                 Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31,
                 2165-2166 (1996).",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Ito:1996:SRI
author: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
title: Square rooting by iterative multiply-additions
journal: j-INFO-PROC-LETT
volume: 60
number: 5
pages: 267--269
day: 8
month: dec
monthnumber: 12
year: 1996
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07
MRnumber: 97i:68014
bibdate: Wed Nov 11 12:16:26 MST 1998
bibtimestamp: 1998.11.11 12:16:26 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
corpsource: Dept. of Inf. Sci., Kyoto Univ., Japan
journalURL: http://www.sciencedirect.com/science/journal/00200190
treatment: T Theoretical or Mathematical
rawauthor: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
rawtitle: Square rooting by iterative multiply-additions
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
computer arithmetic; convergence of numerical methods; digital arithmetic; iterative methods; iterative multiply-additions; linear converging ratio; multiplicative methods; Newton--Raphson method; read-only storage; ROM sizes; square root algorithm

entry:
@Article{Ito:1996:SRI,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Square rooting by iterative multiply-additions",
  journal =      j-INFO-PROC-LETT,
  volume =       "60",
  number =       "5",
  pages =        "267--269",
  day =          "8",
  month =        dec,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07",
  MRnumber =     "97i:68014",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Dept. of Inf. Sci., Kyoto Univ., Japan",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computer arithmetic; convergence of numerical methods;
                 digital arithmetic; iterative methods; iterative
                 multiply-additions; linear converging ratio;
                 multiplicative methods; Newton--Raphson method;
                 read-only storage; ROM sizes; square root algorithm",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Jeffrey:1996:UBL
author: D. J. Jeffrey and D. E. G. Hare and Robert M. Corless
title: Unwinding the branches of the Lambert $W$ function
journal: j-MATH-SCI
volume: 21
number: 1
pages: 1--7
month: jun
monthnumber: 6
year: 1996
ISSN: 0312-3685 (print), 1475-6080 (electronic) OR 03123685 (print), 14756080 (electronic)
ISSNL: 0312-3685 OR 03123685
bibdate: Sat Oct 06 09:02:19 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.10.06 09:02:19 ???
URL: http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf
fjournal: The Mathematical Scientist
acknowledgement: ack-nhfb
journalURL: http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues
rawauthor: D. J. Jeffrey and D. E. G. Hare and Robert M. Corless
rawtitle: Unwinding the branches of the {Lambert $W$} function
entry:
@Article{Jeffrey:1996:UBL,
  author =       "D. J. Jeffrey and D. E. G. Hare and Robert M.
                 Corless",
  title =        "Unwinding the branches of the {Lambert $W$} function",
  journal =      j-MATH-SCI,
  volume =       "21",
  number =       "1",
  pages =        "1--7",
  month =        jun,
  year =         "1996",
  ISSN =         "0312-3685 (print), 1475-6080 (electronic)",
  ISSN-L =       "0312-3685",
  bibdate =      "Sat Oct 06 09:02:19 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Scientist",
  journal-URL =  "http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues",
}


bibtype: unpublished
filename: elefunt.bib
label: Kahan:1996:TCR
author: W. Kahan
title: A Test for Correctly Rounded SQRT
pages: 4
year: 1996
bibdate: Mon Apr 25 05:47:38 2005
bibtimestamp: 2005.04.25 05:47:38 ???
note: Lecture notes.
URL: http://www.cs.berkeley.edu/~wkahan/SQRTest.ps
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Lecture notes.
rawtitle: A Test for Correctly Rounded {SQRT}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Unpublished{Kahan:1996:TCR,
  author =       "W. Kahan",
  title =        "A Test for Correctly Rounded {SQRT}",
  pages =        "4",
  year =         "1996",
  bibdate =      "Mon Apr 25 05:47:38 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Lecture notes.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SQRTest.ps",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: elefunt.bib
label: Kalantari:1996:HOI
author: B. Kalantari and I. Kalantari
title: High order iterative methods for approximating square roots
journal: j-BIT-NUM-MATH
volume: 36
number: 2
pages: 395--399
month: jun
monthnumber: 6
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01731991
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D15 (65H99)
MRnumber: 97k:65039
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: B. Kalantari and I. Kalantari
rawtitle: High order iterative methods for approximating square roots
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395

entry:
@Article{Kalantari:1996:HOI,
  author =       "B. Kalantari and I. Kalantari",
  title =        "High order iterative methods for approximating square
                 roots",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "395--399",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731991",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D15 (65H99)",
  MRnumber =     "97k:65039",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Kantabutra:1996:HCE
author: V. Kantabutra
title: On hardware for computing exponential and trigonometric functions
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 328--339
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485571
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. Kantabutra
rawtitle: On hardware for computing exponential and trigonometric functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Kantabutra:1996:HCE,
  author =       "V. Kantabutra",
  title =        "On hardware for computing exponential and
                 trigonometric functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "328--339",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485571",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571",
  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: elefunt.bib
label: Kolbig:1996:PF
author: K. S. Kolbig
title: The polygamma function $ psi ^(k)(x) $ for $ x = 1 / 4 $ and $ x = 3 / 4 $
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 1
pages: 43--46
day: 12
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(96)00055-6
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000556
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: K. S. K{\"o}lbig
rawtitle: The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 / 4 $ and $ x = 3 / 4 $
entry:
@Article{Kolbig:1996:PF,
  author =       "K. S. K{\"o}lbig",
  title =        "The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 /
                 4 $ and $ x = 3 / 4 $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "1",
  pages =        "43--46",
  day =          "12",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(96)00055-6",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000556",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lang:1996:BPU
author: T. Lang and R. Wong
journal: j-J-COMPUT-APPL-MATH
volume: 71
number: 2
pages: 311--329
day: 27
month: jul
monthnumber: 7
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:56 MST 2017
bibtimestamp: 2017.02.25 12:35:56 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795002200
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: T. Lang and R. Wong
title:
``Best possible'' upper bounds for the first two positive zeros of the Bessel function $ J_v(x) $: the infinite case

rawtitle:
``{Best} possible'' upper bounds for the first two positive zeros of the {Bessel} function {$ J_v(x) $}: the infinite case

entry:
@Article{Lang:1996:BPU,
  author =       "T. Lang and R. Wong",
  title =        "``{Best} possible'' upper bounds for the first two
                 positive zeros of the {Bessel} function {$ J_v(x) $}:
                 the infinite case",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "71",
  number =       "2",
  pages =        "311--329",
  day =          "27",
  month =        jul,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lehoucq:1996:CEU
author: R. B. Lehoucq
title: The Computation of Elementary Unitary Matrices
journal: j-TOMS
volume: 22
number: 4
pages: 393--400
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: R. B. Lehoucq
rawtitle: The Computation of Elementary Unitary Matrices
abstract:
The construction of elementary unitary matrices that transform a complex vector to a multiple of $ e_1 $, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the LAPACK subroutine CLARFG. Comparisons are also given.

subject:
bf F.2: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. bf G.1.3: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
The construction of elementary unitary matrices that transform a complex vector to a multiple of $ e_1 $, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the {LAPACK} subroutine {CLARFG}. Comparisons are also given.

entry:
@Article{Lehoucq:1996:CEU,
  author =       "R. B. Lehoucq",
  title =        "The Computation of Elementary Unitary Matrices",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "393--400",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The construction of elementary unitary matrices that
                 transform a complex vector to a multiple of $ e_1 $,
                 the first column of the identity matrix, is studied. We
                 present four variants and their software
                 implementation, including a discussion on the {LAPACK}
                 subroutine {CLARFG}. Comparisons are also given.",
  accepted =     "June 1996",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}


bibtype: article
filename: elefunt.bib
label: Lether:1996:RAF
author: Frank G. Lether
title: Rational approximation formulas for computing the positive zeros of $ J_0 (x) $
journal: j-J-COMPUT-APPL-MATH
volume: 67
number: 1
pages: 167--172
day: 20
month: feb
monthnumber: 2
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795002197
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Frank G. Lether
rawtitle: Rational approximation formulas for computing the positive zeros of {$ J_0 (x) $}
entry:
@Article{Lether:1996:RAF,
  author =       "Frank G. Lether",
  title =        "Rational approximation formulas for computing the
                 positive zeros of {$ J_0 (x) $}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "1",
  pages =        "167--172",
  day =          "20",
  month =        feb,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002197",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Li:1996:NNR
author: Yamin Li and Wanming Chu
title: A new non-restoring square root algorithm and its VLSI implementations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 538--544
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Yamin Li and Wanming Chu
rawtitle: A new non-restoring square root algorithm and its {VLSI} implementations
booktitle:
Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '96

rawbooktitle:
Proceedings of the {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '96}

entry:
@InProceedings{Li:1996:NNR,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD '96}",
  title =        "A new non-restoring square root algorithm and its
                 {VLSI} implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "538--544",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a new non-restoring square root algorithm
                 that is very efficient to implement. The new algorithm
                 presented here has the following features unlike other
                 square root algorithms. First, the focus of the
                 ``non-restoring'' is on the {\&} \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lorch:1996:BPU
author: Lee Lorch and Riccardo Uberti
title: ``Best possible'' upper bounds for the first positive zeros of Bessel functions --- the finite part
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 2
pages: 249--258
day: 28
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000659
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Lee Lorch and Riccardo Uberti
rawtitle:
``{Best} possible'' upper bounds for the first positive zeros of {Bessel} functions --- the finite part

entry:
@Article{Lorch:1996:BPU,
  author =       "Lee Lorch and Riccardo Uberti",
  title =        "``{Best} possible'' upper bounds for the first
                 positive zeros of {Bessel} functions --- the finite
                 part",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "2",
  pages =        "249--258",
  day =          "28",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000659",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1996:PST
author: Daniel W. Lozier
title: A Proposed Software Test Service for Special Functions
type: Technical Report
number: NISTIR 5916
institution: pub-NIST
address: pub-NIST:adr
pages: 11
month: oct
monthnumber: 10
year: 1996
bibdate: Fri Jul 09 06:02:16 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:02:16 ???
note: Published in cite Lozier:1997:PST.
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawnote: Published in \cite{Lozier:1997:PST}.
rawtitle: A Proposed Software Test Service for Special Functions
entry:
@TechReport{Lozier:1996:PST,
  author =       "Daniel W. Lozier",
  title =        "A Proposed Software Test Service for Special
                 Functions",
  type =         "Technical Report",
  number =       "NISTIR 5916",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "11",
  month =        oct,
  year =         "1996",
  bibdate =      "Fri Jul 09 06:02:16 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Lozier:1997:PST}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Lozier:1996:SNS
author: Daniel W. Lozier
title: Software Needs in Special Functions
journal: j-J-COMPUT-APPL-MATH
volume: 66
pages: 345--358
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Fri Jul 09 05:51:55 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 05:51:55 ???
fjournal: Journal of Computational and Applied Mathematics
remark: See preprint cite Lozier:1994:SNS.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Daniel W. Lozier
rawtitle: Software Needs in Special Functions
entry:
@Article{Lozier:1996:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "66",
  number =       "??",
  pages =        "345--358",
  month =        "????",
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Jul 09 05:51:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "See preprint \cite{Lozier:1994:SNS}.",
}


bibtype: article
filename: elefunt.bib
label: Macleod:1996:AMS
author: Allan J. Macleod
title: Algorithm 757: MISCFUN, a software package to compute uncommon special functions
journal: j-TOMS
volume: 22
number: 3
pages: 288--301
month: sep
monthnumber: 9
year: 1996
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 31 16:07:02 MDT 1996
bibtimestamp: 1996.08.31 16:07:02 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Allan J. Macleod
rawtitle: {Algorithm 757}: {MISCFUN}, a software package to compute uncommon special functions
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

URL:
http://doi.acm.org/10.1145/232826.232846; http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/

abstract:
MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.

subject:
bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.

rawabstract:
MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.

entry:
@Article{Macleod:1996:AMS,
  author =       "Allan J. Macleod",
  title =        "{Algorithm 757}: {MISCFUN}, a software package to
                 compute uncommon special functions",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "288--301",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/232826.232846;
                 http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/",
  abstract =     "MISCFUN (MISCellaneous FUNctions) is a Fortran package
                 for the evaluation of several special functions, which
                 are not used often enough to have been included in the
                 standard libraries or packages. The package uses
                 Chebyshev expansions as the underlying method of
                 approximation, with the Chebyshev coefficients given to
                 20D. A wide variety of functions are included, and the
                 package is designed so that other functions can be
                 added in a standard manner.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Certification and
                 testing.",
}


bibtype: article
filename: elefunt.bib
label: Oleksy:1996:CAM
author: Cz. Oleksy
title: A convergence acceleration method of Fourier series
journal: j-COMP-PHYS-COMM
volume: 96
number: 1
pages: 17--26
year: 1996
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(96)00044-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
MRclass: 65B05
MRnumber: 1396682 (97c:65012)
bibdate: Thu Dec 1 17:36:45 2011
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Computer Physics Communications
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Cz. Oleksy
rawtitle: A convergence acceleration method of {Fourier} series
entry:
@Article{Oleksy:1996:CAM,
  author =       "Cz. Oleksy",
  title =        "A convergence acceleration method of {Fourier}
                 series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "96",
  number =       "1",
  pages =        "17--26",
  year =         "1996",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(96)00044-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65B05",
  MRnumber =     "1396682 (97c:65012)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Panteliou:1996:DII
author: S. D. Panteliou and A. D. Dimarogonas and I. N. Katz
journal: j-COMPUT-MATH-APPL
volume: 32
number: 8
pages: 51--57
month: oct
monthnumber: 10
year: 1996
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:33 MST 2017
bibtimestamp: 2017.03.01 21:48:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122196001666
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S. D. Panteliou and A. D. Dimarogonas and I. N. Katz
title:
Direct and inverse interpolation for Jacobian elliptic functions, zeta function of Jacobi and complete elliptic integrals of the second kind

rawtitle:
Direct and inverse interpolation for {Jacobian} elliptic functions, zeta function of {Jacobi} and complete elliptic integrals of the second kind

entry:
@Article{Panteliou:1996:DII,
  author =       "S. D. Panteliou and A. D. Dimarogonas and I. N. Katz",
  title =        "Direct and inverse interpolation for {Jacobian}
                 elliptic functions, zeta function of {Jacobi} and
                 complete elliptic integrals of the second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "32",
  number =       "8",
  pages =        "51--57",
  month =        oct,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122196001666",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


