%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "3.22",
%%%     date            = "27 March 2009",
%%%     time            = "07:55:14 MST",
%%%     filename        = "elefunt.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "39110 18847 83023 790157",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "BibTeX; bibliography; elementary functions;
%%%                        special functions",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications about
%%%                        the computation of the elementary functions
%%%                        (square root, exponential, logarithm,
%%%                        trigonometric, inverse trigonometric,
%%%                        hyperbolic, inverse hyperbolic, ...), and
%%%                        some selected special functions (Bessel,
%%%                        exponential integral, Gamma, log-Gamma, psi,
%%%                        ...) , in computer programming languages.
%%%
%%%                        At version 3.22, the year coverage looked
%%%                        like this:
%%%
%%%                             1925 (   1)    1954 (   2)    1983 (  20)
%%%                             1926 (   0)    1955 (   1)    1984 (  13)
%%%                             1927 (   0)    1956 (   0)    1985 (  15)
%%%                             1928 (   0)    1957 (   4)    1986 (  17)
%%%                             1929 (   0)    1958 (   4)    1987 (  24)
%%%                             1930 (   0)    1959 (   6)    1988 (  35)
%%%                             1931 (   0)    1960 (   9)    1989 (  62)
%%%                             1932 (   0)    1961 (   5)    1990 (  16)
%%%                             1933 (   0)    1962 (   0)    1991 (  27)
%%%                             1934 (   0)    1963 (   5)    1992 (  17)
%%%                             1935 (   0)    1964 (   5)    1993 (  22)
%%%                             1936 (   0)    1965 (   5)    1994 (  29)
%%%                             1937 (   0)    1966 (   7)    1995 (  22)
%%%                             1938 (   0)    1967 (   3)    1996 (  12)
%%%                             1939 (   0)    1968 (   7)    1997 (  16)
%%%                             1940 (   0)    1969 (   8)    1998 (   7)
%%%                             1941 (   0)    1970 (   5)    1999 (  31)
%%%                             1942 (   0)    1971 (  15)    2000 (  23)
%%%                             1943 (   1)    1972 (  15)    2001 (  17)
%%%                             1944 (   2)    1973 (   9)    2002 (   8)
%%%                             1945 (   2)    1974 (   8)    2003 (  12)
%%%                             1946 (   1)    1975 (  11)    2004 (  20)
%%%                             1947 (   0)    1976 (  11)    2005 (  13)
%%%                             1948 (   1)    1977 (   6)    2006 (   7)
%%%                             1949 (   0)    1978 (  13)    2007 (   6)
%%%                             1950 (   0)    1979 (  13)    2008 (   1)
%%%                             1951 (   3)    1980 (  11)    2009 (   2)
%%%                             1952 (   3)    1981 (  15)
%%%                             1953 (   1)    1982 (  27)
%%%
%%%                             Article:        459
%%%                             Book:            39
%%%                             InBook:           1
%%%                             InCollection:    19
%%%                             InProceedings:  118
%%%                             Manual:           1
%%%                             MastersThesis:    3
%%%                             Misc:             3
%%%                             PhdThesis:       13
%%%                             Proceedings:     43
%%%                             TechReport:      39
%%%                             Unpublished:      1
%%%
%%%                             Total entries:  739
%%%
%%%                        This bibliography has been collected from
%%%                        bibliographies in the author's personal
%%%                        files, from the OCLC WorldCat and
%%%                        Contents1st databases, from the American
%%%                        Mathematical Society MathSciNet database,
%%%                        from the ACM Computing Archive CD-ROM,
%%%                        and from the computer science bibliography
%%%                        collection on ftp.ira.uka.de in
%%%                        /pub/bibliography to which many people of
%%%                        have contributed.
%%%
%%%                        Numerous errors in the sources noted above
%%%                        have been corrected.  Spelling has been
%%%                        verified with the UNIX spell and GNU ispell
%%%                        programs using the exception dictionary
%%%                        stored in the companion file with extension
%%%                        .sok.
%%%
%%%                        BibTeX citation tags are uniformly chosen as
%%%                        name:year:abbrev, where name is the family
%%%                        name of the first author or editor, year is a
%%%                        4-digit number, and abbrev is a 3-letter
%%%                        condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed for the
%%%                        BibNet Project.
%%%
%%%                        This bibliography is sorted by year, and
%%%                        within each year, by author and title key,
%%%                        using ``bibsort -byyear''.  Cross-referenced
%%%                        proceedings entries appear at the end,
%%%                        because of a restriction in the current
%%%                        BibTeX.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

%%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here.
%%% The more conventional undelimited form \toenglish{...} has braces
%%% that prevent BibTeX's downcasing operation, and the alternate form
%%% {\toenglish{...}} is considered a `special character' by BibTeX,
%%% and all of {...} gets downcased.  We avoid the name \english to
%%% prevent conflicts with language options in packages like Babel.
%%%
%%% To suppress output of English translations of non-English titles,
%%% use
%%%     "\def \toenglish #1\endtoenglish{\unskip}"
%%% instead.
%%%
%%% Alternative Cyrillic definitions are supplied in the event that
%%% cyracc.def is not loaded.

@Preamble{"\input bibnames.sty" #
  "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " #
  "\ifx \undefined \cyr \let \cyr = \relax \fi " #
  "\ifx \undefined \cdprime \def \cdprime{''} \fi " #
  "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" #
  "\hyphenation{
                 Rich-ard
  }"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|http://www.math.utah.edu/~beebe/|"}

@String{ack-nj =  "Norbert Juffa,
                  2445 Mission College Blvd.,
                  Santa Clara, CA 95054,
                  USA,
                  e-mail: \path|norbert@@iit.com|"}

@String{ack-rfb = "Ronald F. Boisvert,
                  Applied and Computational Mathematics Division,
                  National Institute of Standards and Technology,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975 3812,
                  e-mail: \path=boisvert@cam.nist.gov="}

%%% ====================================================================
%%% Institution abbreviations:

@String{inst-ANL                = "Argonne National Laboratory"}

@String{inst-ANL:adr            = "9700 South Cass Avenue, Argonne, IL
                                  60439-4801, USA"}

@String{inst-CPAM-UCB           = "Center for Pure and Applied Mathematics,
                                  University of California, Berkeley"}

@String{inst-CPAM-UCB:adr       = "Berkeley, CA, USA"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-ACTA-INFO             = "Acta Informatica"}

@String{j-ADV-APPL-MATH         = "Advances in Applied Mathematics"}

@String{j-AM-J-MATH             = "American Journal of Mathematics"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
                                  Intelligence"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-AUSTRALIAN-J-PHYS     = "Australian Journal of Physics"}

@String{j-AUTOMATICA            = "Automatica: the journal of IFAC, the
                                  International Federation of Automatic
                                  Control"}

@String{j-BIT                   = "BIT (Nordisk tidskrift for
                                  informationsbehandling)"}

@String{j-BIT-NUM-MATH          = "BIT Numerical Mathematics"}

@String{j-C-R-ACAD-BULGARE-SCI  = "Comptes rendus de l'Acad{\'e}mie bulgare
                                  des sciences"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-CCCUJ                 = "C/C++ Users Journal"}

@String{j-COMP-MATH-APPL-B      = "Computers and Mathematics with Applications.
                                   Part B"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}

@String{j-COMPUTER              = "Computer"}

@String{j-COMPUTING             = "Computing: Archiv fur informatik und
                                  numerik"}

@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}

@String{j-CONST-APPROX          = "Constructive Approximation"}

@String{j-DDJ                   = "Dr. Dobb's Journal of Software Tools"}

@String{j-ELECT-LETTERS         = "Electronics Letters"}

@String{j-ELEK-RECHENANLAGEN    = "Elektronische Rechenanlagen"}

@String{j-IBM-JRD               = "IBM Journal of Research and Development"}

@String{j-IBM-SYS-J             = "IBM Systems Journal"}

@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital Techniques"}

@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}

@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE signal processing letters"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and
                                  systems. 2, Analog and digital signal
                                  processing"}

@String{j-IEEE-TRANS-COMPUT     = "IEEE Transactions on Computers"}

@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}

@String{j-IEEE-TRANS-SIG-PROC   = "IEEE Transactions on Signal Processing"}

@String{j-IEEE-TRANS-VLSI-SYST  = "IEEE Transactions on Very Large Scale
                                  Integration (VLSI) Systems"}

@String{j-IJQC                  = "International Journal of Quantum Chemistry"}

@String{j-IJSAHPC               = "The International Journal of Supercomputer
                                  Applications and High Performance Computing"}

@String{j-INFO-PROC-LETT        = "Information Processing Letters"}

@String{j-INT-J-COMPUT-INF-SCI  = "International Journal of Computer and
                                  Information Sciences"}

@String{j-INT-J-MATH-EDU-SCI-TECH = "International journal of mathematical
                                  education in science and technology"}

@String{j-INT-J-MATH-MATH-SCI   = "International Journal of Mathematics and
                                  Mathematical Sciences"}

@String{j-INTEGRATION-VLSI-J    = "Integration, the VLSI journal"}

@String{j-INTEL-TECH-J          = "Intel Technology Journal"}

@String{j-INTERVAL-COMP         = "Interval Computations = Interval'nye
                                  vychisleniia"}

@String{j-J-ACM                 = "Journal of the Association for Computing
                                  Machinery"}

@String{j-J-ALG                 = "Journal of Algorithms"}

@String{j-J-APPROX-THEORY       = "Journal of Approximation Theory"}

@String{j-J-COMP-APPL-MATH      = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-J-COMPLEXITY          = "Journal of complexity"}

@String{j-J-COMPUT-PHYS         = "Journal of Computational Physics"}

@String{j-J-MULTIVAR-ANAL       = "Journal of multivariate analysis"}

@String{j-J-PAR-DIST-COMP       = "Journal of Parallel and Distributed
                                  Computing"}

@String{j-J-PHYS-A              = "Journal of Physics A (Mathematical and General)"}

@String{j-J-STAT-COMPUT-SIMUL   = "Journal of Statistical Computation and
                                  Simulation"}

@String{j-J-STAT-SOFT           = "Journal of Statistical Software"}

@String{j-J-SYMBOLIC-COMP       = "Journal of Symbolic Computation"}

@String{j-J-SYMBOLIC-LOGIC      = "Journal of Symbolic Logic"}

@String{j-J-UCS                 = "J.UCS: The Journal of Universal Computer Science"}

@String{j-J-VLSI-SIGNAL-PROC    = "Journal of VLSI Signal Processing"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LIN-MULT-ALGEBRA      = "Linear and Multilinear Algebra"}

@String{j-LOGIN                 = ";login: the USENIX Association newsletter"}

@String{j-MATH-COMP             = "Mathematics of Computation"}

@String{j-MATH-COMP-SIM         = "Mathematics and Computers in Simulation"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MATH-MODEL-NUM-ANA    = "Mathematical modelling and numerical
                                  analysis = Modelisation math{\'e}matique et
                                  analyse num{\'e}rique: $M^2AN$"}

@String{j-MATH-OP-RES           = "Mathematics of Operations Research"}

@String{j-MATH-PROG             = "Mathematical Programming"}

@String{j-MATH-TABLES-AIDS-COMPUT = "Mathematical Tables and Aids to
                                  Computation"}

@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
                                  to Computation"}

@String{j-MICROPROC-MICROPROG   = "Microprocessing and Microprogramming"}

@String{j-MICROPROC-MICROSYS    = "Microprocessors and Microsystems"}

@String{j-NACH-ELEK             = "Nachrichtentechnik Elektronik"}

@String{j-NEURAL-COMP           = "Neural Computation"}

@String{j-NEURAL-NETWORKS       = "Neural Networks"}

@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
                                  informationsbehandling"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-NUCL-INSTR-METH       = "Nuclear Instruments and Methods"}

@String{j-NUMER-ALGORITHMS      = "Numerical Algorithms"}

@String{j-OPER-RES              = "Operations Research"}

@String{j-PAC-J-MATH            = "Pacific Journal of Mathematics"}

@String{j-PARALLEL-COMPUTING    = "Parallel Computing"}

@String{j-PHYS-TODAY            = "Physics Today"}

@String{j-PHYSICA-D             = "Physica D"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROG-COMP-SOFT        = "Programming and Computer Software;
                                  translation of Programmirovaniye (Moscow,
                                  USSR) Plenum"}

@String{j-PROGRAMMIROVANIE      = "Programmirovanie"}

@String{j-RUSS-J-MATH-PHYS      = "Russian Journal of Mathematical Physics"}

@String{j-SIAM-J-APPL-MATH      = "SIAM Journal on Applied Mathematics"}

@String{j-SIAM-J-CONTROL-OPTIM  = "SIAM Journal on Control and Optimization"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-J-MATH-ANA       = "SIAM journal on mathematical analysis"}

@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
                                  Applied Mathematics: Series B, Numerical
                                  Analysis"}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-SIGADA-LETTERS        = "ACM SIGADA Ada Letters"}

@String{j-SIGNUM                = "ACM SIGNUM Newsletter"}

@String{j-SIGPLAN               = "ACM SIGPLAN Notices"}

@String{j-TECHNIQUE-SCI-INFORMATIQUES = "Technique et Science Informatiques"}

@String{j-THEOR-COMP-SCI        = "Theoretical Computer Science"}

@String{j-TOKYO-J-MATH          = "Tokyo journal of mathematics"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@String{j-TRANS-AM-MATH-SOC     = "Transactions of the American Mathematical
                                  Society"}

@String{j-TRANS-SOC-COMP-SIM    = "Transactions of the Society for Computer
                                  Simulation"}

@String{j-Z-ANAL-ANWEND         = "Zeitschrift f{\"u}r Analysis und ihre
                                  Anwendungen"}

@String{j-Z-MATH-LOGIK-GRUNDL-MATH = "Zeitschrift f{\\\"u}r mathematische
                                  Logik und Grundlagen der Mathematik"}

%%% ====================================================================
%%% Publishers and their addresses:

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-AFIPS               = "AFIPS Press"}
@String{pub-AFIPS:adr           = "Montvale, NJ, USA"}

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-AP                  = "Academic Press"}
@String{pub-AP:adr              = "New York, NY, USA"}

@String{pub-BIRKHAUSER          = "Birkh{\"a}user"}
@String{pub-BIRKHAUSER:adr      = "Cambridge, MA, USA; Berlin, Germany; Basel,
                                  Switzerland"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-CHAPMAN-HALL        = "Chapman and Hall, Ltd."}
@String{pub-CHAPMAN-HALL:adr    = "London, UK"}

@String{pub-CHAPMAN-HALL-CRC    = "Chapman and Hall/CRC"}
@String{pub-CHAPMAN-HALL-CRC:adr = "Boca Raton, FL, USA"}

@String{pub-CLARENDON-PRESS     = "Clarendon Press"}
@String{pub-CLARENDON-PRESS:adr = "Oxford, UK"}

@String{pub-CRC                 = "CRC Press"}
@String{pub-CRC:adr             = "2000 N.W. Corporate Blvd., Boca Raton,
                                  FL 33431-9868, USA"}

@String{pub-ELLIS-HORWOOD       = "Ellis Horwood"}
@String{pub-ELLIS-HORWOOD:adr   = "New York, NY, USA"}

@String{pub-ENH                 = "Elsevier North-Holland, Inc."}
@String{pub-ENH:adr             = "New York, NY, USA"}

@String{pub-IBM                 = "IBM Corporation"}
@String{pub-IBM:adr             = "San Jose, CA, USA"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300, Silver
                                   Spring, MD 20910, USA"}

@String{pub-KLUWER              = "Kluwer Academic Publishers"}
@String{pub-KLUWER:adr          = "Dordrecht, The Netherlands"}

@String{pub-MCGRAW-HILL         = "Mc{\-}Graw-Hill"}
@String{pub-MCGRAW-HILL:adr     = "New York, NY, USA"}

@String{pub-NIST                = "National Institute for Standards and Technology"}
@String{pub-NIST:adr            = "Gaithersburg, MD, USA"}

@String{pub-NORTH-HOLLAND       = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PERGAMON            = "Pergamon Press"}
@String{pub-PERGAMON:adr        = "New York, NY, USA"}

@String{pub-PRINCETON           = "Princeton University Press"}
@String{pub-PRINCETON:adr       = "Princeton, NJ, USA"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}
@String{pub-PH:adr              = "Englewood Cliffs, NJ 07632, USA"}

@String{pub-REK                 = "Robert E. Krieger Publishing Company"}
@String{pub-REK:adr             = "Huntington, NY, USA"}

@String{pub-SIAM                = "Society for Industrial and Applied
                                  Mathematics"}
@String{pub-SIAM:adr            = "Philadelphia, PA, USA"}

@String{pub-SPIE                = "Society of Photo-optical
                                  Instrumentation Engineers (SPIE)"}
@String{pub-SPIE:adr            = "Bellingham, WA, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-TEUBNER             = "Teubner"}
@String{pub-TEUBNER:adr         = "Stuttgart, Leipzig"}

@String{pub-USENIX              = "USENIX"}
@String{pub-USENIX:adr          = "San Francisco, CA, USA"}

@String{pub-WCB                 = "William C. Brown Company Publishers"}
@String{pub-WCB:adr             = "Dubuque, IA, USA"}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

@String{pub-WORLD-SCI           = "World Scientific Publishing
                                  Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr       = "P. O. Box 128, Farrer Road,
                                  Singapore 9128"}

%%% ====================================================================
%%% Series abbreviations:

@String{ser-LNCS                = "Lecture Notes in Computer Science"}

%%% ====================================================================
%%% Bibliography entries, sorted by year and citation label:

@Article{Ritt:1925:EFT,
  author =       "J. F. Ritt",
  title =        "Elementary functions and their inverses",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "27",
  number =       "1",
  pages =        "68--90",
  year =         "1925",
  CODEN =        "TAMTAM",
  ISSN =         "0002-9947",
  MRclass =      "30A05 (33B10)",
  MRnumber =     "MR1501299",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
}

@Article{RCA:1943:TTF,
  author =       "{R. C. A.}",
  title =        "Tables of Trigonometric Functions in Non-Sexagesimal
                 Arguments",
  journal =      j-MATH-TABLES-AIDS-COMPUT,
  volume =       "1",
  number =       "2",
  pages =        "33--44",
  month =        apr,
  year =         "1943",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "JSTOR database",
  note =         "Original journal has only `R. C. A.' as author:
                 possibly R. C. Archibald.",
  acknowledgement = ack-nhfb,
}

@Article{Bateman:1944:GTB,
  author =       "Harry Bateman and Raymond Clare Archibald",
  title =        "A Guide to Tables of {Bessel} Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "7",
  pages =        "205--308",
  month =        jul,
  year =         "1944",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  MRclass =      "",
  MRnumber =     "6,132b",
  MRreviewer =   "G. Szeg{\"o}",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{DHL:1944:NCB,
  author =       "{D. H. L.}",
  title =        "Note on the Computation of the {Bessel} Function
                 ${I}_n({X})$",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "5",
  pages =        "133--135",
  month =        apr,
  year =         "1944",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "JSTOR database",
  note =         "Original journal has only `D. H. L.' as author:
                 probably D. H. Lehmer.",
  acknowledgement = ack-nhfb,
}

@Article{Abramowitz:1945:ZCB,
  author =       "Milton Abramowitz",
  title =        "Zeros of certain {Bessel} functions of fractional
                 order",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "9",
  pages =        "353--354",
  month =        jan,
  year =         "1945",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "6,132c",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Book{Emde:1945:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    "Edwards Bros.",
  address =      "Ann Arbor, MI, USA",
  pages =        "xii + 181",
  year =         "1945",
  LCCN =         "????",
  bibdate =      "Fri Jun 11 12:34:09 1999",
  note =         "Original edition published in 1940.",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1946:MZC,
  author =       "Anonymous",
  title =        "More Zeros of Certain {Bessel} Functions of Fractional
                 Order",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "2",
  number =       "15",
  pages =        "118--119",
  month =        jul,
  year =         "1946",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Book{Emde:1948:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  edition =      "Second",
  pages =        "xii + 181",
  year =         "1948",
  LCCN =         "QA55 .E5 1948",
  MRclass =      "65.0X",
  MRnumber =     "11,263k",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Fogel:1951:FTE,
  author =       "{\`E}. K. Fogel'",
  title =        "A finite theory of elementary functions. {I}.
                 Logarithmic and exponential functions. ({Russian})",
  journal =      "Latvijas PSR Zin\=at{\c{n}}u Akad. V\=estis",
  volume =       "5",
  number =       "46",
  pages =        "801--813",
  year =         "1951",
  MRclass =      "33.0X",
  MRnumber =     "15,218b",
  MRreviewer =   "H. N. Shapiro",
  bibdate =      "Sat Apr 25 13:05:19 1998",
  acknowledgement = ack-nhfb,
}

@Article{Salzer:1951:FCE,
  author =       "H. E. Salzer",
  title =        "Formulas for Calculating the Error Function of a
                 Complex Variable",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "34",
  pages =        "67--70",
  month =        apr,
  year =         "1951",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Salzer:1951:RTT,
  author =       "H. E. Salzer",
  title =        "Radix Table for Trigonometric Functions and their
                 Inverses to High Accuracy",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "33",
  pages =        "9--11",
  month =        jan,
  year =         "1951",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@InBook{Goncarov:1952:EFC,
  author =       "V. L. Gon{\v{c}}arov",
  booktitle =    "Encyclopaedia of elementary mathematics. Book III.
                 Functions and limits (the foundations of analysis)",
  title =        "Elementary functions of a complex variable",
  publisher =    "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
  address =      "Moscow-Leningrad, USSR",
  pages =        "491--552",
  year =         "1952",
  MRclass =      "30.0X",
  MRnumber =     "14,1073c",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InCollection{Goncarov:1952:EFR,
  author =       "V. L. Gon{\v{c}}arov",
  booktitle =    "Encyclopaedia of elementary mathematics. Book III.
                 Functions and limits (the foundations of analysis)",
  title =        "Elementary functions of a real variable. Limits of
                 sequences and functions. The general concept of a
                 function",
  publisher =    "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
  address =      "Moscow-Leningrad, USSR",
  pages =        "9--296",
  year =         "1952",
  MRclass =      "27.2X",
  MRnumber =     "14,1070d",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Kuipers:1952:PSE,
  author =       "L. Kuipers",
  title =        "Properties of some elementary functions",
  journal =      "Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes
                 Math.",
  volume =       "55",
  number =       "14",
  pages =        "388--393",
  year =         "1952",
  MRclass =      "27.0X",
  MRnumber =     "14,360e",
  MRreviewer =   "E. Frank",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Scherberg:1953:ACP,
  author =       "Max G. Scherberg and John F. Riordan",
  title =        "Analogue Calculation of Polynomial and Trigonometric
                 Expansions (in {Other Aids to Computation})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "7",
  number =       "41",
  pages =        "61--65",
  month =        jan,
  year =         "1953",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Clenshaw:1954:PAE,
  author =       "C. W. Clenshaw",
  title =        "Polynomial approximations to elementary functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  pages =        "143--147",
  year =         "1954",
  ISSN =         "0891-6837",
  MRclass =      "41.1X",
  MRnumber =     "16,128f",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Book{Hastings:1955:ADC,
  author =       "Cecil {Hastings, Jr.}",
  title =        "Approximations for digital computers",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "viii + 201",
  year =         "1955",
  ISBN =         "0-691-07914-5",
  LCCN =         "QA76 .H37",
  bibdate =      "Mon Oct 01 15:59:48 2007",
  bibsource =    "z3950.loc.gov:7090/Voyager",
  note =         "Assisted by Jeanne T. Hayward and James P. Wong, Jr.",
  series =       "The Rand series",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted 1957, 1959, 1962, 1966, and 1970. I have
                 fourth printing (1962).",
  subject =      "Electronic digital computers; Numerical analysis",
}

@Article{LaFara:1954:MCI,
  author =       "Robert L. LaFara",
  title =        "A Method for Calculating Inverse Trigonometric
                 Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  number =       "47",
  pages =        "132--139",
  month =        jul,
  year =         "1954",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Kogbetliantz:1957:CEN,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $e^N$ for $-\infty < N < +\infty$ Using
                 an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "2",
  pages =        "110--115",
  month =        apr,
  year =         "1957",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  MRclass =      "68.0X",
  MRnumber =     "19,775d",
  bibdate =      "Tue Sep 06 20:55:54 1994",
  acknowledgement = ack-nhfb,
  reviewer =     "W. F. Freiberger",
}

@Article{Linskii:1957:CEF,
  author =       "V. S. Linski{\u{\i}}",
  title =        "Calculation of elementary functions on automatic
                 digital machines. ({Russian})",
  journal =      "Vy{\v{c}}isl. Mat.",
  volume =       "2",
  pages =        "90--119",
  year =         "1957",
  MRclass =      "68.00",
  MRnumber =     "21 \#982",
  MRreviewer =   "J. W. Carr, III",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Luke:1957:C,
  author =       "Yudell L. Luke",
  title =        "On the Computation of $\log {Z}$ and
                 ${\rm arc} \tan {Z}$",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "57",
  pages =        "16--18",
  month =        jan,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Stegun:1957:GBF,
  author =       "Irene A. Stegun and Milton Abramowitz",
  title =        "Generation of {Bessel} Functions on High Speed
                 Computers",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "60",
  pages =        "255--257",
  month =        oct,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Goldstein:1958:BFL,
  author =       "M. Goldstein and R. M. Thaler",
  title =        "{Bessel} Functions for Large Arguments",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "12",
  number =       "61",
  pages =        "18--26",
  month =        jan,
  year =         "1958",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Kogbetliantz:1958:CANa,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arctan {N} for $-\infty < {N} <
                 +\infty$ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "1",
  pages =        "43--53",
  month =        jan,
  year =         "1958",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  MRclass =      "65.3X",
  MRnumber =     "19,982e",
  bibdate =      "Wed Aug 31 13:40:00 1994",
  acknowledgement = ack-nhfb,
  reviewer =     "C. B. Haselgrove",
}

@Article{Kogbetliantz:1958:CANb,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arcsin {N} for $0<{N}<1$ Using an
                 Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "3",
  pages =        "218--222",
  month =        jul,
  year =         "1958",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  MRclass =      "65.3X",
  MRnumber =     "19,1197c",
  bibdate =      "Wed Aug 31 13:41:37 1994",
  acknowledgement = ack-nhfb,
  reviewer =     "C. B. Haselgrove",
}

@Article{Wadey:1958:TSR,
  author =       "W. G. Wadey",
  title =        "Two Square-Root Approximations",
  journal =      j-CACM,
  volume =       "1",
  number =       "11",
  pages =        "13--14",
  month =        nov,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://portal.acm.org/;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58",
  acknowledgement = ack-nhfb,
  oldlabel =     "Wadey58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}

@Article{Davis:1959:LEI,
  author =       "P. J. Davis",
  title =        "{Leonhard Euler}'s integral: {A} historical profile of
                 the gamma function: In Memoriam: {Milton Abramowitz}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "66",
  number =       "??",
  pages =        "849--869",
  month =        "????",
  year =         "1959",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890",
  MRclass =      "00 (33.00)",
  MRnumber =     "MR0106810 (21 #5540)",
  bibdate =      "Mon Nov 24 20:57:26 2008",
  acknowledgement = ack-nhfb,
}

@Article{Goldstein:1959:RTC,
  author =       "M. Goldstein and R. M. Thaler",
  title =        "Recurrence Techniques for the Calculation of {Bessel}
                 Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "66",
  pages =        "102--108",
  month =        apr,
  year =         "1959",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Kogbetliantz:1959:CSC,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $\sin{N}$, $\cos{N}$, and ${M}$th Root
                 of ${N}$ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "3",
  number =       "2",
  pages =        "147--152",
  month =        apr,
  year =         "1959",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  MRclass =      "65.00",
  MRnumber =     "21 \#964",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nhfb,
  reviewer =     "B. A. Chartres",
}

@Article{Sarafyan:1959:NMC,
  author =       "Diran Sarafyan",
  title =        "A New Method of Computation of Square Roots Without
                 Using Division",
  journal =      j-CACM,
  volume =       "2",
  number =       "11",
  pages =        "23--24",
  month =        nov,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  bibdate =      "Wed Jul 14 15:48:24 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
                 http://portal.acm.org/",
  note =         "See comments \cite{Traub:1960:CNM}.",
  acknowledgement = ack-nhfb,
  oldlabel =     "Sarafyan59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}

@Article{Sherry:1959:CGF,
  author =       "M. E. Sherry and S. Fulda",
  title =        "Calculation of Gamma Functions to High Accuracy (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "68",
  pages =        "314--315",
  month =        oct,
  year =         "1959",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Volder:1959:CCT,
  author =       "Jack Volder",
  title =        "The {CORDIC} Computing Technique",
  journal =      "Proceedings of the Western Joint Computer Conference",
  pages =        "257--261",
  year =         "1959",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Haimovici:1960:MRE,
  author =       "Corina Haimovici",
  title =        "A method of representing elementary functions in
                 algebras of finite order. ({Romanian})",
  journal =      "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i
                 Sec{\c{t}} I. (N.S.)",
  volume =       "6",
  pages =        "507--515",
  year =         "1960",
  MRclass =      "26.00",
  MRnumber =     "24 \#A1342",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InCollection{Kogbetliantz:1960:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of elementary functions",
  crossref =     "Ralston:1960:MMD",
  pages =        "7--35",
  year =         "1960",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "22 \#8681",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Manual{Maehly:1960:ACD,
  author =       "Hans J. Maehly",
  title =        "Approximations for the {Control Data 1604}",
  organization = "Institute for Advanced Study",
  address =      "Princeton, NJ",
  pages =        "ii + 44",
  day =          "15",
  month =        jan,
  year =         "1960",
  bibdate =      "Tue Nov 06 00:39:07 2007",
  URL =          "http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "$\arctan(x)$; $\cos(x)$; $\exp(x)$; $\log(x)$;
                 $\sin(x)$; $\sqrt(x)$; $\tan(x)$; CDC 1604",
}

@Article{Philip:1960:FI,
  author =       "J. R. Philip",
  title =        "The function inverfc $\theta$",
  journal =      j-AUSTRALIAN-J-PHYS,
  volume =       "13",
  number =       "1",
  pages =        "13--20",
  month =        mar,
  year =         "1960",
  CODEN =        "AUJPAS",
  ISSN =         "0004-9506",
  MRnumber =     "22 \9626",
  bibdate =      "Tue Sep 11 20:53:59 2007",
  abstract =     "The function inverfc $\theta$ arises in certain
                 differential equations when concentration is taken as
                 an independent variable. It enters into a general
                 method of exact solution of the concentration-dependent
                 diffusion equation. An account is given of the
                 properties of this function, and of its derivatives and
                 integrals. The function\par

                 $$B(\theta) = (2/\pi^{1/2}) \exp[-({\rm inverfc} \theta)^2]$$

                 \noindent is intimately connected with the first
                 integral of inverfc $\theta$ and with its
                 derivatives. Tables of inverfc $\theta$ and $B(\theta)$
                 are given.",
  acknowledgement = ack-nhfb,
  ZMnumber =     "135.28302",
}

@Article{Sarafyan:1960:DCS,
  author =       "Diran Sarafyan",
  title =        "Divisionless computation of square roots through
                 continued squaring",
  journal =      j-CACM,
  volume =       "3",
  number =       "5",
  pages =        "319--321",
  month =        may,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  MRclass =      "65.00",
  MRnumber =     "22\#8639",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/",
  acknowledgement = ack-nhfb,
  keywords =     "$\sqrt(x)$; elementary functions",
  ZMreviewer =   "M. Lotkin",
}

@Article{Sholander:1960:AEE,
  author =       "Marlow Sholander",
  title =        "Analytical expressions and elementary functions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "67",
  pages =        "213--214",
  year =         "1960",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890",
  MRclass =      "26.00",
  MRnumber =     "22 \#9553",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Traub:1960:CNM,
  author =       "J. F. Traub",
  title =        "Comments on a recent paper [{``A New Method of
                 Computation of Square Roots Without Using
                 Division''}]",
  journal =      j-CACM,
  volume =       "3",
  number =       "2",
  pages =        "86--86",
  month =        feb,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  bibdate =      "Fri Nov 25 18:19:25 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
                 http://www.acm.org/pubs/contents/journals/cacm/",
  note =         "See \cite{Sarafyan:1959:NMC}.",
  acknowledgement = ack-nhfb,
  oldlabel =     "Traub60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}

@Book{Warmus:1960:TEF,
  author =       "Mieczys{\l}aw Warmus",
  title =        "Tables of elementary functions",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "vii + 567",
  year =         "1960",
  LCCN =         "QA55 .W3 1960",
  MRclass =      "65.05",
  MRnumber =     "23 \#B1141",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  note =         "Pa\'nstwowe Wydawnictwo Naukowe, Warsaw. Separately
                 bound table of proportional parts, 30 pp.",
  acknowledgement = ack-nhfb,
}

@Article{Barakat:1961:EIG,
  author =       "Richard Barakat",
  title =        "Evaluation of the Incomplete Gamma Function of
                 Imaginary Argument by {Chebyshev} Polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "73",
  pages =        "7--11",
  month =        jan,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Froberg:1961:RCA,
  author =       "Carl-Erik Fr{\"o}berg",
  title =        "Rational {Chebyshev} Approximations of Elementary
                 Functions",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "4",
  pages =        "256--262",
  month =        dec,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01933243",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4",
  note =         "See erratum \cite{Froberg:1963:ERC}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Spielberg:1961:ECF,
  author =       "Kurt Spielberg",
  title =        "Efficient Continued Fraction Approximations To
                 Elementary Functions",
  journal =      j-MATH-COMP,
  volume =       "15",
  number =       "76",
  pages =        "409--417",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65.20",
  MRnumber =     "MR0134842 (24 \#B894)",
  MRreviewer =   "M. E. Rose",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Article{Thacher:1961:ISR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Iterated Square Root Expansions for the Inverse Cosine
                 and Inverse Hyperbolic Cosine",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "399--403",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Werner:1961:CAG,
  author =       "Helmut Werner and Robert Collinge",
  title =        "{Chebyshev} Approximations to the Gamma Function (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "74",
  pages =        "195--197",
  month =        apr,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Carlitz:1963:IEF,
  author =       "L. Carlitz",
  title =        "The Inverse of the Error Function",
  journal =      j-PAC-J-MATH,
  volume =       "13",
  number =       "2",
  pages =        "459--470",
  year =         "1963",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730",
  bibdate =      "Thu Sep 13 21:30:05 2007",
  URL =          "http://pjm.math.berkeley.edu/pjm;
                 http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1",
  acknowledgement = ack-nhfb,
}

@Article{Froberg:1963:ERC,
  author =       "C.-E. Fr{\"o}berg",
  title =        "Erratum: {``Rational Chebyshev Approximations of
                 Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261,
                 line 12]}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "3",
  number =       "1",
  pages =        "68--68",
  month =        mar,
  year =         "1963",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01963538",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1",
  note =         "See \cite{Froberg:1961:RCA}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Book{Ljusternik:1963:MVF,
  author =       "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R.
                 Janpol'ski{{\u{\i}}}",
  title =        "{\cyr Matematicheski{\u{\i}}analiz. Vychislenie
                 {\`e}lementarnykh funktsi{\u{\i}}}. [Mathematical
                 analysis. Computation of the elementary functions]",
  publisher =    "Gosudarstv. Izdat. Fiz-Mat. Lit.",
  address =      "Moscow, USSR",
  pages =        "247",
  year =         "1963",
  MRclass =      "65.25",
  MRnumber =     "28 \#1733",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Peuizulaev:1963:AEF,
  author =       "{\v{S}}. I. Pe{\u{\i}}zulaev",
  title =        "An approximation by elementary functions.
                 ({Russian})",
  journal =      "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
  volume =       "3",
  pages =        "769--770",
  year =         "1963",
  MRclass =      "41.30",
  MRnumber =     "28 \#398",
  MRreviewer =   "D. D. Stancu",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Whittlesey:1963:IGF,
  author =       "John R. B. Whittlesey",
  title =        "Incomplete Gamma Functions for Evaluating {Erlang}
                 Process Probabilities",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "81",
  pages =        "11--17",
  month =        jan,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Burgoyne:1964:GTF,
  author =       "F. D. Burgoyne",
  title =        "Generalized Trigonometric Functions (in {Technical
                 Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "86",
  pages =        "314--316",
  month =        apr,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Lanczos:1964:PAG,
  author =       "C. Lanczos",
  title =        "A Precision Approximation of the Gamma Function",
  journal =      j-SIAM-J-NUM-ANALYSIS-B,
  volume =       "1",
  number =       "??",
  pages =        "86--96",
  month =        "????",
  year =         "1964",
  ISSN =         "0887-459X",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Morelock:1964:AAE,
  author =       "J. C. Morelock",
  title =        "{ACM} Algorithm 229: Elementary Functions by Continued
                 Fractions",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "296",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  bibdate =      "Thu Sep 08 09:32:21 1994",
  acknowledgement = ack-nhfb,
}

@Article{Simauti:1964:AFS,
  author =       "Takakazu Simauti",
  title =        "Approximation formulas for some elementary functions",
  journal =      "Comment. Math. Univ. St. Paul.",
  volume =       "12",
  pages =        "23--35",
  year =         "1964",
  CODEN =        "COMAAC",
  ISSN =         "0010-258X",
  MRclass =      "65.25",
  MRnumber =     "28 \#5552",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Wengert:1964:SAD,
  author =       "R. E. Wengert",
  title =        "A simple automatic derivative evaluation program",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "463--464",
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz",
  abstract =     "A procedure for automatic evaluation of total and
                 partial derivatives of arbitrary algebraic functions is
                 presented. The numerical values of derivatives are
                 computed without developing analytic expressions for
                 the derivatives. The function is decomposed into a
                 sequence of elementary expressions A library is
                 provided for differentiating of elementary functions.",
  acknowledgement = ack-nhfb,
  keywords =     "point algorithm; differentiation arithmetic; computer
                 program.",
  referred =     "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a];
                 [Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a];
                 [Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a];
                 [Wilk64a].",
}

@Article{Fraser:1965:SMC,
  author =       "W. Fraser",
  title =        "A Survey of Methods for Computing Minimax and
                 Near-Minimax Polynomial Approximations for Functions of
                 a Single Independent Variable",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "3",
  pages =        "295--314",
  month =        jul,
  year =         "1965",
  CODEN =        "JACOAH",
  DOI =          "http://doi.acm.org/10.1145/321281.321282",
  ISSN =         "0004-5411",
  bibdate =      "Thu Nov 03 08:47:50 1994",
  abstract =     "Methods are described for the derivation of minimax
                 and near-minimax polynomial approximations. For minimax
                 approximations techniques are considered for both
                 analytically defined functions and functions defined by
                 a table of values. For near-minimax approximations
                 methods of determining the coefficients of the
                 Fourier--Chebyshev expansion are first described. These
                 consist of the rearrangement of the coefficients of a
                 power polynomial, and also direct determination of the
                 coefficients from the integral which defines them, or
                 the differential equation which defines the function.
                 Finally there is given a convenient modification of an
                 interpolation scheme which finds coefficients of a
                 near-minimax approximation without requiring numerical
                 integration or the numerical solution of a system of
                 equations.",
  acknowledgement = ack-nhfb,
}

@Article{Kazangapov:1965:REF,
  author =       "A. N. Kazangapov",
  title =        "Representation of elementary function in the system of
                 residual classes. ({Russian})",
  journal =      "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk",
  volume =       "3",
  pages =        "79--84",
  year =         "1965",
  MRclass =      "65.25",
  MRnumber =     "33 \#5090",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Book{Lyusternik:1965:HCE,
  author =       "L. A. Lyusternik and O. A. Chervonenkis and A. R.
                 Yanpol'skii",
  title =        "Handbook for Computing Elementary Functions",
  volume =       "76",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "xiii + 251",
  year =         "1965",
  LCCN =         "QA221.L513",
  MRclass =      "65.25",
  MRnumber =     "32 \#584",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  note =         "Translated from the Russian by G. J. Tee. Translation
                 edited by K. L. Stewart.",
  series =       "International series of monographs on pure and applied
                 mathematics",
  acknowledgement = ack-nhfb,
}

@Article{Maklovic:1965:IIC,
  author =       "S. T. Maklovi{\v{c}}",
  title =        "Investigation of integrals containing {Bessel} and
                 elementary functions. ({Russian})",
  journal =      "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.",
  volume =       "82",
  pages =        "75--81",
  year =         "1965",
  MRclass =      "33.25",
  MRnumber =     "34 \#387",
  MRreviewer =   "H. A. Lauwerier",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Medhurst:1965:EI,
  author =       "R. G. Medhurst and J. H. Roberts",
  title =        "Evaluation of the Integral ${I}_n(b) = \frac{2}{\pi}
                 \int^\infty_0 \bigg(\frac{\sin x}{x}\bigg)^n \cos (bx)
                 dx$",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "113--117",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Filippi:1966:BEE,
  author =       "S. Filippi",
  title =        "{Die Berechnung einiger elementarer transzendenter
                 Funktionen mit Hilfe des Richardson-Algorithmus}
                 \toenglish {The Computation of Some Elementary
                 Transcendental Functions by Means of the {Richardson}
                 Algorithm} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "1",
  number =       "??",
  pages =        "127--132",
  month =        "????",
  year =         "1966",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Glasser:1966:ESI,
  author =       "M. L. Glasser",
  title =        "Evaluation of Some Integrals Involving the
                 $\psi$-Function (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "332--333",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Book{Jurimae:1966:KFT,
  author =       "E. J{\"u}rim{\"a}e",
  title =        "Kompleksmuutuja funktsioonide teooria. {I}:
                 Elementaarsed funktsioonid. ({Estonian}) [Theory of
                 functions of a complex variable. {I}: Elementary
                 functions]",
  publisher =    "Tartu Riiklik {\"U}likool",
  address =      "Tartu, Estonia",
  pages =        "131",
  year =         "1966",
  MRclass =      "30.00",
  MRnumber =     "40 \#5827a",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InCollection{Kogbetliantz:1966:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of Elementary Functions",
  crossref =     "Ralston:1960:MMD",
  pages =        "7--35",
  year =         "1966",
  bibdate =      "Sat Dec 09 14:09:27 1995",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@TechReport{Kuki:1966:CAE,
  author =       "H. Kuki",
  title =        "Comments on the {ANL} Evaluation of the {OS\slash 360
                 FORTRAN} Math Function Library",
  type =         "????",
  number =       "SSD 169, C4773",
  institution =  "SHARE Secretary Distribution",
  address =      "????",
  pages =        "47--53",
  year =         "1966",
  bibdate =      "Wed Feb 14 19:13:50 2007",
  acknowledgement = ack-nhfb,
}

@Article{Takenaga:1966:EIG,
  author =       "Roy Takenaga",
  title =        "On the Evaluation of the Incomplete Gamma Function (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "606--610",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Thompson:1966:ESI,
  author =       "Rory Thompson",
  title =        "Evaluation of ${I}_n(b) = 2\pi^{-1} \int^\infty_0
                 \big(\frac{sin x}{x}\big) ^n \cos (bx) dx$ and of
                 Similar Integrals (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "330--332",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Cody:1967:CAN,
  author =       "W. J. Cody and K. E. Hillstrom",
  title =        "{Chebyshev} Approximations for the Natural Logarithm
                 of the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "198--203",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Fettis:1967:MCI,
  author =       "Henry E. Fettis",
  title =        "More on the Calculation of the Integral ${I}_n(b) =
                 \frac{2}{\pi}\int^\infty_0\big(\frac{\sin x}{x}\big)^n
                 \cos bx dx$ (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "100",
  pages =        "727--730",
  month =        oct,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Moody:1967:ADF,
  author =       "William T. Moody",
  title =        "Approximations for the Psi (Digamma) Function (in
                 Technical Notes and Short Notices)",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "97",
  pages =        "112--112",
  month =        jan,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Book{Fike:1968:CEM,
  author =       "C. T. Fike",
  title =        "Computer Evaluation of Mathematical Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 227",
  year =         "1968",
  LCCN =         "QA297 .F5",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  acknowledgement = ack-nj,
}

@Article{Galant:1968:HAG,
  author =       "D. C. Galant and P. F. Byrd",
  title =        "High Accuracy Gamma Function Values for Some Rational
                 Arguments (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "104",
  pages =        "885--887",
  month =        oct,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Book{Hart:1968:CAa,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-REK,
  address =      pub-REK:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-88275-642-7",
  ISBN-13 =      "978-0-88275-642-4",
  LCCN =         "QA 297 C64 1978",
  bibdate =      "Tue Dec 14 22:55:11 1993",
  note =         "Reprinted 1978 with corrections.",
  acknowledgement = ack-nhfb,
}

@Book{Hart:1968:CAb,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-471-35630-1",
  ISBN-13 =      "978-0-471-35630-1",
  LCCN =         "????",
  bibdate =      "Sat Jan 14 14:53:06 2006",
  acknowledgement = ack-nhfb,
}

@Article{Nagashima:1968:EFN,
  author =       "Takashi Nagashima",
  title =        "On elementary functions of natural numbers",
  journal =      "Hitotsubashi J. Arts Sci.",
  volume =       "9",
  pages =        "50--58",
  year =         "1968",
  ISSN =         "0073-2788",
  MRclass =      "02.72",
  MRnumber =     "MR0232678 (38 \#1001)",
  MRreviewer =   "R. L. Goodstein",
  fjournal =     "Hitotsubashi Journal of Arts \&amp; Sciences",
}

@Article{Richardson:1968:SUP,
  author =       "Daniel Richardson",
  title =        "Some Undecidable Problems Involving Elementary
                 Functions of a Real Variable",
  journal =      j-J-SYMBOLIC-LOGIC,
  volume =       "33",
  number =       "4",
  pages =        "514--520",
  month =        dec,
  year =         "1968",
  CODEN =        "JSYLA6",
  ISSN =         "0022-4812",
  MRclass =      "02.75",
  MRnumber =     "39 #1330",
  bibdate =      "Mon May 19 13:04:20 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Wrench:1968:CTS,
  author =       "John W. {Wrench, Jr.}",
  title =        "Concerning Two Series for the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "617--626",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Carlson:1969:CBE,
  author =       "B. C. Carlson",
  title =        "A connection between elementary functions and higher
                 transcendental functions",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "17",
  pages =        "116--148",
  year =         "1969",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399",
  MRclass =      "33.20 (30.00)",
  MRnumber =     "40 \#408",
  MRreviewer =   "S. K. Bose",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InProceedings{Clark:1969:SCE,
  author =       "N. W. Clark and W. J. Cody",
  title =        "Self-contained exponentiation",
  crossref =     "AFIPS:1969:ACPb",
  pages =        "701--706",
  year =         "1969",
  bibdate =      "Wed Sep 07 10:49:33 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt,
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib",
  acknowledgement = ack-nj,
}

@Article{Herman:1969:NHE,
  author =       "G. T. Herman",
  title =        "A new hierarchy of elementary functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "20",
  pages =        "557--562",
  year =         "1969",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939",
  MRclass =      "02.77",
  MRnumber =     "40 \#4110",
  MRreviewer =   "G. E. Sacks",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Lewis:1969:FII,
  author =       "Richard L. Lewis",
  title =        "On Finite Integrals Involving Trigonometric, {Bessel},
                 and {Legendre} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "106",
  pages =        "259--273",
  month =        apr,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tesler:1969:AEF,
  author =       "G. S. Tesler",
  booktitle =    "Mathematical provisioning of electronic digital
                 computers and effective organization of the computing
                 process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2",
  title =        "The approximation of elementary functions by means of
                 polynomials of degree zero and one. ({Russian})",
  publisher =    "Akad. Nauk Ukrain. SSR",
  address =      "Kiev, USSR",
  pages =        "75--88",
  year =         "1969",
  MRclass =      "65D15",
  MRnumber =     "45 \#4600",
  MRreviewer =   "I. Selihova",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Turner:1969:DSC,
  author =       "L. R. Turner",
  title =        "Difficulty in {$\sin$\slash$\cos$} Routine",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "3",
  pages =        "13--13",
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778",
  bibdate =      "Thu Feb 15 15:23:23 2007",
  acknowledgement = ack-nhfb,
}

@Article{Zaker:1969:CCE,
  author =       "T. A. Zaker",
  title =        "Calculation of the complementary error function of
                 complex argument",
  journal =      j-J-COMPUT-PHYS,
  volume =       "4",
  number =       "3",
  pages =        "427--430",
  month =        oct,
  year =         "1969",
  CODEN =        "JCTPAH",
  DOI =          "http://dx.doi.org/10.1016/0021-9991(69)90011-4",
  ISSN =         "0021-9991",
  bibdate =      "Thu Dec 04 16:20:39 2008",
  acknowledgement = ack-nhfb,
}

@TechReport{DeLugish:1970:CAA,
  author =       "Bruce Gene DeLugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Functions in a Binary Computer",
  number =       "399",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, Illinois",
  pages =        "191",
  year =         "1970",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Kolbig:1970:CZI,
  author =       "K. S. Kolbig",
  title =        "Complex Zeros of an Incomplete {Riemann} Zeta Function
                 and of the Incomplete Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "111",
  pages =        "679--696",
  month =        jul,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@TechReport{Lugish:1970:CAA,
  author =       "B. G. de Lugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Function in a Binary Computer",
  type =         "Report",
  number =       "399",
  institution =  "Department of Computer Science, University of
                 Illinois",
  pages =        "????",
  month =        jun,
  year =         "1970",
  bibdate =      "Fri Sep 02 22:49:20 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Ninomiya:1970:BRS,
  author =       "Ichizo Ninomiya",
  title =        "Best Rational Starting Approximations and Improved
                 {Newton} Iteration for the Square Root",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "391--404",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Nagoya Univ., Chikua ku, Japan",
  keywords =     "computing procedure; function approximation; iterative
                 methods; Newton iteration; rational approximation;
                 square root",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Rothmaier:1970:DSB,
  author =       "B. Rothmaier",
  title =        "{Dokumentation der Standardfunktionen des
                 Betriebssystems {Hydra X8}} \toenglish {Documentation}
                 of the Elementary Functions of the Operating System
                 {Hydra X8} \endtoenglish",
  type =         "Interner {Bericht}",
  number =       "Nr. 70/8",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1970",
  bibdate =      "Fri Jun 11 12:37:53 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Bohan:1971:ADC,
  author =       "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov",
  title =        "The analytic definition of certain elementary
                 functions. ({Russian}) Questions of modern mathematics
                 and methods of teaching it at institutions of higher
                 learning",
  journal =      "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.",
  volume =       "404",
  pages =        "59--78",
  year =         "1971",
  MRclass =      "26A09",
  MRnumber =     "55 \#10612",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InCollection{Cody:1971:SEF,
  author =       "W. J. Cody",
  title =        "Software for the Elementary Functions",
  crossref =     "Rice:1971:MS",
  pages =        "171--186",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:47 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Herman:1971:EDH,
  author =       "G. T. Herman",
  title =        "The equivalence of different hierarchies of elementary
                 functions",
  journal =      "Z. Math. Logik Grundlagen Math.",
  volume =       "17",
  pages =        "219--224",
  year =         "1971",
  MRclass =      "02.77 (68.00)",
  MRnumber =     "44 \#6494",
  MRreviewer =   "D. A. Clarke",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Kuki:1971:FEP,
  author =       "H. Kuki and J. Ascoly",
  title =        "{FORTRAN} extended-precision library",
  journal =      j-IBM-SYS-J,
  volume =       "10",
  number =       "1",
  pages =        "39--61",
  year =         "1971",
  coden =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:51:32 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt,
                 ftp://ftp.math.utah.edu/pub/tex/bib/ibmsysj.bib,
                 ftp://ftp.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxmonth =      "(none)",
}

@InCollection{Kuki:1971:MFS,
  author =       "H. Kuki",
  title =        "Mathematical Function Subprograms for Basic System
                 Libraries{}\emdash Objectives, Constraints, and
                 Trade-Off",
  crossref =     "Rice:1971:MS",
  pages =        "187--199",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:27:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  acknowledgement = ack-nj,
}

@Article{Liron:1971:ISR,
  author =       "N. Liron",
  title =        "Infinite Sums of Roots for a Class of Transcendental
                 Equations and {Bessel} Functions of Order One-Half",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "769--781",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Luke:1971:MTBa,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "323--330",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Luke:1971:MTBb,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions, {II}",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "789--795",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Matta:1971:UCE,
  author =       "F. Matta and A. Reichel",
  title =        "Uniform Computation of the Error Function and Other
                 Related Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "339--344",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Rothmaier:1971:BEF,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der elementaren Funktionen mit
                 beliebiger Genauigkeit} \toenglish {The Computation of
                 Elementary Functions with Arbitrary Accuracy}
                 \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Spellucci:1971:DPA,
  author =       "P. Spellucci",
  title =        "Double precision approximations to the elementary
                 functions using {Jacobi-fractions}",
  journal =      j-NUM-MATH,
  volume =       "18",
  pages =        "127--143",
  year =         "1971/1972",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "45 \#7938",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Spira:1971:CGF,
  author =       "Robert Spira",
  title =        "Calculation of the Gamma Function by {Stirling}'s
                 Formula",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "317--322",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Walther:1971:UAE,
  author =       "J. S. Walther",
  title =        "A unified algorithm for elementary functions",
  crossref =     "AFIPS:1971:ACP",
  volume =       "38",
  pages =        "379--385",
  year =         "1971",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Book{Bark:1972:MTF,
  author =       "L. S. Bark",
  title =        "{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh
                 funktsi{\u{\i}}} (${\rm sin} x$, ${\rm cos} x$, $e^{x}$
                 {\cyr i} $e^{-x}$). ({Russian}) [Multiplace tables of
                 the elementary functions (${\rm sin}\ x$, ${\rm cos}\
                 x$, $e^{x}$ and $e^{-x}$)]",
  publisher =    "Vy{\v{c}}isl. Centr Akad. Nauk SSSR",
  address =      "Moscow, USSR",
  edition =      "Second, unrevised",
  pages =        "134",
  year =         "1972",
  MRclass =      "65A05",
  MRnumber =     "50 \#6100",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  note =         "Tables processed and text translated from the English
                 by L. S. Bark. Library of Mathematical Tables, No. 9.
                 1972",
  acknowledgement = ack-nhfb,
}

@Article{Carlson:1972:ACL,
  author =       "B. C. Carlson",
  title =        "An algorithm for computing logarithms and
                 arctangents",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "543--549",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Iowa State Univ., Ames, IA, USA",
  keywords =     "acceleration; arctangents; auxiliary; Borchardt's
                 algorithm; convergence; fast; function approximation;
                 functions; inverse circular functions; inverse
                 hyperbolic; iterative algorithm; logarithms; numerical
                 methods; rational operations; recurrence relation;
                 square roots",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Chen:1972:ACE,
  author =       "Tien Chi Chen",
  title =        "Automatic Computation of Exponentials, Logarithms,
                 Ratios and Square Roots",
  journal =      j-IBM-JRD,
  volume =       "16",
  number =       "4",
  pages =        "380--388",
  month =        jul,
  year =         "1972",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  MRclass =      "65D20",
  MRnumber =     "49 \#1738",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  URL =          "http://www.research.ibm.com/journal/rd/164/chen.pdf",
  abstract =     "It is shown how a relatively simple device can
                 evaluate exponentials, logarithms, ratios and square
                 roots for fraction arguments, employing only shifts,
                 adds, high-speed table lookups, and bit counting. The
                 scheme is based on the cotransformation of a number
                 pair $(x, y)$ such that the $F(x, y) = f(x_0)$ is
                 invariant; when $x$ is driven towards a known value
                 $x_w$, $y$ is driven towards the result. For an $N$-bit
                 fraction about $N / 4$ iterations are required, each
                 involving two or three adds; then a termination
                 algorithm, based on an add and an abbreviated multiply,
                 completes the process, for a total cost of about one
                 conventional multiply time. Convergence, errors and
                 simulation using APL are discussed.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, San Jose, CA, USA",
  keywords =     "adds; APL; bit counting; convergence;
                 cotransformation; digital arithmetic; errors;
                 exponentials; high speed table; iteration; logarithms;
                 lookups; ratios; shifts; simulation; square roots;
                 termination algorithm",
  reviewer =     "F. Gotze",
  treatment =    "P Practical",
}

@TechReport{Ercegovac:1972:RES,
  author =       "Milos D. Ercegovac",
  title =        "Radix 16 Evaluation of Some Elementary Functions",
  number =       "540",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, Illinois",
  pages =        "30",
  year =         "1972",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Hunter:1972:NEC,
  author =       "D. B. Hunter and T. Regan",
  title =        "A note on the evaluation of the complementary error
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "539--541",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. Bradford, UK",
  keywords =     "complementary error function; complex variable;
                 evaluation; integration; method of Matta and Reichel;
                 modification; numerical; stability",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Kolbig:1972:ZIG,
  author =       "K. S. Kolbig",
  title =        "On the Zeros of the Incomplete Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "119",
  pages =        "751--755",
  month =        jul,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "CERN, Geneva, Switzerland",
  keywords =     "asymptotic formulae; complex w plane; function
                 approximation; incomplete gamma function; poles and
                 zeros; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ling:1972:EM,
  author =       "Chih-Bing Ling and Jung Lin",
  title =        "On Evaluation of Moments of ${K}_\nu(t)/{I}_\nu(t)$",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "529--537",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods)",
  corpsource =   "Virginia Politech. Inst., Blacksburg, VA, USA",
  keywords =     "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t);
                 numerical methods; Watson's method",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Linz:1972:MCB,
  author =       "Peter Linz",
  title =        "A Method for Computing {Bessel} Function Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "509--513",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. California, Davis, CA, USA",
  keywords =     "Abel; Bessel function integrals; Fourier integrals;
                 infinite integrals; integration; numerical computation;
                 transform",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Luke:1972:MTB,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions. {III}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "117",
  pages =        "237--240",
  month =        jan,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods)",
  corpsource =   "Univ. Missouri, Kansas City, KS, USA",
  keywords =     "Bessel functions; miniaturized tables; numerical
                 methods",
  treatment =    "T Theoretical or Mathematical",
}

@Article{MacKinnon:1972:AEH,
  author =       "Robert F. MacKinnon",
  title =        "The asymptotic expansions of {Hankel} transforms and
                 related integrals",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "515--527",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0230 (Integral transforms); C1130 (Integral
                 transforms)",
  corpsource =   "Defence Res. Establ., Pacific, Victoria, BC, Canada",
  keywords =     "asymptotic expansions; Bessel; functions; Hankel
                 transforms; integrals; transforms",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Manos:1972:CCA,
  author =       "Paul Manos and L. Richard Turner",
  title =        "Constrained {Chebyshev} approximations to some
                 elementary functions suitable for evaluation with
                 floating-point arithmetic",
  type =         "{NASA} Technical Note",
  number =       "TN D-6698",
  institution =  "NASA",
  address =      "Washington, DC, USA",
  pages =        "iii + 68",
  month =        mar,
  year =         "1972",
  bibdate =      "Mon May 22 11:27:24 2006",
  URL =          "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Marino:1972:NAA,
  author =       "D. Marino",
  title =        "New Algorithms for the Approximate Evaluation in
                 Hardware of Binary Logarithms and Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "21",
  number =       "12",
  pages =        "1416--1421",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Thu Sep 08 08:05:51 1994",
  acknowledgement = ack-nj,
}

@Article{Olver:1972:NBR,
  author =       "F. W. J. Olver and D. J. Sookne",
  title =        "Note on Backward Recurrence Algorithms",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "941--947",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290Z (Other numerical methods); C4190 (Other
                 numerical methods)",
  corpsource =   "Univ. Maryland, College Park, MD, USA",
  keywords =     "backward recurrence algorithms; Bessel; Bessel
                 functions; difference equations; functions; recessive
                 solution; second order linear difference equation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Parnes:1972:CZM,
  author =       "R. Parnes",
  title =        "Complex zeros of the modified {Bessel} function
                 {$K_n(Z)$}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "949--953",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "City Univ., New York, NY, USA",
  keywords =     "and zeros; Bessel functions; complex zeros;
                 interpolation; interpolation scheme; iterative;
                 iterative methods; modified Bessel function; poles",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Turunov:1972:EFD,
  author =       "M. Turunov",
  title =        "Elementary functions of a discrete real and complex
                 argument. ({Russian})",
  journal =      "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy",
  volume =       "418 Voprosy Mat.",
  pages =        "263--271, 386",
  year =         "1972",
  MRclass =      "30A95",
  MRnumber =     "50 \#13556",
  MRreviewer =   "G. Berzsenyi",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Baker:1973:PAS,
  author =       "P. W. Baker",
  title =        "Predictive algorithms for some elementary functions in
                 radix $2$",
  journal =      j-ELECT-LETTERS,
  volume =       "9",
  pages =        "493--494",
  year =         "1973",
  CODEN =        "ELLEAK",
  ISBN =         "0013-5194",
  ISBN-13 =      "0013-5194",
  ISSN =         "0013-5194",
  MRclass =      "68A10",
  MRnumber =     "57 \#18203",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Cody:1973:CAP,
  author =       "W. J. Cody and Anthony J. Strecok and Henry C.
                 {Thacher, Jr.}",
  title =        "{Chebyshev} Approximations for the Psi Function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "121",
  pages =        "123--127",
  month =        jan,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65-06 (68-06)",
  MRnumber =     "50 6095",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  keywords =     "Chebyshev approximation; Chebyshev approximations;
                 digamma function; psi function",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ercegovac:1973:REC,
  author =       "M. D. Ercegovac",
  title =        "Radix-16 Evaluation of Certain Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "561--566",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Fettis:1973:CZE,
  author =       "Henry E. Fettis and James C. Caslin and Kenneth R.
                 Cramer",
  title =        "Complex zeros of the error function and of the
                 complementary error function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "401--407",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Wright-Patterson Air Force Base, OH, USA",
  keywords =     "asymptotic formula; complementary error function;
                 complex zeros; error function; errors; first one
                 hundred zeros; function evaluation; poles and zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fettis:1973:SPC,
  author =       "Henry E. Fettis and James C. Caslin and Kenneth R.
                 Cramer",
  title =        "Saddle Points of the Complementary Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "409--412",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Sandia Labs., Albuquerque, NM, USA",
  keywords =     "asymptotic; complementary error function; errors;
                 formula; function evaluation; poles and zeros; saddle
                 points",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Hemker:1973:SDL,
  author =       "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen}
                 and H. L. Oudshoorn and D. T. Winter",
  title =        "Single- and double-length computation of elementary
                 functions",
  number =       "NW 7",
  institution =  "Mathematical Centre",
  address =      "Amsterdam",
  year =         "1973",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib",
  acknowledgement = ack-nhfb,
}

@Article{Linz:1973:NCI,
  author =       "Peter Linz and T. E. Kropp",
  title =        "A note on the computation of integrals involving
                 products of trigonometric and {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "124",
  pages =        "871--872",
  month =        oct,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. California, Davies, CA, USA",
  keywords =     "Bessel functions; computation; integration; numerical;
                 numerical methods; products; trigonometric",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Lozier:1973:BCP,
  author =       "D. W. Lozier and L. C. Maximon and W. L. Sadowski",
  title =        "A bit comparison program for algorithm testing",
  journal =      j-COMP-J,
  volume =       "16",
  number =       "2",
  pages =        "111--117",
  month =        may,
  year =         "1973",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620",
  bibdate =      "Fri Sep 29 08:52:11 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Nat. Bur. Stand., Washington, DC, USA",
  keywords =     "accuracy; algorithm testing; bit comparison program;
                 computer algorithms; program debugging",
  treatment =    "P Practical",
}

@Article{McNolty:1973:SPD,
  author =       "Frank McNolty",
  title =        "Some probability density functions and their
                 characteristic functions",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "123",
  pages =        "495--504",
  month =        jul,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0240 (Probability and statistics); C1140 (Probability
                 and statistics)",
  corpsource =   "Lockheed Palo Alto Res. Lab., CA, USA",
  keywords =     "Bessel function; characteristic functions; functions;
                 hypergeometric function; probability; probability
                 density functions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Amos:1974:CMB,
  author =       "D. E. Amos",
  title =        "Computation of modified {Bessel} functions and their
                 ratios",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "125",
  pages =        "239--251",
  month =        jan,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Sandia Labs., Albuquerque, NM, USA",
  keywords =     "Bessel functions; computation; low order Bessel
                 functions; modified Bessel functions; monotonicity;
                 properties; ratios; recursion; relation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Blair:1974:RCA,
  author =       "J. M. Blair",
  title =        "Rational {Chebyshev} approximations for the modified
                 {Bessel} functions {$I_0(x)$} and {$I_1(x)$}",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "581--583",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy Canada Ltd., Chalk River, Ont., Canada",
  keywords =     "Chebyshev approximation; functions; modified Bessel;
                 nearly best rational approximations; rational Chebyshev
                 approximations; series (mathematics)",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Buschman:1974:FSR,
  author =       "R. G. Buschman",
  title =        "Finite sum representations for partial derivatives of
                 special functions with respect to parameters",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "817--824",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. Wyoming, Laramie, WY, USA",
  keywords =     "Bessel functions; differentiation; finite sum
                 representations; finite sums; functions; G function;
                 Gegenbauer functions; hypergeometric; Legendre; Mellin
                 transformation; partial derivatives; special functions;
                 Whittaker functions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fettis:1974:SAC,
  author =       "Henry E. Fettis",
  title =        "A stable algorithm for computing the inverse error
                 function in the `tail-end' region",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "585--587",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Wright-Patterson Air Force Base, OH, USA",
  keywords =     "function evaluation; inverse error function; iterative
                 algorithm; stability; stable algorithm; tail end
                 region",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Glasser:1974:SDI,
  author =       "M. L. Glasser",
  title =        "Some definite integrals of the product of two {Bessel}
                 functions of the second kind: (order zero)",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "613--615",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Battelle Memorial Inst., Columbus, OH, USA",
  keywords =     "Bessel functions; definite integrals; evaluate;
                 function evaluation; integral representation; order;
                 second kind; zero",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Nasell:1974:IMB,
  author =       "Ingemar Nasell",
  title =        "Inequalities for Modified {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "125",
  pages =        "253--256",
  month =        jan,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Bell Labs., Holmdel, NJ, USA",
  keywords =     "Bessel functions; inequalities; modified Bessel
                 functions; sharp versions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Pisarskii:1974:QCD,
  author =       "A. V. Pisarski{{\u{\i}}} and A. F. Kurgaev and A. V.
                 Palagin",
  title =        "On the question of the convergence of the {``digit by
                 digit''} methods of computing the elementary
                 functions",
  journal =      "Kibernetika (Kiev)",
  volume =       "4",
  pages =        "147--149",
  year =         "1974",
  CODEN =        "KBRNA5",
  ISSN =         "0023-1274",
  MRclass =      "65D20",
  MRnumber =     "53 \#1915",
  MRreviewer =   "V. V. Ivanov",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Wang:1974:UEZ,
  author =       "Paul S. Wang",
  title =        "The Undecidability of the Existence of Zeros of Real
                 Elementary Functions",
  journal =      j-J-ACM,
  volume =       "21",
  number =       "4",
  pages =        "586--589",
  month =        oct,
  year =         "1974",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database,
                 ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib",
  abstract =     "From Richardson's undecidability results, it is shown
                 that the predicate ``there exists a real number such
                 that G(r) equals 0'' is recursively undecidable for
                 G(x) in a class of functions which involves polynomials
                 and the sine function. The deduction follows that the
                 convergence of a class of improper integrals is
                 recursively undecidable.",
  acknowledgement = ack-nhfb,
  classification = "921",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "mathematical techniques",
}

@Article{Baker:1975:MER,
  author =       "P. W. Baker",
  title =        "More efficient radix-$2$ algorithms for some
                 elementary functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "11",
  pages =        "1049--1054",
  month =        nov,
  year =         "1975",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  MRclass =      "68A10",
  MRnumber =     "52 \#7193",
  MRreviewer =   "I. Kaufmann",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nhfb,
}

@TechReport{Brent:1975:MZM,
  author =       "R. P. (Richard P.) Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "26",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  acknowledgement = ack-nhfb,
  keywords =     "Iterative methods (Mathematics)",
  searchkey =    "ti:elementary n1 function",
}

@Article{Carta:1975:LOA,
  author =       "David G. Carta",
  title =        "Low-Order Approximations for the Normal Probability
                 Integral and the Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "856--862",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0260 (Optimisation techniques); B0290R (Integral
                 equations); C1180 (Optimisation techniques); C4180
                 (Integral equations)",
  corpsource =   "Jet Propulsion Lab., California Inst. of Technol.,
                 Pasadena, CA, USA",
  keywords =     "error function; fraction; integral equations; linear
                 minimax problems; linear programming; low; normal
                 probability integral; order approximations;
                 polynomials; rational",
  treatment =    "T Theoretical or Mathematical",
}

@PhdThesis{Epstein:1975:AET,
  author =       "Harvey Irwin Epstein",
  title =        "Algorithms for elementary transcendental function
                 arithmetic",
  school =       "University of Wisconsin",
  address =      "Madison, WI, USA",
  pages =        "409",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  acknowledgement = ack-nhfb,
  annote =       "Typescript. Vita. Thesis (Ph. D.)--University of
                 Wisconsin--Madison, 1975.",
  keywords =     "Functions, Transcendental.; Algorithms.; Functions --
                 Data processing.",
  searchkey =    "ti:elementary n1 function",
}

@Article{Headley:1975:DZG,
  author =       "V. B. Headley and V. K. Barwell",
  title =        "On the distribution of the zeros of generalized {Airy}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "863--877",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290P (Differential equations); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Math., Brock Univ., St. Catherines, Ont.,
                 Canada",
  keywords =     "Bessel functions; boundary rays; differential
                 equations; generalized Airy functions; nonreal zeros;
                 zeros distribution",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Hitotumatu:1975:SRU,
  author =       "Sin Hitotumatu",
  title =        "Some remarks on the unified treatment of elementary
                 functions by microprogramming",
  crossref =     "Miller:1975:TNA",
  pages =        "51--56 (vol. 2)",
  year =         "1975",
  MRclass =      "65D15",
  MRnumber =     "54 \#11733",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Ikebe:1975:ZRC,
  author =       "Yasuhiko Ikebe",
  title =        "The Zeros of Regular {Coulomb} Wave Functions and of
                 Their Derivatives",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "878--887",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290H (Linear algebra); C4140 (Linear algebra)",
  corpsource =   "Centre Numerical Analysis, Univ. of Texas, Austin, TX,
                 USA",
  keywords =     "Bessel function; compact matrix; eigenvalues;
                 eigenvalues and eigenfunctions; function zeros
                 characterisation; matrix algebra; methods; numerical;
                 operators; regular Coulomb wave functions; wave
                 functions; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ng:1975:CCM,
  author =       "Edward W. Ng",
  title =        "A Comparison of Computational Methods and Algorithms
                 for the Complex Gamma Function",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "56--70",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/355626.355635",
  ISSN =         "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "52 #2148",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  acknowledgement = ack-nhfb,
  reviewer =     "R. H. Bartels",
}

@Article{Temme:1975:UAE,
  author =       "N. M. Temme",
  title =        "Uniform asymptotic expansions of the incomplete gamma
                 functions and the incomplete beta function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "132",
  pages =        "1109--1114",
  month =        oct,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Appl. Math., Amsterdam, Netherlands",
  keywords =     "asymptotic expansions; asymptotic series;
                 complementary error function; function approximation;
                 incomplete beta function; incomplete gamma functions;
                 uniform",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Warner:1975:PDG,
  author =       "D. D. Warner",
  title =        "A partial derivative generator",
  type =         "Computing Science Technical Report",
  number =       "28",
  institution =  "Bell Telephone Laboratories",
  address =      "Murray Hill, NJ, USA",
  year =         "1975",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "Theory/auto.diff.bib",
  abstract =     "A precompiler is described which takes a specification
                 of a function as input and produces a Fortran
                 subroutine which will evaluate the component functions
                 and the corresponding Jacobian. Many of the Fortran
                 elementary functions are provided, as well as a
                 facility which allows the user to specify their own
                 differentiation rules.",
  acknowledgement = ack-nhfb,
  keywords =     "differentiation arithmetic; precompiler.",
  referred =     "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].",
}

@Article{Blair:1976:RCA,
  author =       "J. M. Blair and C. A. Edwards and J. H. Johnson",
  title =        "Rational {Chebyshev} approximations for the inverse of
                 the error function",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "136",
  pages =        "827--830",
  month =        oct,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy of Canada Ltd., Chalk River Nuclear
                 Lab., Chalk River, Ont., Canada",
  keywords =     "Chebyshev approximation; Chebyshev approximations;
                 error function; inverse; rational",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brent:1976:FMP,
  author =       "Richard P. Brent",
  title =        "Fast Multiple-Precision Evaluation of Elementary
                 Functions",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "242--251",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "http://doi.acm.org/10.1145/321941.321944",
  ISSN =         "0004-5411",
  MRclass =      "68A20 (68A10)",
  MRnumber =     "52 \#16111",
  MRreviewer =   "Amnon Barak",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  abstract =     "Let $f(x)$ be one of the usual elementary functions
                 ($\exp$, $\log$, $\artan$, $\sin$, $\cosh$, etc.), and
                 let $M(n)$ be the number of single-precision operations
                 required to multiply $n$-bit integers. It is shown that
                 $f(x)$ can be evaluated, with relative error $O(2-n)$,
                 in $O(M(n)log (n))$ operations as $n \rightarrow
                 \infty$, for any floating-point number $x$ (with an
                 $n$-bit fraction) in a suitable finite interval. From
                 the Sch{\"o}nhage--Strassen bound on $M(n)$, it follows
                 that an $n$-bit approximation to $f(x)$ may be
                 evaluated in $O(n \log_(n) \log \log(n))$ operations.
                 Special cases include the evaluation of constants such
                 as $\pi$ $e$, and $e^\pi$. The algorithms depend on the
                 theory of elliptic integrals, using the
                 arithmetic-geometric mean iteration and ascending
                 Landen transformations.",
  acknowledgement = ack-nhfb,
  classification = "723",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "computational complexity; computer arithmetic;
                 computer programming",
}

@InProceedings{Brent:1976:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  crossref =     "Traub:1976:ACC",
  pages =        "151--176",
  year =         "1976",
  MRclass =      "68A20",
  MRnumber =     "54 \#11843",
  MRreviewer =   "Claus-Peter Schnorr",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Buschman:1976:IHF,
  author =       "R. G. Buschman",
  title =        "Inequalities for Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "134",
  pages =        "303--305",
  month =        apr,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math. and Statistics, Univ. of Guelph,
                 Guelph, Ont., Canada",
  keywords =     "Bessel functions; classical orthogonal polynomials;
                 confluence; dominant diagonal matrix; function;
                 functions; Gauss' hypergeometric; hypergeometric
                 functions; Kummer's hypergeometric function; modified
                 Bessel function; principle",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ellacott:1976:RCA,
  author =       "S. Ellacott and Jack Williams",
  title =        "Rational {Chebyshev} Approximation in the Complex
                 Plane",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "13",
  number =       "3",
  pages =        "310--323",
  month =        jun,
  year =         "1976",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Fettis:1976:CR,
  author =       "Henry E. Fettis",
  title =        "Complex Roots of $\sin z = az, \cos z = az$, and
                 $\cosh z = az$",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "135",
  pages =        "541--545",
  month =        jul,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  keywords =     "complex roots; cos z=az; cosh z=az; functional
                 equations; sin z=az",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Kononova:1976:CEF,
  author =       "N. F. Kononova",
  title =        "The computation of elementary functions by means of
                 polynomial approximations by the method of {V. K.
                 Dzjadik}. ({Russian})",
  journal =      "Vy{\v{c}}isl. Prikl. Mat. (Kiev)",
  volume =       "29",
  pages =        "27--39",
  year =         "1976",
  ISSN =         "0321-4117",
  MRclass =      "151. 65D15",
  MRnumber =     "57 \#18026",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Paul:1976:SEF,
  author =       "George Paul and M. Wayne Wilson",
  title =        "Should the Elementary Function Library Be Incorporated
                 Into Computer Instruction Sets?",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "132--142",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  acknowledgement = ack-nhfb,
}

@InCollection{Salimov:1976:OCE,
  author =       "F. I. Salimov",
  booktitle =    "Probabilistic methods and cybernetics",
  title =        "The organization of calculations of elementary
                 functions into tables. ({Russian})",
  volume =       "12--13",
  publisher =    "Kazan. Univ.,",
  address =      "Kazan, USSR",
  pages =        "77--90",
  year =         "1976",
  MRclass =      "65A05",
  MRnumber =     "58 \#31706",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Siemieniuch:1976:PCR,
  author =       "J. L. Siemieniuch",
  title =        "Properties of certain rational approximations to
                 $e^{-z}$",
  journal =      j-BIT,
  volume =       "16",
  number =       "2",
  pages =        "172--191",
  month =        jun,
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01931369",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172",
  acknowledgement = ack-nhfb,
  keywords =     "elefunt; elementary functions",
}

@Article{Danilcenko:1977:ETC,
  author =       "L. S. Danil'{\v{c}}enko",
  title =        "An efficient technique for the construction of
                 rational approximations of elementary functions.
                 ({Russian}) Optimization of computations (approximation
                 and minimization of functions)",
  journal =      "Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint",
  volume =       "18",
  pages =        "17--21",
  year =         "1977",
  MRclass =      "65D15",
  MRnumber =     "80b:65016",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@TechReport{Dzjadyk:1977:TPA,
  author =       "V. K. Dzjadyk and S. F. Karpenko",
  title =        "Tables of polynomials for the approximate solution of
                 elementary functions. ({Russian})",
  number =       "28",
  institution =  "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
  pages =        "28",
  year =         "1977",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "58 \#19016",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@TechReport{Dzyadyk:1977:OPM,
  author =       "V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko
                 and N. F. Kononova",
  title =        "{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami
                 {\`e}lementarnykh funktsi{\u{\i}}.} ({Russian})
                 [Efficient approximation by polynomials of elementary
                 functions]",
  type =         "Preprint",
  number =       "IM-77-21",
  institution =  "Akad. Nauk Ukrain. SSR Inst. Mat.",
  address =      "Kiev, USSR",
  pages =        "42",
  year =         "1977",
  MRclass =      "65L99",
  MRnumber =     "57 \#11075",
  MRreviewer =   "B. D. Donevski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Gautschi:1977:ACC,
  author =       "Walter Gautschi",
  title =        "Anomalous convergence of a continued fraction for
                 ratios of {Kummer} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "140",
  pages =        "994--999",
  month =        oct,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Mathematical analysis); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  keywords =     "apparent; Bessel functions; continued fraction;
                 convergence; differential equations; gamma functions;
                 Kummer functions; wrong limit",
  treatment =    "T Theoretical or Mathematical",
}

@Article{McCarthy:1977:OAE,
  author =       "D. P. McCarthy",
  title =        "The optimal algorithm to evaluate $x^n$ using
                 elementary multiplication methods",
  journal =      j-MATH-COMP,
  volume =       "31",
  number =       "137",
  pages =        "251--256",
  month =        jan,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis); C4240 (Programming and
                 algorithm theory)",
  keywords =     "computational complexity; function evaluation; optimal
                 multiplication chains; symbolic algebraic
                 manipulation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Pexton:1977:RTTa,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations involving
                 spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "139",
  pages =        "752--753",
  month =        jul,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Univ. of California, Livermore, CA, USA",
  keywords =     "Bessel functions; root; spherical Bessel functions;
                 transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Andrews:1978:UEF,
  author =       "M. Andrews and T. Mraz",
  title =        "Unified elementary function generator",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "5",
  pages =        "270--273",
  month =        oct,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Benton:1978:CZT,
  author =       "T. C. Benton and H. D. Knoble",
  title =        "Common Zeros of Two {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "533--535",
  month =        apr,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Pennsylvania State Univ., University Park, PA, USA",
  keywords =     "Bessel functions; common zeros; poles and zeros;
                 positive zeros; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Blair:1978:RCA,
  author =       "J. M. Blair and C. A. Edwards and J. H. Johnson",
  title =        "Rational {Chebyshev} approximations for the {Bickley}
                 functions {$Ki_n(x)$}",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "876--886",
  month =        jul,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy of Canada Ltd., Chalk River, Ont.,
                 Canada",
  keywords =     "approximation; Bessel functions; Bickley functions;
                 Chebyshev approximation; Chebyshev approximations;
                 function; recurrence; relation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Chin:1978:DAD,
  author =       "R. C. Y. Chin and G. W. Hedstrom",
  title =        "A dispersion analysis for difference schemes: tables
                 of generalized {Airy} functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1163--1170",
  month =        oct,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations)",
  corpsource =   "Univ. of California, Lawrence Livermore Lab.,
                 Livermore, CA, USA",
  keywords =     "artificial viscosity; difference schemes; dispersion
                 analysis; function approximation; functions;
                 generalized Airy; linear hyperbolic equation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{DiDonato:1978:AR,
  author =       "A. R. DiDonato",
  title =        "An Approximation for $\int^\infty_x e^{-t^2/2} t^p dt,
                 x > 0, p$ Real",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "271--275",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Naval Surface Weapons Center, Dahlgren, VA, USA",
  keywords =     "integral approximation; integration; numerical
                 analysis",
  treatment =    "A Application; N New Development; T Theoretical or
                 Mathematical",
}

@Article{Dzjadyk:1978:CRP,
  author =       "V. K. Dzjadyk and L. \=I. F{\'\i}lozof",
  title =        "The convergence rate of Pad{\'e} approximants for some
                 elementary functions. ({Russian})",
  journal =      "Mat. Sb. (N.S.)",
  volume =       "107(149)",
  number =       "3",
  pages =        "347--363, 463",
  year =         "1978",
  ISSN =         "0368-8666",
  MRclass =      "41A21 (30E10 41A25)",
  MRnumber =     "81b:41043",
  MRreviewer =   "B. D. Donevski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InProceedings{Frankowski:1978:RME,
  author =       "Krzysztof S. Frankowski",
  title =        "A Realistic Model for Error Estimates in the
                 Evaluation of Elementary Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "70--74",
  year =         "1978",
  MRclass =      "65G05 (65D20)",
  MRnumber =     "80g:65050",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nhfb,
}

@Article{Gautschi:1978:CMB,
  author =       "Walter Gautschi and Josef Slavik",
  title =        "On the computation of modified {Bessel} function
                 ratios",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "865--875",
  month =        jul,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Mathematical analysis); C4130 (Interpolation
                 and function approximation)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  keywords =     "Bessel; Bessel functions; continued fraction;
                 fraction; function approximation; functions; Gauss'
                 continued; modified Bessel function ratios; Perron's
                 continued fraction",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Hull:1978:DFP,
  author =       "T. E. Hull",
  title =        "Desirable Floating-Point Arithmetic and Elementary
                 Functions for Numerical Computation",
  crossref =     "IEEE:1978:PSC",
  pages =        "63--69",
  year =         "1978",
  bibdate =      "Thu Sep 01 12:14:34 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Pexton:1978:RTT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations as functions of
                 a continuous real parameter",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "511--518",
  month =        apr,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  keywords =     "continuous real parameter; equations; roots; spherical
                 Bessel functions; transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Schmidt:1978:EI,
  author =       "Paul W. Schmidt",
  title =        "Evaluation of the Integral $\int^\infty_0
                 \frac{t^{2\alpha-1} J_\nu(x\sqrt{1 + t^2})}{(1 +
                 t^2)^{\alpha+\beta-1}} dt$",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "265--269",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Phys. Dept., Univ. of Missouri, Columbia, MO, USA",
  keywords =     "cylinder diameter distribution; first kind Bessel
                 function; integral evaluation; integration; long
                 circular; neutron scattering data; numerical analysis;
                 power series expansions; recurrence; relations",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Schonfelder:1978:CEE,
  author =       "J. L. Schonfelder",
  title =        "{Chebyshev} expansions for the error and related
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1232--1240",
  month =        oct,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Computer Centre, Univ. of Birmingham, Birmingham, UK",
  keywords =     "approximations; Chebyshev approximation; Chebyshev
                 expansions; error analysis; error function; mappings;
                 NAG library",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Atkins:1979:FSC,
  author =       "D. E. Atkins",
  title =        "{Fourth Symposium on Computer Arithmetic}: crunching
                 with quality and {LSI}",
  journal =      j-COMPUTER,
  volume =       "12",
  number =       "4",
  pages =        "94--97",
  month =        apr,
  year =         "1979",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database",
  abstract =     "Computer arithmetic problems --- faster computation
                 rates and more efficient representations of real
                 numbers --- are considered in the paper. Floating-point
                 arithmetic standardization, novel implementation of
                 basic arithmetic operators, evaluation of elementary
                 functions --- these are the main considerations of the
                 conference review.",
  acknowledgement = ack-nhfb,
  classification = "722; 723",
  journalabr =   "Computer",
  keywords =     "computer arithmetic; computer systems, digital; data
                 processing --- data description; mathematical
                 techniques --- digital arithmetic",
}

@Article{Babb:1979:OEC,
  author =       "Stanley E. {Babb, Jr.} and James W. Cafky",
  title =        "Operational evaluation of certain infinite {Bessel}
                 function integrals",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1033--1039",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "44A99",
  MRnumber =     "80e:44002",
  MRreviewer =   "L. Arteaga",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations)",
  corpsource =   "Dept. of Phys. and Astron., Univ. of Oklahoma, Norman,
                 OK, USA",
  keywords =     "Bessel function integral; integration; numerical
                 methods; Schafheitlin method; trigonometric function;
                 Weber",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Conde:1979:Z,
  author =       "S. Conde and S. L. Kalla",
  title =        "The $\nu $-zeros of ${J}_{-\nu }(x)$",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "145",
  pages =        "423--426",
  month =        jan,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "80b:65021",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4170 (Differential equations); C4190 (Other numerical
                 methods)",
  corpsource =   "Facultad de Ingenieria, Univ. del Zulia, Maracaibo,
                 Venezuela",
  keywords =     "Bessel function; boundary value; boundary-value
                 problems; J/sub -v/(x); partial differential equations;
                 poles and zeros; problems; transforms; v-zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Epstein:1979:STE,
  author =       "H. I. Epstein and B. F. Caviness",
  title =        "A structure theorem for the elementary functions and
                 its application to the identity problem",
  journal =      j-INT-J-COMPUT-INF-SCI,
  volume =       "8",
  number =       "1",
  pages =        "9--37",
  year =         "1979",
  CODEN =        "IJCIAH",
  ISSN =         "0091-7036",
  MRclass =      "12H05 (68C05)",
  MRnumber =     "80k:12032",
  MRreviewer =   "Michael F. Singer",
  bibdate =      "Sat Apr 26 12:45:53 1997",
  acknowledgement = ack-nhfb,
}

@Article{Fettis:1979:AEU,
  author =       "Henry E. Fettis",
  title =        "An asymptotic expansion for the upper percentage
                 points of the $\chi^{2}$-distribution",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1059--1064",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "62E20",
  MRnumber =     "80h:62014",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  keywords =     "approximation theory; asymptotic expansion; upper
                 percentage point",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Gabutti:1979:HPM,
  author =       "Bruno Gabutti",
  title =        "On high precision methods for computing integrals
                 involving {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1049--1057",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D30",
  MRnumber =     "80c:65048",
  MRreviewer =   "K. Jetter",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations); C4240 (Programming and
                 algorithm theory)",
  corpsource =   "Istituto di Calcoli Numerici, Univ. di Torino, Torino,
                 Italy",
  keywords =     "Bessel function integral; computational complexity;
                 exponential function integral; integration",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Glasser:1979:NI,
  author =       "M. L. Glasser",
  title =        "A Note on the Integral $\int^\infty_0t^{2\alpha-1}(1 +
                 t^2)^{1-\alpha-\beta} {J}_\nu(x\sqrt{1 + t^2}) dt$",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "792--793",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A40",
  MRnumber =     "80d:33004",
  MRreviewer =   "T. Erber",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Mathematical analysis); C4180 (Integral
                 equations)",
  corpsource =   "Math. and Computer Sci. Dept., Clarkson Coll. of
                 Technol., Potsdam, NY, USA",
  keywords =     "Bessel functions; hypergeometric series; integral;
                 integral equations",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Johnson:1979:RAF,
  author =       "Donald B. Johnson and Webb Miller and Brian Minnihan
                 and Celia Wrathall",
  title =        "Reducibility Among Floating-Point Graphs",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "739--760",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "80i:65045",
  bibdate =      "Fri Dec 08 11:55:10 1995",
  abstract =     "The graph-theoretic models of this paper can be used
                 to compare the rounding-error behavior of numerical
                 programs. The models follow the approach, popularized
                 by Wilkinson, of assuming independent rounding errors
                 in each arithmetic operation. Models constructed on
                 this assumption are more tractable than would be the
                 case under more realistic assumptions. There are
                 identified two easily tested conditions on programs
                 which guarantee that error analyses are relatively
                 insensitive to the particular graph model employed. The
                 development has the additional benefit of sometimes
                 providing an elementary proof that one program is
                 comparable in stability to another. Examples of such
                 results are given.",
  acknowledgement = ack-nhfb,
}

@Article{Leung:1979:AFE,
  author =       "K. V. Leung and S. S. Ghaderpanah",
  title =        "An application of the finite element approximation
                 method to find the complex zeros of the modified
                 {Bessel} function ${K}_{n}(z)$",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "148",
  pages =        "1299--1306",
  month =        oct,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (33-04)",
  MRnumber =     "80e:65024",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4140 (Linear algebra)",
  corpsource =   "Dept. of Computer Sci., Concordia Univ., Montreal,
                 Que., Canada",
  keywords =     "Bessel function; complex zeros; finite element
                 analysis; finite element approximation method;
                 iterative optimisation scheme; modified; poles and
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Pexton:1979:DRT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Degenerate roots of three transcendental equations
                 involving spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1041--1048",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "loose microfiche suppl. 65H10 (65D20)",
  MRnumber =     "80g:65057",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  keywords =     "function approximation; spherical Bessel function;
                 transcendental equation",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Phillips:1979:FAC,
  author =       "G. Phillips",
  title =        "A fast approximation to the complementary error
                 function for use in fitting gamma-ray peaks",
  journal =      j-NUCL-INSTR-METH,
  volume =       "164",
  number =       "??",
  pages =        "561--563",
  month =        sep,
  year =         "1979",
  CODEN =        "NUIMAL",
  DOI =          "http://dx.doi.org/10.1016/0029-554X(79)90094-6",
  ISSN =         "0029-554X",
  URL =          "http://adsabs.harvard.edu/abs/1979NucIM.164..561P",
  abstract =     "A fast approximation to the complementary error
                 function has been programmed and tested for use in the
                 peak-shape function for fitting peaks in gamma-ray
                 spectra. The function was compared for speed and
                 accuracy on the NRL ASC 7 computer to the mathematical
                 library version of the complementary error
                 function. The approximation has resulted in a 50\% time
                 savings in the computer program HYPERMET which was
                 developed at NRL for automatic analysis of gamma-ray
                 spectra from germanium detectors.",
}

@Article{Risch:1979:APE,
  author =       "Robert H. Risch",
  title =        "Algebraic properties of the elementary functions of
                 analysis",
  journal =      j-AM-J-MATH,
  volume =       "101",
  number =       "4",
  pages =        "743--759",
  year =         "1979",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327",
  MRclass =      "12H05",
  MRnumber =     "81b:12029",
  MRreviewer =   "J. L. Johnson",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Thacher:1979:NBR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "New Backward Recurrences for {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "744--764",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (33A40)",
  MRnumber =     "81b:65019",
  MRreviewer =   "R. G. Langebartel",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Mathematical analysis)",
  corpsource =   "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
                 KY, USA",
  keywords =     "backward recurrences; Bessel functions; converges",
  treatment =    "N New Development; T Theoretical or Mathematical",
}

@InProceedings{Brent:1980:UAE,
  author =       "R. P. Brent",
  title =        "Unrestricted Algorithms for Elementary and Special
                 Functions",
  crossref =     "Lavington:1980:IPP",
  pages =        "613--619",
  year =         "1980",
  bibdate =      "Thu Sep 01 11:55:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Book{Cody:1980:SME,
  author =       "W. J. Cody and W. Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 269",
  year =         "1980",
  ISBN =         "0-13-822064-6",
  ISBN-13 =      "978-0-13-822064-8",
  LCCN =         "QA331 .C635 1980",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Ditkin:1980:CSF,
  author =       "V. A. Ditkin and K. A. Karpov and M. K. Kerimov",
  title =        "The computation of special functions",
  journal =      "U.S.S.R. computational mathematics and mathematical
                 physics",
  volume =       "20",
  number =       "5",
  pages =        "3--12",
  year =         "1980",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.2.1; G.1.2",
  CRclass =      "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Generating functions; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "algorithms; design",
  guideno =      "09092",
  journalabr =   "USSR Comput. Math. Math. Phys",
  jrldate =      "1980",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Fransen:1980:HPV,
  author =       "Arne Frans{\'e}n and Staffan Wrigge",
  title =        "High-precision values of the gamma function and of
                 some related coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "150",
  pages =        "553--566",
  month =        apr,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "81f:65004",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Sat Apr 01 10:12:58 2000",
  bibsource =    "JSTOR database",
  note =         "See addendum and corrigendum
                 \cite{Fransen:1981:ACH}.",
  acknowledgement = ack-nhfb,
}

@TechReport{Fullerton:1980:BEM,
  author =       "L. W. Fullerton",
  title =        "A Bibliography on the Evaluation of Mathematical
                 Functions",
  type =         "Technical report",
  number =       "TM 80-1274-4 and CSTR 86",
  institution =  "Bell Telephone Laboratories",
  address =      "Murray Hill, NJ, USA",
  month =        sep,
  year =         "1980",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  acknowledgement = ack-nhfb,
}

@InProceedings{Maksymiv:1980:APT,
  author =       "E. M. Maksymiv",
  booktitle =    "Differentsialnye Uravneniya i ikh Prilozhen",
  title =        "Approximate properties of {Thiele}'s formula in a
                 class of elementary functions. ({Russian})",
  volume =       "141",
  publisher =    "Vestnik L'vov. Politekhn. Inst.",
  address =      "L'vov, USSR",
  pages =        "55--56",
  year =         "1980",
  MRclass =      "119.65D20",
  MRnumber =     "81i:65021",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InProceedings{Olver:1980:UAG,
  author =       "F. W. J. Olver",
  title =        "Unrestricted algorithms for generating elementary
                 functions",
  crossref =     "Alefeld:1980:PSE",
  pages =        "131--140",
  year =         "1980",
  MRclass =      "65G05 (65D15)",
  MRnumber =     "82b:65034",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InCollection{Tretjakov:1980:PSE,
  author =       "V. A. Tret'jakov",
  booktitle =    "Mathematical analysis and the theory of functions
                 ({Russian}),",
  title =        "On the properties of some elementary functions that
                 are defined on the algebra of bicomplex numbers.
                 ({Russian})",
  publisher =    "Moskov. Oblast. Ped. Inst.,",
  address =      "Moscow, USSR",
  pages =        "99--106",
  year =         "1980",
  MRclass =      "30G35 (78A35)",
  MRnumber =     "82i:30069",
  MRreviewer =   "Toma V. Tonev",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@PhdThesis{vonGudenberg:1980:EAR,
  author =       "J. Wolff {von Gudenberg}",
  title =        "{Einbettung allgemeiner Rechnerarithmetik in Pascal
                 mittels eines Operatorkonzepts und Implementierung der
                 Standardfunktionen mit optimaler Genauigkeit}
                 \toenglish {Embedding a General Computer Arithmetic in
                 Pascal by Means of an Operator Concept and the
                 Implementation of Elementary Functions with Optimal
                 Accuracy} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1980",
  bibdate =      "Sun Oct 25 10:29:29 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Chen:1981:AFD,
  author =       "Gang Chen",
  title =        "An attempt to find the derivatives of elementary
                 functions using the algorithmic language {BCY}.
                 ({Chinese})",
  journal =      "Zhejiang Daxue Xuebao",
  volume =       "3",
  pages =        "141--149",
  year =         "1981",
  MRclass =      "26A09",
  MRnumber =     "714 524",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InProceedings{Davis:1981:EFA,
  author =       "Diane F. Davis",
  title =        "Elementary Functions on an Array Processor",
  crossref =     "IEEE:1981:PIS",
  pages =        "170--178",
  year =         "1981",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz",
  acknowledgement = ack-nhfb,
}

@InProceedings{Farmwald:1981:HBE,
  author =       "P. Michael Farmwald",
  title =        "High Bandwidth Evaluation of Elementary Functions",
  crossref =     "IEEE:1981:PIS",
  pages =        "139--142",
  year =         "1981",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Fransen:1981:ACH,
  author =       "Arne Frans{\'e}n",
  title =        "Addendum and corrigendum to: {``High-precision values
                 of the gamma function and of some related
                 coefficients''} {[Math. Comp. {\bf 34} (1980), no. 150,
                 553--566, MR 81f:65004] by Frans{\'e}n and S. Wrigge}",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "155",
  pages =        "233--235",
  month =        jul,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "82m:65002",
  bibdate =      "Sat Apr 01 10:12:58 2000",
  bibsource =    "JSTOR database",
  note =         "See \cite{Fransen:1980:HPV}.",
  acknowledgement = ack-nhfb,
}

@TechReport{Fullerton:1981:FUMa,
  author =       "L. W. Fullerton",
  title =        "{FNLIB} User's Manual Explanatory Table of Contents",
  type =         "Technical report",
  number =       "CSTR 92",
  institution =  "Bell Telephone Laboratories",
  address =      "Murray Hill, NJ, USA",
  month =        mar,
  year =         "1981",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  acknowledgement = ack-nhfb,
}

@TechReport{Fullerton:1981:FUMb,
  author =       "L. W. Fullerton",
  title =        "{FNLIB} User's Manual",
  type =         "Technical report",
  number =       "CSTR 95",
  institution =  "Bell Telephone Laboratories",
  address =      "Murray Hill, NJ, USA",
  month =        mar,
  year =         "1981",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  acknowledgement = ack-nhfb,
}

@Article{Glasser:1981:CBS,
  author =       "M. L. Glasser",
  title =        "A Class of {Bessel} Summations",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "156",
  pages =        "499--501",
  month =        oct,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A40 (42A16 44A15)",
  MRnumber =     "82j:33015",
  MRreviewer =   "B. D. Agrawal",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math. and Computer Sci., Clarkson Coll.,
                 Potsdam, NY, USA",
  keywords =     "Bessel functions; Bessel summations; infinite series",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hough:1981:API,
  author =       "D. Hough",
  title =        "Application of the proposed {IEEE 754} standard for
                 floating-point arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "70--74",
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1981.bib.gz",
  acknowledgement = ack-nhfb,
  annote =       "Various features of the proposed standard provide an
                 especially convenient environment for programming
                 numerical procedures such as the familiar elementary
                 functions.",
  bydate =       "MB",
  byrev =        "Le",
  country =      "USA",
  date =         "14/06/82",
  descriptors =  "Computer arithmetic; floating point; computation
                 structure; method; application; standard;",
  enum =         "1418",
  language =     "English",
  location =     "RWTH-AC-DFV: Bibl.",
  references =   "10",
  revision =     "21/04/91",
}

@Article{James:1981:LTS,
  author =       "D. G. James",
  title =        "Linear transformations of the second elementary
                 function",
  journal =      j-LIN-MULT-ALGEBRA,
  volume =       "10",
  number =       "4",
  pages =        "347--349",
  year =         "1981",
  CODEN =        "LNMLAZ",
  ISSN =         "0308-1087",
  MRclass =      "15A69 (10C15)",
  MRnumber =     "83c:15023",
  MRreviewer =   "E. W. Ellers",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Markov:1981:ICE,
  author =       "S. M. Markov",
  title =        "On the interval computation of elementary functions",
  journal =      j-C-R-ACAD-BULGARE-SCI,
  volume =       "34",
  number =       "3",
  pages =        "319--322",
  year =         "1981",
  CODEN =        "DBANAD",
  ISSN =         "0366-8681",
  MRclass =      "65G10",
  MRnumber =     "83e:65084",
  MRreviewer =   "David F. Griffiths",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{McCullagh:1981:RCS,
  author =       "Peter McCullagh",
  title =        "A rapidly convergent series for computing $\psi (z)$
                 and its derivatives",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "247--248",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (33A15)",
  MRnumber =     "81m:65028",
  MRreviewer =   "J. Gregor",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Imperial Coll. of Sci. and Technol., London, UK",
  keywords =     "(mathematics); convergence; function evaluation; log
                 gamma function; poles; poles and zeros; rapidly
                 convergent series; series; series expansion; uniformly
                 convergent",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Smith:1981:ERA,
  author =       "J. M. Smith and F. W. J. Olver and D. W. Lozier",
  title =        "Extended-Range Arithmetic and Normalized {Legendre}
                 Polynomials",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "93--105",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65D20 (65G05)",
  MRnumber =     "83a:65017",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  URL =          "http://doi.acm.org/10.1145/355934.355940",
  acknowledgement = ack-nhfb,
  keywords =     "angular momentum; extended-range arithmetic; Legendre
                 polynomials; overflow; underflow",
}

@Article{Steinberg:1981:LSE,
  author =       "D. Steinberg and M. Rodeh",
  title =        "A layout for the shuffle-exchange network with
                 {$O(N^2/\log^{3/2}N)$} area",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-30",
  number =       "12",
  pages =        "977--982",
  month =        dec,
  year =         "1981",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "C.1.2; G.1.2",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Interconnection architectures;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Interconnection architectures;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "design",
  guideno =      "06519",
  jrldate =      "Dec. 1981",
  subject =      "C. Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Vogelius:1981:DRM,
  author =       "M. Vogelius and I. Babuska",
  title =        "On a dimensional reduction method. {II}. Some
                 approximation-theoretic results",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "155",
  pages =        "47--68",
  month =        jul,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.7 Ordinary Differential Equations;
                 G.1.7 Boundary value problems",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems",
  genterm =      "theory",
  guideno =      "09396",
  jrldate =      "July 1981",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Armengou:1982:ASQ,
  author =       "Santiago Zarzuela Armengou",
  title =        "About some questions of differential algebra
                 concerning to elementary functions",
  journal =      "Publ. Sec. Mat. Univ. Aut{\`o}noma Barcelona",
  volume =       "26",
  number =       "1",
  pages =        "5--15",
  year =         "1982",
  MRclass =      "12H05",
  MRnumber =     "86i:12009",
  MRreviewer =   "Michael F. Singer",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@TechReport{Bazarov:1982:EEF,
  author =       "M. B. Bazarov and Yu. I. Shokin and Z. Kh. Yuldashev",
  title =        "On the Evaluation of Elementary Functions in Interval
                 Analysis (In {Russian})",
  institution =  "Applied Mathematics and Mechanics, Tashkent State
                 Univ.",
  address =      "Tashkent, USSR",
  pages =        "26--31",
  year =         "1982",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  acknowledgement = ack-jr,
}

@Article{Belevitch:1982:SIT,
  author =       "V. Belevitch and J. Boersma",
  title =        "On {Stieltjes} integral transforms involving ${\Gamma}
                 $-functions",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "157",
  pages =        "223--226",
  month =        jan,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "44A15 (33A15 33A45)",
  MRnumber =     "83d:44001",
  MRreviewer =   "V. M. Bhise",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0230 (Integral transforms); C1130 (Integral
                 transforms)",
  corpsource =   "Philips Res Lab., Brussels, Belgium",
  keywords =     "Gamma functions; integral transforms; Stieltjes
                 transforms; systematic classification; transforms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Borwein:1982:MNT,
  author =       "P. B. Borwein",
  title =        "On a method of {Newman} and a theorem of {Bernstein}",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "1",
  pages =        "37--41",
  month =        jan,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "06012",
  jrldate =      "Jan. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Chambers:1982:UBF,
  author =       "Ll. G. Chambers",
  title =        "An upper bound for the first zero of {Bessel}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "158",
  pages =        "589--591",
  month =        apr,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A65",
  MRnumber =     "83h:33011",
  MRreviewer =   "S. Ahmed",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cody:1982:TTP,
  author =       "W. J. Cody",
  title =        "Transportable test procedures for elementary function
                 software",
  crossref =     "Mulvey:1982:EMP",
  pages =        "236--247",
  year =         "1982",
  bibdate =      "Thu Nov 17 06:39:08 1994",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib",
  acknowledgement = ack-wjc,
}

@Article{Crick:1982:IRB,
  author =       "S. E. Crick",
  title =        "Inclusion relations for {Bernstein} quasi-analytic
                 classes",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "4",
  pages =        "375--379",
  month =        apr,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms; theory",
  guideno =      "07841",
  jrldate =      "April 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Cruz:1982:ZHF,
  author =       "Andr{\'e}s Cruz and Javier Sesma",
  title =        "Zeros of the {Hankel} function of real order and of
                 its derivative",
  journal =      j-MATH-COMPUT,
  volume =       "39",
  number =       "160",
  pages =        "639--645",
  month =        oct,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A40",
  MRnumber =     "83j:33005",
  MRreviewer =   "S. Ahmed",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "Dept. de Fisica Teorica, Univ. de Zaragoza, Zaragoza,
                 Spain",
  keywords =     "approximation; derivative; evaluation; function
                 approximation; function evaluation; Hankel function;
                 poles and zeros; real order; trajectories; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Danielopoulos:1982:CEP,
  author =       "S. D. Danielopoulos",
  title =        "On the Cost of Evaluating Polynomials and Their
                 Derivatives",
  journal =      j-COMPUTING,
  volume =       "29",
  number =       "4",
  pages =        "373--380",
  year =         "1982",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (printed version), 1436-5057 (electronic
                 version)",
  MRclass =      "68C25 (68C20)",
  MRnumber =     "84a:68039",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "Compendex database; MathSciNet database; ACM Computing
                 Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Ioannina, Greece",
  catcode =      "G.1.2; G.4; G.1.0",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.4 Algorithm analysis; G.1.0 General;
                 G.1.0 Computer arithmetic",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic",
  genterm =      "economics; theory",
  guideno =      "04049",
  journalabr =   "Computing (Vienna/New York)",
  jrldate =      "1982",
  keywords =     "mathematical techniques",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Epstein:1982:UAF,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {I}: function data types",
  journal =      j-MATH-COMP-SIM,
  volume =       "24",
  number =       "1",
  pages =        "1--18",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1; G.1.2; G.1.2",
  CRclass =      "G.1.5 Roots of Nonlinear Equations; G.1.2
                 Approximation; G.1.2 Chebyshev approximation and
                 theory; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms",
  guideno =      "09324",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Epstein:1982:UAI,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {II}: intervals of polynomials",
  journal =      j-MATH-COMP-SIM,
  volume =       "24",
  number =       "1",
  pages =        "19--29",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.1; G.1.0",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.1 Interpolation; G.1.1 Spline and
                 piecewise polynomial interpolation; G.1.0 General;
                 G.1.0 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Error analysis",
  genterm =      "algorithms",
  guideno =      "09325",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Gawronski:1982:ACF,
  author =       "W. Gawronski and U. Stadtm{\"u}ller",
  title =        "Approximation of continuous functions by generalized
                 {Favard} operators",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "4",
  pages =        "384--396",
  month =        apr,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory; algorithms",
  guideno =      "06038",
  jrldate =      "April 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Gordon:1982:RAN,
  author =       "H. T. Gordon",
  title =        "Rough approximation numerical algorithms",
  journal =      j-DDJ,
  volume =       "7",
  number =       "7",
  pages =        "54--56",
  month =        jul,
  year =         "1982",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 http://www.ddj.com/index/author/index.htm",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; G.1.2",
  CRclass =      "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  guideno =      "04547",
  jrldate =      "July 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Greaves:1982:AHM,
  author =       "G. Greaves",
  title =        "An algorithm for the {Hausdorff} moment problem",
  journal =      j-NUM-MATH,
  volume =       "39",
  number =       "2",
  pages =        "231--238",
  month =        aug,
  year =         "1982",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms",
  guideno =      "07489",
  jrldate =      "Aug. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@TechReport{Kahan:1982:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions",
  type =         "Technical Report",
  number =       "PAM-105",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  year =         "1982",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/Matrix.bib.gz",
  acknowledgement = ack-nhfb,
  keywords =     "na, elementary function",
}

@Article{Keener:1982:CLB,
  author =       "L. L. Keener",
  title =        "Characterizing local best {SAIN} approximations",
  journal =      j-J-APPROX-THEORY,
  volume =       "36",
  number =       "1",
  pages =        "55--63",
  month =        sep,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Chebyshev approximation and
                 theory; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Chebyshev approximation and theory;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "06074",
  jrldate =      "Sept. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Lassey:1982:CCI,
  author =       "Keith R. Lassey",
  title =        "On the computation of certain integrals containing the
                 modified {Bessel} function ${I}_{0}(\xi )$",
  journal =      j-MATH-COMPUT,
  volume =       "39",
  number =       "160",
  pages =        "625--637",
  month =        oct,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "83j:65029",
  MRreviewer =   "Walter Gautschi",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 C4130 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Inst. of Nuclear Sci., DSIR, Lower Hutt, New Zealand",
  keywords =     "approximation; approximation theory; convergence of
                 numerical methods; convergent series; function;
                 function approximation; integration; limiting
                 behaviour; modified Bessel; numerical integration;
                 one-dimensional integrals; two-dimensional integrals",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ling:1982:EIH,
  author =       "Chih Bing Ling and Ming Jing Wu",
  title =        "Evaluation of integrals of {Howland} type involving a
                 {Bessel} function",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "157",
  pages =        "215--222",
  month =        jan,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "82m:65003",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); B0290M (Numerical
                 integration and differentiation); C1120 (Mathematical
                 analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Maths., Virginia Polytech. Inst. and State
                 Univ., Blacksburg, VA, USA",
  keywords =     "10D; 20D; accuracy; Bessel function; Bessel functions;
                 Howland type; integrals; integration; tabulated
                 values",
  treatment =    "T Theoretical or Mathematical",
}

@InCollection{Mori:1982:ARS,
  author =       "S. Mori and C. Y. Suen",
  editor =       "Ching Y. Suen and Renato De Mori",
  key =          "Scanners",
  booktitle =    "Computer analysis and perception: vol. I, Visual
                 signals",
  title =        "Automatic recognition of symbols and architecture of
                 the recognition unit",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "17--40",
  year =         "1982",
  ISBN =         "0-8493-6305-5 (vol. 1), 0-8493-6306-3 (vol. 2)",
  ISBN-13 =      "978-0-8493-6305-4 (vol. 1), 978-0-8493-6306-1 (vol.
                 2)",
  LCCN =         "TA1650 .C65 1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bookpages =    "various",
  catcode =      "I.5; G.1.2; C.3; B.7; I.5.4",
  CRclass =      "I.5.2 Design Methodology; G.1.2 Approximation; G.1.2
                 Elementary function approximation; C.3 Signal
                 processing systems; B.7.1 Types and Design Styles;
                 I.5.4 Applications; I.5.4 Signal processing",
  descriptor =   "Computing Methodologies, PATTERN RECOGNITION, Design
                 Methodology; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Computer Systems Organization,
                 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal
                 processing systems; Hardware, INTEGRATED CIRCUITS,
                 Types and Design Styles; Computing Methodologies,
                 PATTERN RECOGNITION, Applications, Signal processing",
  genterm =      "documentation; theory; design",
  guideno =      "01691",
  subject =      "I. Computing Methodologies; I.5 PATTERN RECOGNITION;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; C.
                 Computer Systems Organization; C.3 SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS; B. Hardware; B.7 INTEGRATED
                 CIRCUITS; I. Computing Methodologies; I.5 PATTERN
                 RECOGNITION",
}

@Article{Ollin:1982:CFE,
  author =       "H. Z. Ollin and I. Gerst",
  title =        "Classes of functions with explicit best uniform
                 approximations",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "3",
  pages =        "264--276",
  month =        mar,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "06030",
  jrldate =      "March 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Rack:1982:GIV,
  author =       "H.-J Rack",
  title =        "A generalization of an inequality of {V. Markov} to
                 multivariate polynomials",
  journal =      j-J-APPROX-THEORY,
  volume =       "35",
  number =       "1",
  pages =        "94--97",
  month =        may,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "06047",
  jrldate =      "May 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@PhdThesis{Rockey:1982:DMS,
  author =       "S. A. Rockey",
  title =        "Discrete methods of state approximation, parameter
                 identification and optimal control for hereditary
                 systems",
  type =         "{Ph.D} Thesis",
  school =       "Brown University",
  address =      "Providence, RI",
  pages =        "208",
  year =         "1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.2; G.1.5",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Linear
                 approximation; G.1.5 Roots of Nonlinear Equations;
                 G.1.5 Convergence",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Convergence",
  guideno =      "15449",
  source =       "UMI order no. DA8228325",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Sommer:1982:EPL,
  author =       "M. Sommer",
  title =        "Existence of pointwise-{Lipschitz}-continuous
                 selections of the metric projection for a class of
                 {$Z$}-spaces",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "2",
  pages =        "115--130",
  month =        feb,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "06018",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@PhdThesis{Wang:1982:AME,
  author =       "J.-L Wang",
  title =        "Asymptotically minimax estimators for distributions
                 with increasing failure rate",
  type =         "{Ph.D} Thesis",
  school =       "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "42",
  year =         "1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "design",
  guideno =      "15084",
  source =       "UMI order no. DA8300696",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Whitley:1982:MBI,
  author =       "R. Whitley",
  title =        "{Markov} and {Bernstein}'s inequalities, and compact
                 and strictly singular operators",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "3",
  pages =        "277--285",
  month =        mar,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "06031",
  jrldate =      "March 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Wills:1982:RCA,
  author =       "C. A. Wills and J. M. Blair and P. L. Ragde",
  title =        "Rational {Chebyshev} approximations for the {Bessel}
                 functions ${J}_{0}(x)$, ${J}_{1}(x)$, ${Y}_{0}(x)$,
                 ${Y}_{1}(x)$",
  journal =      j-MATH-COMPUT,
  volume =       "39",
  number =       "160",
  pages =        "617--623",
  month =        oct,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (33A40 41A50)",
  MRnumber =     "83j:65030",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0260 (Optimisation techniques); B0290F (Interpolation
                 and function approximation); C1180 (Optimisation
                 techniques); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "AEG Ltd., Chalk River Nuclear Labs., Ont., Canada",
  keywords =     "approximations; Bessel functions; Chebyshev; Chebyshev
                 approximation; formulae; McMahon asymptotic; minimax
                 techniques; near-minimax rational approximation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Benton:1983:CZT,
  author =       "T. C. Benton",
  title =        "Common Zeros of Two {Bessel} Functions. Part {II}.
                 Approximations and Tables",
  journal =      j-MATH-COMPUT,
  volume =       "41",
  number =       "163",
  pages =        "203--217",
  month =        jul,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A40 (65A05)",
  MRnumber =     "85a:33010",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math., Pennsylvania State Univ., University
                 Park, PA, USA",
  keywords =     "Bessel functions; computer program; poles and zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Cash:1983:BRKa,
  author =       "J. R. Cash",
  title =        "Block {Runge--Kutta} Methods for the Numerical
                 Integration of Initial Value Problems in Ordinary
                 Differential Equations. Part {I}. The Nonstiff Case",
  journal =      j-MATH-COMPUT,
  volume =       "40",
  number =       "161",
  pages =        "175--191",
  month =        jan,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65L05",
  MRnumber =     "84d:65044a",
  MRreviewer =   "W. C. Rheinboldt",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 B0290P (Differential equations); C4130 (Interpolation
                 and function approximation); C4160 (Numerical
                 integration and differentiation); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Math., Imperial Coll., London, UK",
  keywords =     "approximate numerical integration; approximation
                 theory; block implicit formulae; block Runge--Kutta
                 formulae; C. W. Gear; differential equations;
                 equations; first order; formulae; initial value;
                 initial value problems; integration; linear multistep
                 methods; nonstiff problems; order; ordinary
                 differential; problems; Runge--Kutta methods;
                 Runge--Kutta starters; stepsize; stiff problems;
                 systems; variable order; variable order block
                 explicit",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Cody:1983:ASM,
  author =       "W. J. Cody",
  title =        "Algorithm 597: Sequence of Modified {Bessel} Functions
                 of the First Kind",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "242--245",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, MISCELLANEOUS",
  genterm =      "algorithms",
  guideno =      "02186",
  jrldate =      "June 1983",
  keywords =     "algorithms",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation G
                 Mathematics of Computing, MISCELLANEOUS",
}

@Article{Coleman:1983:CEB,
  author =       "J. P. Coleman and A. J. Monaghan",
  title =        "{Chebyshev} expansions for the {Bessel} function
                 ${J}_{n}(z)$ in the complex plane",
  journal =      j-MATH-COMPUT,
  volume =       "40",
  number =       "161",
  pages =        "343--366",
  month =        jan,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65A05 (30E10 33A40 65D20)",
  MRnumber =     "84c:65013",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Cruz:1983:MPR,
  author =       "Andr{\'e}s Cruz and Javier Sesma",
  title =        "Modulus and phase of the reduced logarithmic
                 derivative of the {Hankel} function",
  journal =      j-MATH-COMPUT,
  volume =       "41",
  number =       "164",
  pages =        "597--605",
  month =        oct,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A40 (65H05 81F10)",
  MRnumber =     "85b:33006",
  MRreviewer =   "H. E. Fettis",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Ellacott:1983:FTE,
  author =       "S. W. Ellacott",
  title =        "On the {Faber} transform and efficient numerical
                 rational approximation",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "20",
  number =       "5",
  pages =        "989--1000",
  month =        oct,
  year =         "1983",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  MRclass =      "41A20 (41A21)",
  MRnumber =     "85f:41010",
  MRreviewer =   "Lee L. Keener",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Fukushima:1983:OAA,
  author =       "M. Fukushima",
  title =        "An outer approximation algorithm for solving general
                 convex programs",
  journal =      j-OPER-RES,
  volume =       "31",
  number =       "1",
  pages =        "101--113",
  month =        feb,
  year =         "1983",
  CODEN =        "OPREAI",
  ISSN =         "0030-364X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.4",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.4 Efficiency",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency",
  genterm =      "algorithms; documentation; performance; reliability;
                 theory",
  guideno =      "09992",
  jrldate =      "Jan./Feb. 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE",
}

@Article{Giordano:1983:EAZ,
  author =       "C. Giordano and A. Laforgia",
  title =        "Elementary approximations for zeros of {Bessel}
                 functions",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "9",
  number =       "3",
  pages =        "221--228",
  month =        sep,
  year =         "1983",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "08115",
  jrldate =      "Sept. 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Hasson:1983:C,
  author =       "M. Hasson and O. Shisha",
  title =        "On the condition
                 $\sum^{\infty}_{n=1}n^{p-1}{E}^{*}_{n}(f) < \infty$",
  journal =      j-J-APPROX-THEORY,
  volume =       "39",
  number =       "4",
  pages =        "389--398",
  month =        dec,
  year =         "1983",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  MRclass =      "42A10 (41A10)",
  MRnumber =     "85a:42002",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  note =         "See corrigendum \cite{}.",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "07952",
  jrldate =      "Dec. 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Kershaw:1983:SEW,
  author =       "D. Kershaw",
  title =        "Some extensions of {W. Gautschi}'s inequalities for
                 the gamma function",
  journal =      j-MATH-COMPUT,
  volume =       "41",
  number =       "164",
  pages =        "607--611",
  month =        oct,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A15 (26D20 65D20)",
  MRnumber =     "84m:33003",
  MRreviewer =   "P. Anandani",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Lehnhoff:1983:NPT,
  author =       "H.-G Lehnhoff",
  title =        "A new proof of {Teljakowskii}'s theorem",
  journal =      j-J-APPROX-THEORY,
  volume =       "38",
  number =       "2",
  pages =        "177--181",
  month =        jun,
  year =         "1983",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "07897",
  jrldate =      "June 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Lehnhoff:1983:SPF,
  author =       "H.-G Lehnhoff",
  title =        "A simple proof of a {A.F. Timan}'s theorem",
  journal =      j-J-APPROX-THEORY,
  volume =       "38",
  number =       "2",
  pages =        "172--176",
  month =        jun,
  year =         "1983",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory",
  guideno =      "07896",
  jrldate =      "June 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Little:1983:CCS,
  author =       "F. Little",
  editor =       "Robert E. Barnhill and Wolfgang Boehm",
  booktitle =    "Surfaces in computer aided geometric design:
                 proceedings of a conference held at Mathematisches
                 Forschungsinstitut Oberwolfach, F.R.G., April 25--30,
                 1982, organized by Wolfgang Boehm and Josef Hoschek",
  title =        "Convex combination surfaces",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "99--109",
  year =         "1983",
  ISBN =         "0-444-86550-0",
  ISBN-13 =      "978-0-444-86550-2",
  LCCN =         "T385 .S827 1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bookpages =    "xvi + 215",
  catcode =      "G.1.1; G.1.1; G.1.2",
  CRclass =      "G.1.1 Interpolation; G.1.1 Interpolation formulas;
                 G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Interpolation formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation,
                 Smoothing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory",
  guideno =      "13093",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@TechReport{Lutskii:1983:VFT,
  author =       "G. M. Lutski{\u{\i}} and O. I. Penchev",
  title =        "{\cyr Vychislenie {\`e}lementarnykh
                 funktsi{\u{\i}}metodom tsifra za tsifro{\u{\i}}v
                 izbytochnykh sistemakh schisleniya}. ({Russian})
                 [Calculation of elementary functions by the
                 digit-by-digit method in redundant number systems]",
  type =         "Preprint",
  number =       "83-22",
  institution =  "Akad. Nauk Ukrain. SSR, Inst. Kibernet.",
  address =      "Kiev, USSR",
  pages =        "30",
  year =         "1983",
  MRclass =      "65D20",
  MRnumber =     "719 021",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@TechReport{McCurdy:1983:ACD,
  author =       "A. McCurdy and K. C. Ng and Beresford N. Parlett",
  title =        "Accurate computation of divided differences of the
                 exponential function",
  type =         "Report",
  number =       "PAM-160",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1983",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  acknowledgement = ack-nhfb,
}

@Article{Meister:1983:MYF,
  author =       "B. Meister",
  title =        "On {Murphy}'s yield formula",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "545--548",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "B.7.1; G.1.2",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Input/Output
                 circuits; G.1.2 Approximation; G.1.2 Elementary
                 function approximation",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Input/Output circuits; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "theory; design; reliability",
  guideno =      "06316",
  jrldate =      "Nov. 1983",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS; G. Mathematics
                 of Computing; G.1 NUMERICAL ANALYSIS",
}

@PhdThesis{Monk:1983:SFE,
  author =       "P. B. Monk",
  title =        "Some finite element methods for the approximation of
                 the biharmonic equation",
  type =         "{Ph.D} Thesis",
  school =       "Rutgers University, The State University of New
                 Jersey",
  address =      "New Brunswick, NJ, USA",
  pages =        "242",
  year =         "1983",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.8; G.1.2",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Finite
                 element methods; G.1.2 Approximation; G.1.2 Elementary
                 function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Finite element methods;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "design; algorithms; experimentation",
  guideno =      "15929",
  source =       "UMI order no. DA8308441",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Nave:1983:ITF,
  author =       "Rafi Nave",
  key =          "Nav83",
  title =        "Implementation of Transcendental Functions on a
                 Numerics Processor",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "11",
  pages =        "221--225",
  year =         "1983",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Volz:1983:CAA,
  author =       "H. V{\"o}lz",
  title =        "{{CORDIC} und {\"a}hnliche Algorithmen der elementaren
                 Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}
                 \toenglish {CORDIC and Similar Algorithms for
                 Elementary Functions with Particular Aptitude for
                 Microcomputers} \endtoenglish",
  journal =      j-NACH-ELEK,
  volume =       "33",
  number =       "12",
  pages =        "506--510",
  month =        "????",
  year =         "1983",
  CODEN =        "NTELAP",
  ISSN =         "0323-4657",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Xu:1983:HPG,
  author =       "Xian Yu Xu and Jia Kai Li and Gui Jing Xiong and Guo
                 Liang Xu and Chun Qing Lu",
  title =        "High-precision generation of elementary functions.
                 ({Chinese})",
  journal =      "Appl. Math. Math. Comput.",
  volume =       "6",
  pages =        "24--32",
  year =         "1983",
  MRclass =      "65D20",
  MRnumber =     "86e:65031",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InCollection{Berges:1984:AFE,
  author =       "J. C. Berges",
  booktitle =    "Space mathematics",
  title =        "Arithm{\'e}tique et fonctions {\'e}l{\'e}mentaires sur
                 mini-micro calculateurs. ({French}) [Arithmetic and
                 elementary functions on mini-micro computers]",
  publisher =    "C{\'e}padu{\`e}s",
  address =      "Toulouse, France",
  pages =        "193--229",
  year =         "1984",
  MRclass =      "65-01 (65-04)",
  MRnumber =     "849 200",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Black:1984:NIS,
  author =       "Cheryl M. Black and Robert P. Burton and Thomas H.
                 Miller",
  title =        "The Need for an Industry Standard of Accuracy for
                 Elementary-Function Programs",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "361--366",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "792 000",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; G.1.2; G.4",
  CRclass =      "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.4 Efficiency",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency",
  genterm =      "theory; algorithms; reliability; standardization",
  guideno =      "02897",
  jrldate =      "Dec. 1984",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE",
}

@Article{Borwein:1984:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic-Geometric Mean and Fast Computation of
                 Elementary Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "351--366",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445",
  MRclass =      "65D20 (26A09)",
  MRnumber =     "86d:65029",
  MRreviewer =   "S. Conde",
  bibdate =      "Mon Jan 20 10:31:25 MST 1997",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  abstract =     "We produce a self contained account of the
                 relationship between the Gaussian arithmetic-geometric
                 mean iteration and the fast computation of elementary
                 functions. A particularly pleasant algorithm for pi is
                 one of the by-products.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
  classification = "921; 723",
  journalabr =   "SIAM Rev",
  keywords =     "arithmetic-geometric mean; calculation of pi;
                 computational methods; elliptic functions; Iterative
                 Methods; mathematical techniques; numerical
                 mathematics",
}

@Article{Fransen:1984:CMM,
  author =       "Arne Frans{\'e}n and Staffan Wrigge",
  title =        "Calculation of the moments and the moment generating
                 function for the reciprocal gamma distribution",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "166",
  pages =        "601--616",
  month =        apr,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (60E10 62E15 65U05)",
  MRnumber =     "86f:65042a",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C1210B (Reliability theory); C4130 (Interpolation and
                 function approximation)",
  corpsource =   "Nat. Defence Res. Inst., Stockholm, Sweden",
  keywords =     "kurtosis; moment generating function; moments;
                 polynomials; reciprocal gamma distribution; reliability
                 theory; skewness; variance",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Glaeske:1984:LTS,
  author =       "H.-J. Glaeske and O. I. Mari{\v{c}}ev",
  title =        "The {Laguerre} transform of some elementary
                 functions",
  journal =      j-Z-ANAL-ANWEND,
  volume =       "3",
  number =       "3",
  pages =        "237--244",
  year =         "1984",
  ISSN =         "0232-2064",
  MRclass =      "44A15 (34A10)",
  MRnumber =     "86a:44005",
  MRreviewer =   "Ram Kishore Saxena",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Laforgia:1984:FIG,
  author =       "Andrea Laforgia",
  title =        "Further Inequalities for the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "166",
  pages =        "597--600",
  month =        apr,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A15",
  MRnumber =     "85i:33001",
  MRreviewer =   "H. E. Fettis",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math., Univ. of Torino, Torino, Italy",
  keywords =     "gamma function; inequalities; polynomials",
  treatment =    "T Theoretical or Mathematical",
}

@Article{McCurley:1984:EE,
  author =       "Kevin S. McCurley",
  title =        "Explicit Estimates for $\theta (x; 3, l)$ and $\psi
                 (x; 3, l)$",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "165",
  pages =        "287--296",
  month =        jan,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "11N56",
  MRnumber =     "85g:11085",
  MRreviewer =   "G. J. Rieger",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Maths., Michigan State Univ., East Lansing,
                 MI, USA",
  keywords =     "arithmetic progressions; Chebyshev approximation;
                 Chebyshev functions; Dirichlet L-; explicit estimates;
                 functions; prime number; theorem; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Newman:1984:ABS,
  author =       "J. N. Newman",
  title =        "Approximations for the {Bessel} and {Struve}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "43",
  number =       "168",
  pages =        "551--556",
  month =        oct,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (33A40)",
  MRnumber =     "86c:65021",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C1120 (Mathematical analysis); C4130 (Interpolation and
                 function approximation)",
  corpsource =   "Dept. of Ocean Eng., MIT, Cambridge, MA, USA",
  keywords =     "accuracy; Bessel functions; function approximation;
                 functions; IBM PC computer; minimax; polynomial
                 approximations; polynomials; rational-fraction
                 approximations; single-precision computations; Struve",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Ng:1984:DAA,
  author =       "K. C. Ng",
  title =        "Contributions to the computation of the matrix
                 exponential",
  type =         "Report",
  number =       "PAM-212",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        feb,
  year =         "1984",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  note =         "Based on the author's Ph.D. thesis.",
  acknowledgement = ack-nhfb,
  keywords =     "$\exp(Bt)$",
}

@Article{Nishimoto:1984:TFD,
  author =       "Katsuyuki Nishimoto",
  title =        "Tables of fractional differintegrations of elementary
                 functions",
  journal =      "J. College Engrg. Nihon Univ. Ser. B",
  volume =       "25",
  pages =        "41--46",
  year =         "1984",
  ISSN =         "0285-6182",
  MRclass =      "30E20 (26A33)",
  MRnumber =     "85f:30065",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Piessens:1984:SEF,
  author =       "R. Piessens",
  title =        "A Series Expansion for the First Positive Zero of the
                 {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "165",
  pages =        "195--197",
  month =        jan,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A40 (65D20)",
  MRnumber =     "84m:33014",
  MRreviewer =   "M. E. Muldoon",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database; Theory/Comp.Alg.1.bib",
  acknowledgement = ack-nhfb,
  annote =       "Gives explicit series for first positive zero for 4
                 terms, using REDUCE.",
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Computer Sci., Univ. of Leuven, Heverlee,
                 Belgium",
  keywords =     "Bessel functions; poles and zeros; positive zero;
                 Reduce; series (mathematics); series expansion",
  treatment =    "T Theoretical or Mathematical",
}

@Article{vonGudenberg:1984:BMG,
  author =       "J. Wolff {von Gudenberg}",
  title =        "{Berechnung maximal genauer Standardfunktionen mit
                 einfacher Mantissenl{\"a}nge} \toenglish {Computation
                 of Maximally Accurate Elementary Functions Using Simple
                 Mantissa Length} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "26",
  number =       "5",
  pages =        "230--238",
  month =        oct,
  year =         "1984",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sun Oct 25 10:29:27 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Wrigge:1984:NMG,
  author =       "Staffan Wrigge",
  title =        "A note on the moment generating function for the
                 reciprocal gamma distribution",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "166",
  pages =        "617--621",
  month =        apr,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (60E10 62E15 65U05)",
  MRnumber =     "86f:65042b",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Nat. Defence Res. Inst., Stockholm, Sweden",
  keywords =     "Euler-Maclaurin expansion; moment generating function;
                 polynomials; reciprocal gamma distribution",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Akrivis:1985:ENC,
  author =       "G. Akrivis",
  title =        "The error norm of certain {Gaussian} quadrature
                 formulae",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "513--519",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D32",
  MRnumber =     "87a:65051",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Math. Inst., Munchen Univ., West Germany",
  keywords =     "error analysis; error functional; error norm; function
                 approximation; Gaussian quadrature formulae;
                 integration; weight functions; wide class",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Frenzen:1985:NAE,
  author =       "C. L. Frenzen and R. Wong",
  title =        "A note on asymptotic evaluation of some {Hankel}
                 transforms",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "537--548",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "41A60 (44A15 65R10)",
  MRnumber =     "87c:41024",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0230 (Integral transforms); B0290Z (Other numerical
                 methods)C1130 (Integral transforms); C4190 (Other
                 numerical methods)",
  corpsource =   "Dept. of Math., British Columbia Univ., Vancouver, BC,
                 Canada",
  keywords =     "asymptotic expansion; Bessel function; Bessel
                 functions; growth condition; Hankel transforms;
                 meromorphic function; transforms",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Gal:1985:CEF,
  author =       "Shmuel Gal",
  title =        "Computing Elementary Functions: {A} New Approach for
                 Achieving High Accuracy and Good Performance",
  crossref =     "Miranker:1985:ASC",
  pages =        "1--16",
  year =         "1985",
  bibdate =      "Sat Nov 09 07:42:53 2002",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Hull:1985:PRV,
  author =       "T. E. Hull and A. Abrham",
  title =        "Properly Rounded Variable Precision Square Root",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "229--237",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65D15 (65G05)",
  MRnumber =     "87a:65041",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/214413.html;
                 http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/",
  abstract =     "The square root function presented here returns a
                 properly rounded approximation to the square root of
                 its argument, or it raises an error condition if the
                 argument is negative. {\em Properly rounded} means
                 rounded to the nearest, or to nearest even in case of a
                 tie. It is {\em variable precision} in that it is
                 designed to return a $p$-digit approximation to a
                 $p$-digit argument, for any $p$ \$>\$ 0. (Precision $p$
                 means $p$ decimal digits.) The program and the analysis
                 are valid for all $p$ \$>\$ 0, but current
                 implementations place some restrictions on $p$.",
  acknowledgement = ack-nhfb,
  catcode =      "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0",
  CRclass =      "G.4 Algorithm analysis; G.4 Verification; G.1.0
                 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.4 Certification and testing; G.1.0 General; G.1.0
                 Error analysis",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis; Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Verification; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Error
                 analysis",
  genterm =      "algorithms; verification",
  guideno =      "02789",
  jrldate =      "Sept. 1985",
  keywords =     "algorithms; verification",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Error analysis. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}

@Article{Kravchuk:1985:ACE,
  author =       "V. R. Kravchuk",
  title =        "Approximation of certain elementary functions by
                 rational functions of order $(n,2)$. ({Russian})",
  journal =      "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
  volume =       "18",
  pages =        "7--40",
  year =         "1985",
  MRclass =      "41A25 (41A10)",
  MRnumber =     "87b:41017",
  MRreviewer =   "R. Smarzewski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Kravchuk:1985:EAE,
  author =       "V. R. Kravchuk",
  title =        "Effective approximation of elementary functions by
                 rational polynomials of order $(n,1)$. ({Russian})",
  journal =      "Ukrain. Mat. Zh.",
  volume =       "37",
  number =       "2",
  pages =        "175--180, 270",
  year =         "1985",
  MRclass =      "41A20 (41A25)",
  MRnumber =     "86h:41013",
  MRreviewer =   "Miguel A. Jim{\'e}nez Pozo",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Lazard:1985:PFD,
  author =       "Daniel Lazard",
  title =        "Primitives des fonctions {\'e}l{\'e}mentaires
                 (d'apr{\`e}s {Risch} et {Davenport}). ({French})
                 [Primitives of elementary functions (following {Risch}
                 and {Davenport})] {Seminar Bourbaki, Vol. 1983/84, No.
                 121-122}",
  journal =      "Ast{\'e}risque",
  volume =       "121--122",
  pages =        "295--308",
  year =         "1985",
  MRclass =      "12H05 (12-04)",
  MRnumber =     "86k:12010",
  MRreviewer =   "J. H. Davenport",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Milgram:1985:GIE,
  author =       "M. S. Milgram",
  title =        "The Generalized Integro-Exponential Function",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "443--458",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A70 (65D15)",
  MRnumber =     "86c:33024",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "AECL, Chalk River, Ont., Canada",
  keywords =     "exponential function; exponential integral;
                 first-order functions; function; function
                 approximation; function evaluation; generalized
                 integro-; incomplete gamma; minimax; rational minimax
                 approximations; techniques",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Muller:1985:DBC,
  author =       "Jean-Michel Muller",
  title =        "Discrete basis and computation of elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "34",
  number =       "9",
  pages =        "857--862",
  year =         "1985",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  MRclass =      "65D20 (65V05)",
  MRnumber =     "87e:65016",
  MRreviewer =   "D. Zwick",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InCollection{Muller:1985:RNR,
  author =       "Jean-Michel Muller",
  booktitle =    "Seminar on number theory, 1984--1985 (Talence,
                 1984/1985),",
  title =        "Repr{\'e}sentation des nombres r{\'e}els et calcul des
                 fonctions {\'e}l{\'e}mentaires. ({French})
                 [Representation of real numbers and calculation of
                 elementary functions]",
  volume =       "12",
  publisher =    "Univ. Bordeaux {I}",
  address =      "Talence, France",
  pages =        "22",
  year =         "1985",
  MRclass =      "26-04 (11B13 11B34 26A09)",
  MRnumber =     "87k:26001",
  MRreviewer =   "S. L. Segal",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
  remark =       "From the MRreview: ``About one third of the paper is
                 devoted to algorithms for calculating quantities like
                 square root, exponential, logarithm, or trigonometric
                 funtions, using discrete bases. Indeed, the major
                 motivation for the present paper is obtaining simple
                 algorithms which can easily be realized by
                 hardware.''",
}

@TechReport{Parlett:1985:DAA,
  author =       "Beresford N. Parlett and K. C. Ng",
  title =        "Development of an accurate algorithm for {$\exp(Bt)$}",
  type =         "Technical Report",
  number =       "PAM-294",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        aug,
  year =         "1985",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  acknowledgement = ack-nhfb,
}

@Article{Pereira:1985:ECF,
  author =       "N. Costa Pereira",
  title =        "Estimates for the {Chebyshev} function $\psi(x)-\theta
                 (x)$",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "169",
  pages =        "211--221",
  month =        jan,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "11A25 (11N45 11Y35 33A70)",
  MRnumber =     "86k:11005",
  bibdate =      "Thu Jun 15 07:26:46 2000",
  bibsource =    "JSTOR database",
  note =         "See corrigendum \cite{Pereira:1987:CEC}.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  keywords =     "Chebyshev approximation; Chebyshev function",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Spijker:1985:SRS,
  author =       "M. N. Spijker",
  title =        "Stepsize restrictions for stability of one-step
                 methods in the numerical solution of initial value
                 problems",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "377--392",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65L20 (65M10)",
  MRnumber =     "86j:65106",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "A0260 (Numerical approximation and analysis); A0560
                 (Transport processes: theory); B0290F (Interpolation
                 and function approximation); B0290P (Differential
                 equations); C4130 (Interpolation and function
                 approximation); C4170 (Differential equations); C7320
                 (Physics and chemistry computing)",
  corpsource =   "Inst. of Appl. Math. and Comput. Sci., Leiden Univ.,
                 Netherlands",
  keywords =     "convection; convergence of numerical methods;
                 differential equations; diffusion;
                 diffusion-convection; error growth; initial value
                 problems; iterative methods; numerical solution;
                 partial; problem; stability of one-step methods;
                 stepsize restrictions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Agarwal:1986:NSV,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "New Scalar and Vector Elementary Functions for the
                 {IBM System\slash 370}",
  journal =      j-IBM-JRD,
  volume =       "30",
  number =       "2",
  pages =        "126--144",
  month =        mar,
  year =         "1986",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "840 341",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "Compendex database",
  note =         "See clarification \cite{Agarwal:1987:CNS}.",
  abstract =     "Algorithms have been developed to compute short-and
                 long-precision elementary functions: SIN, COS, TAN,
                 COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
                 ATAN2, and CABS, in scalar (28 functions) and vector
                 (22 functions) mode. They have been implemented as part
                 of the new VS FORTRAN library recently announced along
                 with the IBM 3090 Vector Facility. These algorithms are
                 essentially table-based algorithms. An important
                 feature of these algorithms is that they produce
                 bitwise-identical results on scalar and vector
                 System\slash 370 machines. Of these, for five functions
                 the computed value result is always the correctly
                 rounded value of the infinite-precision result. For the
                 rest of the functions, the value returned is one of the
                 two floating-point neighbors bordering the
                 infinite-precision result, which implies exact results
                 if they are machine-representable. For the five
                 correctly rounded elementary functions, scalar and
                 vector algorithms are designed independently to
                 optimize performance in each case.",
  acknowledgement = ack-nhfb,
  classification = "723",
  journalabr =   "IBM J Res Dev",
  keywords =     "algorithms; Algorithms; computer metatheory; computer
                 programming; computer programming languages ---
                 fortran; design; elementary functions; fortran library;
                 IBM System/370; infinite-precision result; measurement;
                 performance; table-based algorithms",
  subject =      "C.4 Computer Systems Organization, PERFORMANCE OF
                 SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms \\ F.3.3 Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
                 of Program Constructs, Functional constructs \\ C.1.2
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Array and vector processors",
}

@Article{Bustoz:1986:GFI,
  author =       "Joaquin Bustoz and Mourad E. H. Ismail",
  title =        "On Gamma Function Inequalities",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "659--667",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A15 (26D20)",
  MRnumber =     "87m:33002",
  MRreviewer =   "G. Gasper",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1130 (Integral transforms); C1140Z (Other and
                 miscellaneous)",
  corpsource =   "Dept. of Math., Arizona State Univ., Tempe, AZ, USA",
  keywords =     "gamma function inequalities; infinite divisibility;
                 Laplace; Laplace transforms; monotonic functions;
                 probability; probability distributions; quotients;
                 transforms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Clenshaw:1986:GEL,
  author =       "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
                 and P. R. Turner",
  title =        "Generalized Exponential and Logarithmic Functions",
  journal =      j-COMP-MATH-APPL-B,
  volume =       "12B",
  number =       "5--6",
  pages =        "1091--1101",
  month =        "????",
  year =         "1986",
  CODEN =        "CMAPDK",
  ISSN =         "0886-9561",
  MRclass =      "33A70 (39B10 65G05)",
  MRnumber =     "MR0871348 (88a:33027)",
  bibdate =      "Fri Jul 09 06:27:26 2004",
  acknowledgement = ack-nhfb,
}

@Article{Evans:1986:RIU,
  author =       "D. J. Evans and G. M. Megson",
  title =        "{Romberg} integration using systolic arrays",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "3",
  number =       "4",
  pages =        "289--304",
  month =        oct,
  year =         "1986",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "11019",
  catcode =      "G.1.1; G.1.2",
  CRclass =      "G.1.1 Interpolation; G.1.1 Extrapolation; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Extrapolation; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory; design; algorithms",
  guideno =      "1986-10554",
  journalabbrev = "Parallel Comput.",
  jrldate =      "Oct. 1986",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{FernandezVelicia:1986:HPA,
  author =       "F. J. {Fern{\'a}ndez Velicia}",
  title =        "High-precision analytic approximations for the
                 {Fermi-Dirac} functions by means of elementary
                 functions",
  journal =      "Phys. Rev. A (3)",
  volume =       "34",
  number =       "5",
  pages =        "4387--4395",
  year =         "1986",
  CODEN =        "PLRAAN",
  ISSN =         "1050-2947",
  MRclass =      "33A70 (82A05)",
  MRnumber =     "MR869021 (88b:33024)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review. A. Third Series",
}

@InProceedings{Gal:1986:CEF,
  author =       "Shmuel Gal",
  title =        "Computing elementary functions: a new approach for
                 achieving high accuracy and good performance",
  crossref =     "Miranker:1986:ASC",
  pages =        "1--16",
  year =         "1986",
  MRclass =      "65D20",
  MRnumber =     "868 283",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gustavson:1986:FEF,
  author =       "F. G. Gustavson",
  title =        "Fast Elementary Function Algorithms for 370 Machines",
  crossref =     "Miranker:1986:ASC",
  pages =        "17--17",
  year =         "1986",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Misc/MPG/lncs235.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Hull:1986:VPE,
  author =       "T. E. Hull and A. Abrham",
  title =        "Variable Precision Exponential Function",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "79--91",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65D15 (65D20)",
  MRnumber =     "863 786",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/6498.html;
                 http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/",
  acknowledgement = ack-nhfb,
  bibno =        "91",
  content =      "algorithms; verification; THEORY",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.4 Algorithm analysis; G.4
                 Certification and testing; G.4 Verification",
  CRnumber =     "1986-02428",
  descriptor =   "mathematics of computing, numerical analysis,
                 approximation, elementary function approximation;
                 mathematics of computing, mathematical software,
                 algorithm analysis; mathematics of computing,
                 mathematical software, certification and testing;
                 mathematics of computing, mathematical software,
                 verification",
  fortitle =     "ACM Trans. Math. Softw.",
  genterm =      "June 1986",
  guideno =      "2",
  keywords =     "algorithms; theory; verification",
  review =       "ACM CR 8702-0091",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification.",
  waffil =       "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE;
                 G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE;
                 G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE",
}

@Article{Muller:1986:MDC,
  author =       "Jean-Michel Muller",
  title =        "Une m{\'e}thodologie du calcul hardware des fonctions
                 {\'e}l{\'e}mentaires. ({French}) [{A} methodology for
                 the hardware computation of elementary functions]",
  journal =      j-MATH-MODEL-NUM-ANA,
  volume =       "20",
  number =       "4",
  pages =        "667--695",
  year =         "1986",
  CODEN =        "RMMAEV",
  ISSN =         "0764-583X",
  MRclass =      "65D20 (41-04)",
  MRnumber =     "88h:65043",
  MRreviewer =   "E. W. Cheney",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Reichel:1986:PAU,
  author =       "L. Reichel",
  title =        "On polynomial approximation in the uniform norm by the
                 discrete least squares method",
  journal =      j-BIT,
  volume =       "26",
  number =       "3",
  pages =        "350--368",
  month =        jan,
  year =         "1986",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "12404",
  catcode =      "G.1.2; G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Least squares
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation, Spline
                 and piecewise polynomial approximation",
  genterm =      "algorithms",
  guideno =      "1986-03278",
  jrldate =      "Jan. 1986",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{S:1986:CEF,
  author =       "A. S. Kuz'menko and K. I. Rogozin",
  title =        "Calculation of elementary functions in a number system
                 with arbitrary basis on the basis of order-differential
                 transformations. ({Russian})",
  journal =      "Prace Nauk. Inst. Cybernet. Tech. Politech.
                 Wroc{\l}aw. Ser. Konfer.",
  volume =       "74",
  number =       "31",
  pages =        "259--262",
  year =         "1986",
  MRclass =      "65G99 (65D20)",
  MRnumber =     "894 691",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Shore:1986:AID,
  author =       "Haim Shore",
  title =        "An approximation for the inverse distribution function
                 of a combination of random variables, with an
                 application to operating theatres",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "23",
  number =       "3",
  pages =        "157--181",
  year =         "1986",
  CODEN =        "JSCSAJ",
  ISSN =         "0094-9655",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Ban-llan University, Israel",
  bibno =        "5358",
  catcode =      "G.3; G.m; G.1.2; G.2.1; J.3; G.3",
  content =      "The author worked on a project to predict the
                 percentage of time that operations are carried out
                 relative to the time that the operating theater is
                 available. The numerator of the percentage is a
                 weighted sum of the times required to carry out
                 different kinds of operations, where the weights are
                 the numbers of operations of each kind to be performed.
                 Since different kinds of operations have different mean
                 times, this sum has a skewed distribution.\par

                 Based on the Central Limit Theorem, the normal
                 distribution is the most widely used approximation to
                 the distribution of a weighted sum of random variables.
                 However, this approximation is not very good if the sum
                 has a skewed distribution.\par

                 In a separate paper [1], the author derived an
                 alternative approximation based on the first four
                 moments of the sum. In the present paper, he applies
                 this approximation to the operating theater problem by
                 estimating the moments of the times of the different
                 kinds of operations. The paper also contains a Monte
                 Carlo comparison of the normal approximation with the
                 proposed approximation for four underlying
                 distributions of the sum.",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.2.1 Combinatorics;
                 G.2.1 Generating functions; J.3 Health; G.3
                 Probabilistic algorithms (including Monte Carlo)",
  CRnumber =     "8612-1109",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 MISCELLANEOUS; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Generating functions;
                 Computer Applications, LIFE AND MEDICAL SCIENCES,
                 Health; Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo)",
  genterm =      "algorithms; measurement",
  journalabbrev = "J. Stat. Comput. Simul.",
  jrldate =      "1986",
  reviewer =     "M. Snyder",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.m
                 MISCELLANEOUS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
                 DISCRETE MATHEMATICS; J. Computer Applications; J.3
                 LIFE AND MEDICAL SCIENCES; G. Mathematics of Computing;
                 G.3 PROBABILITY AND STATISTICS",
}

@Article{Skeel:1986:CVS,
  author =       "Robert D. Skeel",
  title =        "Construction of Variable-Stepsize Multistep Formulas",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "503--510, S45--S52",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65L05",
  MRnumber =     "87j:65080",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4110 (Error analysis in numerical methods); C4170
                 (Differential equations)",
  corpsource =   "Dept. of Comput. Sci., Illnois Univ., Urbana, IL,
                 USA",
  keywords =     "Adams formula; adaptable multistep methods;
                 backward-differentiation; differential equations; error
                 analysis; estimation; first Dahlquist barrier; fixed
                 leading coefficient method; fixed-coefficient methods;
                 fixed-stepsize; formula; formula changing; initial
                 value; interpolatory methods; local error; minimum
                 storage variable-stepsize; multistep formula; Nordsieck
                 stepsize changing technique; problems; step methods;
                 variable; variable coefficient methods; variable-order
                 family of variable-coefficient formulas",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Skeel:1986:SCV,
  author =       "Robert D. Skeel",
  title =        "Supplement to Construction of Variable-Stepsize
                 Multistep Formulas",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "S45--S52",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Temme:1986:DIC,
  author =       "N. M. Temme",
  title =        "A double integral containing the modified {Bessel}
                 function: asymptotics and computation",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "683--691",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33A40 (41A60 65D30)",
  MRnumber =     "87m:33006",
  MRreviewer =   "S. D. Bajpai",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Centre for Math. and Comput. Sci., Amsterdam,
                 Netherlands",
  keywords =     "distribution function; double integral; error
                 analysis; error function; integral; integration;
                 modified Bessel function; normal; polynomials;
                 probability; series (mathematics); series expansions;
                 two-dimensional",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Zaritskaya:1986:ACE,
  author =       "Z. V. Zaritskaya and A. I. Shva{\u{\i}} and P. \=E.
                 Antonyuk",
  title =        "Approximation of certain elementary functions in the
                 metric ${L}$. ({Russian})",
  journal =      "Vestnik L'vov. Politekhn. Inst.",
  volume =       "202",
  pages =        "38--40",
  year =         "1986",
  MRclass =      "149.41A10 (33A10)",
  MRnumber =     "87j:41030",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Agarwal:1987:CNS,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "Clarification: {``New scalar and vector elementary
                 functions for the IBM System/370''} [{IBM J. Res.
                 Develop. {\bf 30} (1986), no. 2, 126--144}]",
  journal =      j-IBM-JRD,
  volume =       "31",
  number =       "2",
  pages =        "274--274",
  year =         "1987",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "MR894626",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  note =         "See \cite{Agarwal:1986:NSV}.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Business Machines Corporation. Journal
                 of Research and Development",
}

@PhdThesis{Braune:1987:HSF,
  author =       "K. Braune",
  title =        "{Hochgenaue Standardfunktionen f{\"u}r reelle und
                 komplexe Punkte und Intervalle in beliebigen
                 Gleitpunktrastern} \toenglish {High-Accuracy Elementary
                 Functions for Real and Complex Points and Intervals in
                 Arbitrary Floating-Point Systems} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Crandall:1987:EFE,
  author =       "R. E. Crandall and J. P. Buhler",
  title =        "Elementary function expansions for {Madelung}
                 constants",
  journal =      j-J-PHYS-A,
  volume =       "20",
  number =       "16",
  pages =        "5497--5510",
  year =         "1987",
  CODEN =        "JPHAC5",
  ISSN =         "0305-4470",
  MRclass =      "82A60 (82-08)",
  MRnumber =     "MR924725 (88m:82034)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Physics. A. Mathematical and General",
}

@Article{Dunham:1987:PMAa,
  author =       "Charles B. Dunham",
  title =        "Provably monotone approximations",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "2",
  pages =        "6--11",
  month =        apr,
  year =         "1987",
  CODEN =        "SNEWD6",
  DOI =          "http://doi.acm.org/10.1145/24936.24938",
  ISSN =         "0163-5778",
  bibdate =      "Tue Apr 12 07:50:15 MDT 2005",
  bibsource =    "http://portal.acm.org/",
  acknowledgement = ack-nhfb,
  keywords =     "theory; verification",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@Article{Dunham:1987:PMAb,
  author =       "Charles B. Dunham",
  title =        "Provably monotone approximations, {II}",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "3",
  pages =        "30--31",
  month =        jul,
  year =         "1987",
  CODEN =        "SNEWD6",
  DOI =          "http://doi.acm.org/10.1145/36318.36323",
  ISSN =         "0163-5778",
  bibdate =      "Tue Apr 12 07:50:15 MDT 2005",
  bibsource =    "http://portal.acm.org/",
  acknowledgement = ack-nhfb,
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@Article{Gervais:1987:RAF,
  author =       "R. Gervais and Q. I. Rahman and G. Schmeisser",
  title =        "Representation and approximation of functions via
                 $(0,2)$-interpolation",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "2",
  pages =        "89--110",
  month =        jun,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "30719",
  catcode =      "G.1.2; G.1.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.1 Interpolation; G.1.1 Spline and
                 piecewise polynomial interpolation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation",
  genterm =      "theory; verification",
  guideno =      "1987-09238",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  crossref =     "Iserles:1987:SAN",
  volume =       "9",
  pages =        "165--211",
  year =         "1987",
  MRclass =      "65E05",
  MRnumber =     "88k:65027",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  series =       "Inst. Math. Appl. Conf. Ser. New Ser.",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Kramer:1987:ISR,
  author =       "W. Kr{\"a}mer",
  title =        "Inverse Standardfunktionen f{\"u}r reelle und komplexe
                 Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
                 f{\"u}r beliebige Datenformate \toenglish {Inverse
                 Elementary Functions for Real and Complex Interval
                 Arguments with {A}-Priori Error Estimates for Arbitrary
                 Data Formats} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@MastersThesis{Liu:1987:BEF,
  author =       "Z. A. Liu",
  title =        "{Berkeley} Elementary Function Test Suite",
  type =         "{M.S.} thesis",
  school =       "Computer Science Division, Department of Electrical
                 Engineering and Computer Science, Univerity of
                 California at Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon Sep 12 23:52:34 1994",
  acknowledgement = ack-nj,
}

@InProceedings{Mathis:1987:EFP,
  author =       "Robert F. Mathis",
  title =        "Elementary Functions Package for {Ada}",
  crossref =     "ACM:1987:UAA",
  pages =        "95--100",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/ada.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Moricz:1987:ACF,
  author =       "Ferenc Moricz and Xianliang Shi",
  title =        "Approximation to continuous functions by {Cesaro}
                 means of double {Fourier} series and conjugate series",
  journal =      j-J-APPROX-THEORY,
  volume =       "49",
  number =       "4",
  pages =        "346--377",
  month =        apr,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "30744",
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Least squares
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation",
  genterm =      "theory; verification",
  guideno =      "1987-09224",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Musielak:1987:AEG,
  author =       "J. Musielak",
  title =        "Approximation of elements of a generalized {Orlicz}
                 sequence space by nonlinear, singular kernels",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "4",
  pages =        "366--372",
  month =        aug,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "30716",
  catcode =      "G.2.1; G.1.5; G.1.2",
  CRclass =      "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.5
                 Roots of Nonlinear Equations; G.1.5 Convergence; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Generating functions; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Convergence; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory; verification",
  guideno =      "1987-09257",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Aug. 1987",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Pereira:1987:CEC,
  author =       "N. Costa Pereira",
  title =        "Corrigendum: {``Estimates for the {Chebyshev} function
                 $\psi(x)-\theta(x)$''} {[Math. Comp. {\bf 44} (1985),
                 no. 169, 211--221, MR 86k:11005]}",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "177",
  pages =        "447--447",
  month =        jan,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "11A25 (11N45 11Y35 33A70)",
  MRnumber =     "87k:11006",
  bibdate =      "Thu Jun 15 07:27:03 2000",
  note =         "See \cite{Pereira:1985:ECF}.",
  acknowledgement = ack-nhfb,
}

@Article{Proinov:1987:NIA,
  author =       "Petko D. Proinov",
  title =        "Numerical integration and approximation of
                 differentiable functions, {II}",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "4",
  pages =        "373--393",
  month =        aug,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "30717",
  catcode =      "G.1.4; G.1.2",
  CRclass =      "G.1.4 Quadrature and Numerical Differentiation; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "theory; verification",
  guideno =      "1987-09258",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Aug. 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Smith:1987:BAM,
  author =       "P. W. Smith and J. J. Swetits",
  title =        "Best approximation by monotone functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "49",
  number =       "4",
  pages =        "398--403",
  month =        apr,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "30747",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory; verification",
  guideno =      "1987-09227",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Spanier:1987:AF,
  author =       "Jerome Spanier and Keith B. Oldham",
  title =        "An Atlas of Functions",
  publisher =    "Hemisphere Publishing Corporation",
  address =      "Washington, DC, USA",
  pages =        "ix + 700",
  year =         "1987",
  ISBN =         "0-89116-573-8, 3-540-17395-1",
  ISBN-13 =      "978-0-89116-573-6, 978-3-540-17395-3",
  LCCN =         "QA331 .S685 1987",
  bibdate =      "Fri Aug 31 16:20:13 MDT 2007",
  bibsource =    "z3950.loc.gov:7090/Voyager",
  price =        "US\$90.00 (est.)",
  acknowledgement = ack-nhfb,
  subject =      "elementary functions; special functions; cognate
                 functions; complementary incomplete gamma function;
                 complementary modulus; complete beta function; complex
                 argument when; cosecant functions; cotangent functions;
                 digamma function; economized polynomial; error function
                 complement; eta numbers; function and its reciprocal;
                 hypergeometric algorithm; important definite integrals;
                 incomplete elliptic integrals; inverse gudermannian
                 function; inverse hyperbolic functions; negative
                 integer order; other definite integrals; parabolic
                 cylinder function; polygamma functions; purely
                 imaginary argument; reciprocal linear function;
                 reflection formula",
}

@Article{Stoyanov:1987:AE,
  author =       "Basil J. Stoyanov and Richard A. Farrell",
  title =        "On the Asymptotic Evaluation of $\int^{\pi/2}_0
                 {J}^2_0(\gamma \sin x) dx$",
  journal =      j-MATH-COMPUT,
  volume =       "49",
  number =       "179",
  pages =        "275--279",
  month =        jul,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "41A60 (65D30)",
  MRnumber =     "88e:41067",
  MRreviewer =   "Roderick Wong",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Analysis); C4180 (Integral equations)",
  corpsource =   "Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD,
                 USA",
  keywords =     "analytical expression; asymptotic behavior; asymptotic
                 evaluation; Bessel functions; first kind; integral;
                 integral equations; order Bessel function; positive
                 parameter; zeroth-",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Tanese:1987:PGA,
  author =       "Reiko Tanese",
  editor =       "John J. Grefenstette",
  booktitle =    "Genetic algorithms and their applications: proceedings
                 of the second International Conference on Genetic
                 Algorithms: July 28--31, 1987 at the Massachusetts
                 Institute of Technology, Cambridge, MA",
  title =        "Parallel genetic algorithms for a hypercube",
  publisher =    "Lawrence Erlbaum Associates, Inc.",
  address =      "Hillsdale, NJ, USA",
  pages =        "177--183",
  year =         "1987",
  ISBN =         "0-8058-0158-8, 0-8058-0159-6 (paperback)",
  ISBN-13 =      "978-0-8058-0158-3, 978-0-8058-0159-0 (paperback)",
  LCCN =         "Q334 .I5561 1987",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  price =        "US\$39.95",
  acknowledgement = ack-nhfb,
  bibno =        "42536",
  bookpages =    "260",
  catcode =      "I.2.6; G.1.0; G.1.2; C.1.2",
  CRclass =      "I.2.6 Learning; I.2.6 Analogies; G.1.0 General; G.1.0
                 Parallel algorithms; G.1.2 Approximation; G.1.2
                 Elementary function approximation; C.1.2 Multiple Data
                 Stream Architectures (Multiprocessors); C.1.2 Parallel
                 processors",
  descriptor =   "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Learning, Analogies; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Parallel algorithms;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Parallel processors",
  genterm =      "algorithms; performance; experimentation",
  guideno =      "1988-16888",
  procdate =     "Sponsored by Amer. Assoc. for AI, Naval Res. Lab. and
                 Bolt Beranek & Newman, July 28-31, 1987",
  procloc =      "Cambridge, MA",
  subject =      "I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; C. Computer Systems Organization;
                 C.1 PROCESSOR ARCHITECTURES",
}

@Article{Thompson:1987:IEF,
  author =       "Peter Thompson",
  title =        "Implementing an Elementary Function Library",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "2",
  pages =        "2--5",
  month =        apr,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  bibno =        "24937",
  catcode =      "G.m; D.3.2",
  CRclass =      "D.3.2 Language Classifications; D.3.2 OCCAM",
  descriptor =   "Mathematics of Computing, MISCELLANEOUS; Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 OCCAM",
  genterm =      "theory; languages",
  guideno =      "1987-03363",
  journalabbrev = "SIGNUM Newsl.",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.m MISCELLANEOUS; D.
                 Software; D.3 PROGRAMMING LANGUAGES",
}

@Article{Timan:1987:DFP,
  author =       "A. F. Timan",
  title =        "Distribution of fractional parts and approximation of
                 functions with singularities by {Bernstein}
                 polynomials",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "2",
  pages =        "167--174",
  month =        jun,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "30725",
  catcode =      "G.1.5; G.1.2",
  CRclass =      "G.1.5 Roots of Nonlinear Equations; G.1.5 Polynomials,
                 methods for; G.1.2 Approximation; G.1.2 Elementary
                 function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Polynomials, methods for;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory; verification",
  guideno =      "1987-09244",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Zwick:1987:BAC,
  author =       "D. Zwick",
  title =        "Best approximation by convex functions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "6",
  pages =        "528--534",
  month =        jul,
  year =         "1987",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "University of Vermont, Vermont, NY",
  bibno =        "43727",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory; verification",
  guideno =      "1988-04405",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "June/July 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Aberth:1988:PNA,
  author =       "Oliver Aberth",
  title =        "Precise Numerical Analysis",
  publisher =    pub-WCB,
  address =      pub-WCB:adr,
  pages =        "x + 225",
  year =         "1988",
  ISBN =         "0-697-06760-2",
  ISBN-13 =      "978-0-697-06760-9",
  LCCN =         "QA297 .A28 1988",
  bibsource =    "file://sunrise/u/sy/beebe/tex/bib/all_brec.bib",
  abstract =     "Aberth addresses elementary issues of precise floating
                 point computations using variable precision range
                 arithmetic. Numbers are represented as a variable
                 precision number $\pm$ a range. Rational arithmetic is
                 also considered. Chapters are devoted to
                 \begin{enumerate} \item rootfinding, \item polynomial
                 rootfinding, \item numerical linear algebra, \item
                 differentiation and integration, and \item ordinary
                 differential equations.\end{enumerate} Differentiation
                 is handled by a codelist approach like [Rall81a], and
                 applications to Taylor series are given. Interval
                 techniques for ordinary differential equations are
                 based on using an {\it a priori\/} bound to capture
                 remainder terms. Several methods are illustrated,
                 including Taylor series methods.",
  acknowledgement = ack-nj,
  comment =      "Text for a one semester, junior level course in
                 numerical analysis. Includes PC disk with software
                 written in PBASIC. Sound introductory level discussion
                 of code lists and error capture techniques.",
  keywords =     "general numerical analysis; interval techniques;
                 differentiation arithmetic; variable precision
                 arithmetic; linear algebra; differentiation;
                 integration; ordinary differential equations.",
}

@Article{Alonso:1988:SCN,
  author =       "Javier Alonso and Carlos Benitez",
  title =        "Some characteristic and non-characteristic properties
                 of inner product spaces",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "318--325",
  month =        dec,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "56052",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "theory; verification",
  guideno =      "1988-10198",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Bloom:1988:LCL,
  author =       "Thomas Bloom",
  title =        "The {Lebesgue} constant for {Lagrange} interpolation
                 in the simplex",
  journal =      j-J-APPROX-THEORY,
  volume =       "54",
  number =       "3",
  pages =        "338--353",
  month =        sep,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "56887",
  catcode =      "G.1.1; G.1.2; G.1.2; G.1.7; G.1.7",
  CRclass =      "G.1.1 Interpolation; G.1.1 Interpolation formulas;
                 G.1.2 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; G.1.7 Ordinary Differential
                 Equations; G.1.7 Convergence and stability; G.1.7
                 Ordinary Differential Equations; G.1.7 Boundary value
                 problems",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Interpolation formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Convergence
                 and stability; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems",
  guideno =      "1988-10170",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Borwein:1988:CFF,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the complexity of familiar functions and numbers",
  journal =      j-SIAM-REVIEW,
  volume =       "30",
  number =       "4",
  pages =        "589--601",
  month =        dec,
  year =         "1988",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "58008",
  catcode =      "G.1.2; F.2.1; F.1.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; F.2.1 Numerical Algorithms and Problems;
                 F.1.3 Complexity Classes",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13907",
  journalabbrev = "SIAM Rev.",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1
                 COMPUTATION BY ABSTRACT DEVICES",
}

@Article{Borwein:1988:PAE,
  author =       "Peter B. Borwein",
  title =        "Pad{\'e} approximants for the $q$-elementary
                 functions",
  journal =      j-CONST-APPROX,
  volume =       "4",
  number =       "4",
  pages =        "391--402",
  year =         "1988",
  ISSN =         "0176-4276",
  MRclass =      "41A21 (33A10 41A20)",
  MRnumber =     "89f:41022",
  MRreviewer =   "Annie A. M. Cuyt",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Cartwright:1988:JTC,
  author =       "Donald I. Cartwright and Krzysztof Kucharski",
  title =        "{Jackson's Theorem} for compact connect {Lie} groups",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "352--359",
  month =        dec,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "56056",
  catcode =      "G.2.m; G.1.2",
  CRclass =      "G.2.m Miscellaneous; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "verification; theory",
  guideno =      "1988-10202",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Cover:1988:DII,
  author =       "Thomas M. Cover and Joy A. Thomas",
  title =        "Determinant inequalities via information theory",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "9",
  number =       "3",
  pages =        "384--392",
  month =        jul,
  year =         "1988",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "58040",
  catcode =      "H.1.1; G.1.3; F.2.1; G.1.2",
  CRclass =      "H.1.1 Systems and Information Theory; H.1.1
                 Information theory; G.1.3 Numerical Linear Algebra;
                 G.1.3 Determinants; F.2.1 Numerical Algorithms and
                 Problems; F.2.1 Computations on matrices; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Information Systems, MODELS AND PRINCIPLES, Systems
                 and Information Theory, Information theory; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Determinants; Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13777",
  journalabbrev = "SIAM J. Matrix Anal. Appl.",
  jrldate =      "July 1988",
  subject =      "H. Information Systems; H.1 MODELS AND PRINCIPLES; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@InProceedings{Davenport:1988:ICF,
  author =       "J. H. Davenport",
  editor =       "N. M. Stephens and M. P. Thorne",
  booktitle =    "Computers in mathematical research: based on the
                 proceedings of a conference organized by the Institute
                 of Mathematics and its Applications on computers in
                 mathematical research, held at University College,
                 Cardiff in September 1986",
  title =        "Integration in closed form",
  volume =       "14",
  publisher =    pub-CLARENDON-PRESS,
  address =      pub-CLARENDON-PRESS:adr,
  year =         "1988",
  ISBN =         "0-19-853620-8",
  ISBN-13 =      "978-0-19-853620-8",
  LCCN =         "QA11.A1 C618 1986",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  price =        "US\$57.50",
  series =       "Institute of Mathematics and its applications
                 conference series, new series",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Bath",
  bibno =        "52474",
  bookpages =    "235",
  catcode =      "J.2; F.2.1; G.1.2; G.1.2; I.2.9; F.2.1",
  CRclass =      "J.2 Mathematics and statistics; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Number-theoretic
                 computations; G.1.2 Approximation; G.1.2 Rational
                 approximation; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; I.2.9 Robotics; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computations in finite
                 fields",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Mathematics and statistics; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Robotics; Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations in finite
                 fields",
  genterm =      "algorithms; theory",
  guideno =      "1988-16247",
  page =         "119--134",
  procdate =     "Sept. 1986",
  procloc =      "Cardiff, Wales",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; I. Computing
                 Methodologies; I.2 ARTIFICIAL INTELLIGENCE; F. Theory
                 of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY",
  waffil =       "Univ. College, Cardiff, Wales; Univ. College, Cardiff,
                 Wales",
}

@Article{Dunham:1988:PMA,
  author =       "Charles B. Dunham",
  title =        "Provably monotone approximations, {III}",
  journal =      j-SIGNUM,
  volume =       "23",
  number =       "1",
  pages =        "10--10",
  month =        jan,
  year =         "1988",
  CODEN =        "SNEWD6",
  DOI =          "http://doi.acm.org/10.1145/43931.43934",
  ISSN =         "0163-5778",
  bibdate =      "Tue Apr 12 07:50:16 MDT 2005",
  bibsource =    "http://portal.acm.org/",
  acknowledgement = ack-nhfb,
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@TechReport{Duprat:1988:EPE,
  author =       "J. Duprat and J. M. Muller",
  title =        "Evaluation of Polynomials and elementary Functions by
                 integrated Circuits",
  number =       "RR698-I",
  institution =  "IMAG",
  address =      "Grenoble, France",
  month =        jan,
  year =         "1988",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/eureca.bib.gz",
  acknowledgement = ack-nhfb,
}

@Article{Duprat:1988:HPE,
  author =       "Jean Duprat and Jean-Michel Muller",
  title =        "Hardwired polynomial evaluation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "291--309",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database",
  acknowledgement = ack-nhfb,
  affiliationaddress = "CNRS, Grenoble, Fr",
  classification = "721; 722; 723; 921; C4130 (Interpolation and
                 function approximation); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Inst. Nat. Polytech. de Grenoble, France",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "computer architecture; computers, digital ---
                 Circuits; digital arithmetic; elementary functions;
                 hardwired polynomial evaluation; mathematical
                 functions; mathematical techniques; Polynomials;
                 polynomials; special-purpose circuits; VLSI
                 implementation; VLSI implementation",
  treatment =    "P Practical",
}

@Article{Feng:1988:AIN,
  author =       "Y. Y. Feng and J. Kozak",
  title =        "An approach to the interpolation of nonuniformly
                 spaced data",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "23",
  number =       "2",
  pages =        "169--178",
  month =        aug,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "56475",
  catcode =      "G.1.1; G.1.2; G.1.7; G.1.1; G.1.4",
  CRclass =      "G.1.1 Interpolation; G.1.1 Spline and piecewise
                 polynomial interpolation; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.7 Ordinary
                 Differential Equations; G.1.7 Boundary value problems;
                 G.1.1 Interpolation; G.1.1 Smoothing; G.1.4 Quadrature
                 and Numerical Differentiation; G.1.4 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Smoothing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Error analysis",
  genterm =      "algorithms; theory",
  guideno =      "1988-10490",
  journalabbrev = "J. Comput. Appl. Math.",
  jrldate =      "August 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Gawronski:1988:ZLT,
  author =       "Wolfgang Gawronski and Ulrich Stadtm{\"u}ller",
  title =        "On the zeros of {Lerch}'s transcendental function of
                 real parameters",
  journal =      j-J-APPROX-THEORY,
  volume =       "53",
  number =       "3",
  pages =        "354--364",
  month =        jun,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Trier, Trier, FRG; Univ. of Ulm, Ulm, FRG",
  bibno =        "49727",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "verification; theory",
  guideno =      "1988-10146",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Heilmann:1988:SSM,
  author =       "Margareta Heilmann",
  title =        "{$L_p$}-saturation of some modified {Bernstein}
                 operators",
  journal =      j-J-APPROX-THEORY,
  volume =       "54",
  number =       "3",
  pages =        "260--273",
  month =        sep,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "56880",
  catcode =      "G.1.2; G.1.9; G.1.7; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.9 Integral Equations; G.1.9
                 Integro-differential equations; G.1.7 Ordinary
                 Differential Equations; G.1.7 Boundary value problems;
                 G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Boundary value problems; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Convergence and stability",
  genterm =      "algorithms; theory",
  guideno =      "1988-10163",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Horwitz:1988:TPF,
  author =       "Alan L. Horwitz and Lee A. Rubel",
  title =        "Totally positive functions and totally bounded
                 functions on $[-1,1]$",
  journal =      j-J-APPROX-THEORY,
  volume =       "52",
  number =       "2",
  pages =        "204--216",
  month =        feb,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Pennsylvania State Univ., University Park; Univ. of
                 Illinois, Urbana",
  bibno =        "49653",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "verification; theory",
  guideno =      "1988-10106",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "February 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Johnsson:1988:DPP,
  author =       "S. L. Johnsson",
  editor =       "J. R. Rice",
  booktitle =    "Mathematical aspects of scientific software",
  title =        "Data parallel programming and basic linear algebra
                 subroutines",
  volume =       "14",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "183--196",
  year =         "1988",
  ISBN =         "0-387-96706-0",
  ISBN-13 =      "978-0-387-96706-6",
  LCCN =         "QA76.76.D47 M366 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  series =       "The IMS volumes in mathematics and its applications",
  acknowledgement = ack-nhfb,
  bibno =        "42725",
  bookpages =    "vi + 208",
  catcode =      "G.1.2; D.1.m; G.4",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; D.1.m Miscellaneous",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Software, PROGRAMMING TECHNIQUES, Miscellaneous;
                 Mathematics of Computing, MATHEMATICAL SOFTWARE",
  genterm =      "theory; algorithms; design; languages",
  guideno =      "1988-02324",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 D. Software; D.1 PROGRAMMING TECHNIQUES; G. Mathematics
                 of Computing; G.4 MATHEMATICAL SOFTWARE",
  waffil =       "Purdue Univ., West Lafayette, IN",
}

@Article{Kowalski:1988:ASP,
  author =       "Marek Kowalski and Waldemar Sielski",
  title =        "Approximation of smooth periodic functions in several
                 variables",
  journal =      j-J-COMPLEXITY,
  volume =       "4",
  number =       "4",
  pages =        "356--372",
  month =        dec,
  year =         "1988",
  CODEN =        "JOCOEH",
  ISSN =         "0885-064X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "56811",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms; verification; theory",
  guideno =      "1988-10411",
  journalabbrev = "J. Complexity",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Kramer:1988:ISF,
  author =       "W. Kramer",
  title =        "Inverse standard functions for real and complex point
                 and interval arguments with dynamic accuracy",
  journal =      j-COMPUTING-SUPPLEMENTUM,
  pages =        "185--212",
  year =         "1988",
  CODEN =        "COSPDM",
  ISSN =         "0344-8029",
  bibdate =      "Thu Dec 14 17:19:38 MST 1995",
  note =         "Computer Arithmetic and Scientific Computation.",
  abstract =     "Algorithms to compute inverse standard functions to
                 arbitrary accuracy with safe error bounds are given.
                 Not only approximation errors but also all possible
                 rounding errors are considered. The desired accuracy of
                 the function as well as the base of the number system
                 used are parameters of the error formula. For
                 implementation it is only assumed that the four
                 elementary arithmetic operations are performed with a
                 certain number of correct digits of the function value.
                 The interval routines are constructed out of the point
                 routines considering the monotonicity behaviour of the
                 functions. The ambiguity of the complex functions is
                 briefly discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Karlsruhe Univ., West Germany",
  classification = "B0290F (Interpolation and function approximation);
                 B0290B (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods)",
  confdate =     "30 Sept.-2 Oct. 1987",
  conflocation = "Karlsruhe, West Germany",
  confsponsor =  "Karlsruhe Univ.; GAMM Committee",
  issue =        "no.6 p. 185-212",
  keywords =     "Interval arguments; Dynamic accuracy; Inverse standard
                 functions; Approximation errors; Rounding errors; Error
                 formula; Monotonicity behaviour",
  language =     "English",
  pubcountry =   "Austria",
  thesaurus =    "Error analysis; Function approximation",
}

@Article{Lou:1988:ETR,
  author =       "Lou van den Dries",
  title =        "On the elementary theory of restricted elementary
                 functions",
  journal =      j-J-SYMBOLIC-LOGIC,
  volume =       "53",
  number =       "3",
  pages =        "796--808",
  year =         "1988",
  CODEN =        "JSYLA6",
  ISSN =         "0022-4812",
  MRclass =      "03C65 (03C40 03C68 12L12)",
  MRnumber =     "89i:03074",
  MRreviewer =   "M. Yasuhara",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Mimachi:1988:PRI,
  author =       "Katsuhisa Mimachi",
  title =        "A proof of {Ramanujan}'s identity by use of loop
                 integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "19",
  number =       "6",
  pages =        "1490--1493",
  month =        nov,
  year =         "1988",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "58904",
  catcode =      "G.1.9; G.1.2; F.2.2",
  CRclass =      "G.1.9 Integral Equations; G.1.9 Integro-differential
                 equations; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Geometrical problems and
                 computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  genterm =      "algorithms; theory",
  guideno =      "1988-13744",
  journalabbrev = "SIAM J. Math. Anal.",
  jrldate =      "Nov. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY",
}

@Article{Olver:1988:EBL,
  author =       "F. W. J. Olver",
  title =        "Error Bounds for Linear Recurrence Relations",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "182",
  pages =        "481--499",
  month =        apr,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65Q05 (39A10 65G05)",
  MRnumber =     "89e:65146",
  MRreviewer =   "B. Choczewski",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Maryland Univ., College Park, MD, USA",
  keywords =     "a posteriori methods; analysis; Bessel function;
                 bounds; computational complexity; difference equations;
                 error; homogeneous second order; Legendre function;
                 linear recurrence relations; monotonic systems;
                 numerical examples; O(r) arithmetic operations;
                 oscillatory systems; realistic error; relations;
                 rounded interval arithmetic",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Polyak:1988:SOM,
  author =       "R. A. Polyak",
  title =        "Smooth optimization methods for minimax problems",
  journal =      j-SIAM-J-CONTROL-OPTIM,
  volume =       "26",
  number =       "6",
  pages =        "1274--1286",
  month =        nov,
  year =         "1988",
  CODEN =        "SJCODC",
  ISSN =         "0363-0129",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "57989",
  catcode =      "G.1.6; G.1.2; F.2.1; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Nonlinear programming; G.1.2
                 Approximation; G.1.2 Minimax approximation and
                 algorithms; F.2.1 Numerical Algorithms and Problems;
                 F.2.1 Computation of transforms; G.1.2 Approximation;
                 G.1.2 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computation of
                 transforms; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13621",
  journalabbrev = "SIAM J. Control Optim.",
  jrldate =      "Nov. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@InCollection{Powell:1988:RBF,
  author =       "J. D. Powell",
  editor =       "D. F. (David Francis) Griffiths and G. A. Watson",
  booktitle =    "Numerical analysis 1987",
  title =        "Radial basis function approximations to polynomials",
  volume =       "170",
  publisher =    "Longman, Inc.",
  address =      "New York, NY, USA",
  pages =        "223--241",
  year =         "1988",
  ISBN =         "0-582-02157-X",
  ISBN-13 =      "978-0-582-02157-0",
  LCCN =         "QA297.N828 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  price =        "US\$54.95",
  series =       "Pitman research notes in mathematics series",
  acknowledgement = ack-nhfb,
  bibno =        "54996",
  bookpages =    "300",
  catcode =      "G.1.2; G.1.2; G.1.9; G.1.1; G.3; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation; G.1.9 Integral
                 Equations; G.1.9 Integro-differential equations; G.1.1
                 Interpolation; G.1.1 Spline and piecewise polynomial
                 interpolation; G.3 Statistical computing; G.1.7
                 Ordinary Differential Equations; G.1.7 Convergence and
                 stability",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations, Integro-differential
                 equations; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation; Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Statistical computing;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability",
  genterm =      "algorithms; performance",
  guideno =      "1988-01246",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
  waffil =       "Univ. of Dundee; Univ. of Dundee",
}

@Article{Proinov:1988:ISF,
  author =       "Petko D. Proinov",
  title =        "Integration of smooth functions and
                 $\phi$-discrepancy",
  journal =      j-J-APPROX-THEORY,
  volume =       "52",
  number =       "3",
  pages =        "284--292",
  month =        mar,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Plovdiv, Plovdiv, Bulgaria",
  bibno =        "49659",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "verification; theory",
  guideno =      "1988-10111",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "March 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Richardson:1988:NMT,
  author =       "Daniel Richardson",
  title =        "Nonstandard models of the theory of elementary
                 functions of a real variable",
  journal =      j-Z-MATH-LOGIK-GRUNDL-MATH,
  volume =       "34",
  number =       "4",
  pages =        "355--372",
  year =         "1988",
  CODEN =        "ZMLGAQ",
  ISBN =         "0044-3050",
  ISBN-13 =      "0044-3050",
  ISSN =         "0044-3050",
  MRclass =      "03B30 (03C62 03H15 26E35)",
  MRnumber =     "90a:03009",
  MRreviewer =   "Reuven H. Gurevi{\v{c}}",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Ruscheweyh:1988:EST,
  author =       "Stephan Ruscheweyh",
  title =        "Extension of {Szeg{\H{o}}}'s theorem on the sections
                 of univalent functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "19",
  number =       "6",
  pages =        "1442--1449",
  month =        nov,
  year =         "1988",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "58899",
  catcode =      "G.1.2; G.1.9; F.2.2; F.2.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.9 Integral Equations; G.1.9
                 Integro-differential equations; F.2.2 Nonnumerical
                 Algorithms and Problems; F.2.2 Computations on discrete
                 structures; F.2.2 Nonnumerical Algorithms and Problems;
                 F.2.2 Geometrical problems and computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  genterm =      "algorithms; theory",
  guideno =      "1988-13739",
  journalabbrev = "SIAM J. Math. Anal.",
  jrldate =      "Nov. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}

@InProceedings{Schwarz:1988:CLI,
  author =       "Jerry Schwarz",
  title =        "A {C++} Library for Infinite Precision Floating
                 Point",
  crossref =     "USENIX:1988:UPC",
  pages =        "271--281",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "ftp://ftp.uu.net/library/bibliography",
  abstract =     "The Real library supports infinite precision floating
                 point computation in C++. Arbitrary precision rational
                 arithmetic and transcendental functions are
                 supported.",
  acknowledgement = ack-nhfb,
  affiliation =  "AT\&T Bell Laboratories, Murray Hill",
  bookpages =    "362",
  classification = "C6130 (Data handling techniques); C5230 (Digital
                 arithmetic methods)",
  confdate =     "17--21 Oct. 1988",
  conflocation = "Denver, CO, USA",
  keywords =     "C++ library; Infinite precision floating point; Real
                 library; Rational arithmetic; Transcendental
                 functions",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "C language; Digital arithmetic; Object-oriented
                 programming; Subroutines",
}

@InProceedings{Sobczyk:1988:SMA,
  author =       "Kazimierz Sobczyk",
  editor =       "W. Schiehlen and W. Wedig",
  booktitle =    "Analysis and estimation of stochastic mechanical
                 systems",
  title =        "Stochastic modelling and analysis of fatigue",
  volume =       "303",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "269--313",
  year =         "1988",
  ISBN =         "0-387-82058-2",
  ISBN-13 =      "978-0-387-82058-3",
  LCCN =         "TA350.3.I5 no.303; TJ173 .A531 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  series =       "Courses and lectures",
  acknowledgement = ack-nhfb,
  bibno =        "58064",
  bookpages =    "350",
  catcode =      "J.2; I.6.3; G.1.8; G.3; G.1.2; G.1.9",
  CRclass =      "J.2 Engineering; I.6.3 Applications; G.1.8 Partial
                 Differential Equations; G.1.8 Difference methods; G.3
                 Probabilistic algorithms (including Monte Carlo); G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.9 Integral Equations; G.1.9 Integro-differential
                 equations",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Engineering; Computing Methodologies,
                 SIMULATION AND MODELING, Applications; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Difference methods; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Integral Equations,
                 Integro-differential equations",
  genterm =      "algorithms; theory; design; measurement; reliability",
  guideno =      "1988-17476",
  procdate =     "1987",
  procloc =      "International Centre for Mechanical Sciences in
                 Udine",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; I. Computing Methodologies; I.6 SIMULATION
                 AND MODELING; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
  waffil =       "Univ. of Stuttgart; Univ. of Karlsruhe",
}

@Article{Stephens:1988:SCR,
  author =       "A. J. Stephens and H. C. Williams",
  title =        "Some computational results on a problem concerning
                 powerful numbers",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "182",
  pages =        "619--632",
  month =        apr,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "11R11 (11A51 11R27 11Y16 11Y40)",
  MRnumber =     "89d:11091",
  MRreviewer =   "H. J. Godwin",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0210 (Algebra); B0250 (Combinatorial mathematics);
                 C1110 (Algebra); C1160 (Combinatorial mathematics)",
  corpsource =   "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  keywords =     "computational complexity; continued; fractions; free
                 integer; fundamental unit; number theory; positive
                 square-; real quadratic number fields; regulator
                 algorithm Amdahl 5850; step algorithm; time complexity
                 $O(D^{1/4+\epsilon})$",
  treatment =    "T Theoretical or Mathematical; X Experimental",
}

@InProceedings{Stillinger:1988:CPS,
  author =       "Frank H. Stillinger",
  editor =       "Donald G. Truhlar",
  booktitle =    "Mathematical frontiers in computational chemical
                 physics",
  title =        "Collective phenomena in statistical mechanics and the
                 geometry of potential energy hypersurfaces",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "157--173",
  year =         "1988",
  ISBN =         "0-387-96782-6",
  ISBN-13 =      "978-0-387-96782-0",
  LCCN =         "QD455.3.M3 M38 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  note =         "Proceedings of the Workshop on Atomic and Molecular
                 Structure and Dynamics, held June 15--July 24, 1987, at
                 the Institute for Mathematics and Its Applications,
                 University of Minnesota.",
  price =        "US\$36.80",
  series =       "The IMA volumes in mathematics and its applications",
  acknowledgement = ack-nhfb,
  bibno =        "58051",
  bookpages =    "xii + 349",
  catcode =      "J.2; J.2; J.2; F.2.2; G.3; G.1.2",
  CRclass =      "J.2 Physics; J.2 Chemistry; J.2 Engineering; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; G.3 Statistical computing;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Chemistry; Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Engineering; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations; Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical computing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "algorithms; theory",
  guideno =      "1988-17776",
  procdate =     "1982",
  procloc =      "Univ. of Minnesota, Minneapolis",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING; J. Computer Applications; J.2
                 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of
                 Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
  waffil =       "Univ. of Minnesota, Minneapolis",
}

@Article{Sun:1988:SAF,
  author =       "Xiehua Sun",
  title =        "On the simultaneous approximation of functions and
                 their derivatives by the {Szasz-Mirakyan} operator",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "279--288",
  month =        dec,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "56048",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "verification; theory",
  guideno =      "1988-10194",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@TechReport{Tang:1988:PIG,
  author =       "Ping Tak Peter Tang",
  title =        "Portable Implementation of a Generic Exponential
                 Function",
  type =         "Technical report",
  number =       "ANL-88-3",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  year =         "1988",
  bibdate =      "Fri Dec 28 11:27:51 2007",
  acknowledgement = ack-nhfb,
}

@Book{vanRijckevorsek:1988:CCA,
  editor =       "Jan L. A. van Rijckevorsek and Jan de Leeus",
  title =        "Component and correspondence analysis: dimension
                 reduction by functional approximation",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 146",
  year =         "1988",
  ISBN =         "0-471-91847-4",
  ISBN-13 =      "978-0-471-91847-9",
  LCCN =         "QA278.5 .C6571 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  price =        "US\$40",
  series =       "Wiley series in probability and mathematical
                 statistics",
  acknowledgement = ack-nhfb,
  bibno =        "59092",
  catcode =      "G.1.2; G.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.3 Statistical computing",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing",
  genterm =      "theory; algorithms",
  guideno =      "1988-03042",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS",
}

@Article{Wong:1988:AE,
  author =       "R. Wong",
  title =        "Asymptotic Expansion of $\int^{\pi/2}_0
                 {J}^2_\nu(\lambda \cos \theta) d\theta$",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "181",
  pages =        "229--234",
  month =        jan,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "41A60 (33A40)",
  MRnumber =     "89g:41022",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "A0260 (Numerical approximation and analysis); A0270
                 (Computational techniques); C4130 (Interpolation and
                 function approximation); C4160 (Numerical integration
                 and differentiation)",
  corpsource =   "Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  keywords =     "asymptotic expansion; Bessel function; Bessel
                 functions; crystallography; diffraction theory;
                 function approximation; integral; integration",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Ahmed:1989:EEF,
  author =       "H. M. Ahmed",
  title =        "Efficient Elementary Function Generation with
                 Multipliers",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "52--59",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  acknowledgement = ack-nhfb # " and " # ack-nj,
}

@Article{Armbruster:1989:KSD,
  author =       "Dieter Armbruster and John Guckenheimer and Philip
                 Holmes",
  title =        "{Kuramoto-Sivashinsky} dynamics on the center-unstable
                 manifold",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "676--691",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY;
                 Cornell Univ., Ithaca, NY",
  bibno =        "64938",
  catcode =      "G.1.7; G.1.7; G.1.0; J.2; G.1.2; G.1.8",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability; G.1.7 Ordinary Differential
                 Equations; G.1.7 Boundary value problems; G.1.0
                 General; G.1.0 Numerical algorithms; J.2 Physics; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.8 Partial Differential Equations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Physics; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09707",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Avellaneda:1989:OBE,
  author =       "Marco Avellaneda and Graeme W. Milton",
  title =        "Optimal bounds on the effective bulk modulus of
                 polycrystals",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "824--837",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "64947",
  catcode =      "G.1.8; J.2; G.1.2; G.1.6",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Difference
                 methods; J.2 Physics; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.6 Optimization;
                 G.1.6 Constrained optimization",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Difference methods; Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Physics; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09716",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Belaga:1989:TMM,
  author =       "E. G. Belaga",
  title =        "Through the mincing machine with a {Boolean} layer
                 cake: nonstandard computations over {Boolean} circuits
                 in the lower-bounds-to-circuit-size complexity
                 proving",
  journal =      j-ACTA-INFO,
  volume =       "26",
  number =       "4",
  pages =        "381--407",
  month =        feb,
  year =         "1989",
  CODEN =        "AINFA2",
  ISSN =         "0001-5903",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Louis Pasteur, Strasbourg Cedex, France and
                 Univ. su Pisa, Pisa, Italy",
  bibno =        "69310",
  catcode =      "F.4.1; B.6.1; F.1.1; F.1.3; F.2.2; F.1.2; G.1.2;
                 F.2.2",
  CRclass =      "F.4.1 Mathematical Logic; F.4.1 Computational logic;
                 B.6.1 Design Styles; B.6.1 Combinational logic; F.1.1
                 Models of Computation; F.1.1 Unbounded-action devices;
                 F.1.3 Complexity Classes; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Complexity of proof procedures;
                 F.1.2 Modes of Computation; F.1.2 Alternation and
                 nondeterminism; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Computations on discrete
                 structures",
  descriptor =   "Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic, Computational logic;
                 Hardware, LOGIC DESIGN, Design Styles, Combinational
                 logic; Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Unbounded-action
                 devices; Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Complexity Classes; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Complexity of
                 proof procedures; Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Alternation and
                 nondeterminism; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures",
  genterm =      "algorithms; theory",
  guideno =      "1989-03239",
  journalabbrev = "Acta Inf.",
  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.4 MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES; B. Hardware; B.6 LOGIC DESIGN; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; F. Theory of Computation; F.1 COMPUTATION BY
                 ABSTRACT DEVICES; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY",
}

@Article{Birge:1989:SUB,
  author =       "John R. Birge and Roger J. Wets",
  title =        "Sublinear upper bounds for stochastic programs with
                 recourse",
  journal =      j-MATH-PROG,
  volume =       "43",
  number =       "2",
  pages =        "131--149",
  month =        feb,
  year =         "1989",
  CODEN =        "MHPGA4",
  ISSN =         "0025-5610",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Michigan, Ann Arbor; Univ. of California,
                 Davis",
  bibno =        "65226",
  catcode =      "G.1.6; G.1.7; G.3; G.1.6; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.7
                 Ordinary Differential Equations; G.1.7 Convergence and
                 stability; G.3 Probabilistic algorithms (including
                 Monte Carlo); G.1.6 Optimization; G.1.6 Gradient
                 methods; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Convergence and stability; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Gradient
                 methods; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms; theory; performance",
  guideno =      "1989-09042",
  journalabbrev = "Math. Program.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Borwein:1989:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "{Ramanujan}, modular equations, and approximations to
                 $\pi$ or how to compute one billion digits of $\pi$",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "96",
  number =       "3",
  pages =        "201--219",
  month =        mar,
  year =         "1989",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Dalhouise Univ., Halifax; Dalhouise Univ., Halifax",
  bibno =        "65243",
  catcode =      "I.1.2; G.1.2; G.1.8; G.1.4; I.1.3; F.2.1; F.2.1",
  CRclass =      "I.1.2 Algorithms; I.1.2 Algebraic algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.8 Partial Differential Equations; G.1.8 Elliptic
                 equations; G.1.4 Quadrature and Numerical
                 Differentiation; G.1.4 Multiple quadrature; I.1.3
                 Languages and Systems; F.2.1 Numerical Algorithms and
                 Problems; F.2.1 Computation of transforms; F.2.1
                 Numerical Algorithms and Problems; F.2.1
                 Number-theoretic computations",
  descriptor =   "Computing Methodologies, ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Elliptic equations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Multiple quadrature; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Languages and
                 Systems; Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computation of transforms; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations",
  genterm =      "algorithms; theory",
  guideno =      "1989-03459",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "March 1989",
  subject =      "I. Computing Methodologies; I.1 ALGEBRAIC
                 MANIPULATION; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY",
}

@Article{Bos:1989:CPR,
  author =       "L. Bos",
  title =        "A characteristic of points in {$R^2$} having
                 {Lebesgue} function of polynomial growth",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "316--329",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72254",
  catcode =      "F.2.1; G.1.1; G.1.2; F.2.2; G.1.2; G.1.3",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on matrices; G.1.1 Interpolation; G.1.1
                 Interpolation formulas; G.1.2 Approximation; G.1.2
                 Elementary function approximation; F.2.2 Nonnumerical
                 Algorithms and Problems; F.2.2 Geometrical problems and
                 computations; G.1.2 Approximation; G.1.2 Chebyshev
                 approximation and theory; G.1.3 Numerical Linear
                 Algebra; G.1.3 Sparse and very large systems",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation, Interpolation
                 formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Chebyshev approximation and theory;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Sparse and very large systems",
  genterm =      "algorithms; theory",
  guideno =      "1989-07812",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Bronstein:1989:AIE,
  author =       "Manuel Bronstein",
  title =        "An algorithm for the integration of elementary
                 functions",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "378",
  pages =        "491--497",
  year =         "1989",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743",
  MRclass =      "65D30",
  MRnumber =     "91a:65050",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  note =         "EUROCAL '87 (Leipzig, 1987).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bronstein:1989:SRE,
  author =       "M. Bronstein",
  title =        "Simplification of real elementary functions",
  crossref =     "ACM:1989:PAI",
  pages =        "207--211",
  year =         "1989",
  bibdate =      "Tue Sep 17 06:46:18 MDT 1996",
  bibsource =    "ftp://ftp.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author describes an algorithm, based on Risch's
                 real structure theorem, that determines explicitly all
                 the algebraic relations among a given set of real
                 elementary functions. He provides examples from its
                 implementation in the Scratchpad computer algebra
                 system that illustrate the advantages over the use of
                 complex logarithms and exponentials.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., T. J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "Real elementary functions; Real structure theorem;
                 Scratchpad; Computer algebra system",
  language =     "English",
  thesaurus =    "Functions; Mathematics computing; Symbol
                 manipulation",
}

@Article{Cao:1989:ABS,
  author =       "J.-D. Cao and H. H. Gonska",
  title =        "Approximation by {Boolean} sums of positive linear
                 operators. {II}. {Gopengauz}-type estimates",
  journal =      j-J-APPROX-THEORY,
  volume =       "57",
  number =       "1",
  pages =        "77--89",
  month =        apr,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72266",
  catcode =      "G.1.2; G.1.2; G.3; G.2.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Nonlinear approximation;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.3 Statistical computing; G.2.1
                 Combinatorics; G.2.1 Generating functions",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Generating functions",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-07823",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.2 DISCRETE
                 MATHEMATICS",
}

@Article{Chen:1989:EMB,
  author =       "X. R. Chen and P. R. Krishnaiah and W. W. Liang",
  title =        "Estimation of multivariate binary density using
                 orthogonal functions",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "178--186",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Pittsburgh, Pittsburgh, PA; Univ. of
                 Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh,
                 Pittsburgh, PA",
  bibno =        "69313",
  catcode =      "D.3.3; G.3; G.1.3; G.1.2",
  CRclass =      "D.3.3 Language Constructs; D.3.3 Procedures,
                 functions, and subroutines; G.3 Statistical computing;
                 G.1.3 Numerical Linear Algebra; G.1.3 Linear systems
                 (direct and iterative methods); G.1.2 Approximation;
                 G.1.2 Elementary function approximation",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Language Constructs,
                 Procedures, functions, and subroutines; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "algorithms; theory; verification",
  guideno =      "1989-08483",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
                 of Computing; G.3 PROBABILITY AND STATISTICS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Corliss:1989:IIV,
  author =       "George Corliss and Gary Krenz",
  editor =       "L. Gatteschi",
  title =        "Indefinite Integration with Validation",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "375--393",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65D30 (65-04)",
  MRnumber =     "1 062 497",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/76915.html;
                 http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/",
  acknowledgement = ack-nhfb,
  bibno =        "393",
  content =      "ALGORITHMS; THEORY",
  CRclass =      "G.1.4 Quadrature and Numerical Differentiation; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.2 Approximation; G.1.2 Chebyshev approximation and
                 theory",
  CRnumber =     "1989-03199",
  descriptor =   "mathematics of computing, numerical analysis,
                 quadrature and numerical differentiation; mathematics
                 of computing, numerical analysis, approximation,
                 elementary function approximation; mathematics of
                 computing, numerical analysis, approximation, Chebyshev
                 approximation and theory",
  fortitle =     "ACM Trans. Math. Softw.",
  guideno =      "4",
  keywords =     "algorithms; theory",
  review =       "ACM CR 9007-0598",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory.",
  waffil =       "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Dehling:1989:FLI,
  author =       "Herold Dehling",
  title =        "The functional law of the iterated logarithm for {von
                 Mises} functionals and multiple {Wiener} integrals",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "177--189",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of G{\"o}ttingen, G{\"o}ttingen, FRG",
  bibno =        "64336",
  catcode =      "G.3; G.1.9; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.9 Integral Equations;
                 G.1.9 Integro-differential equations; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Integral Equations,
                 Integro-differential equations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08462",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Demirbas:1989:MSE,
  author =       "K. Demirbas",
  title =        "Multidimensional state estimation using stacks for
                 dynamic systems with interference",
  journal =      j-AUTOMATICA,
  volume =       "25",
  number =       "4",
  pages =        "617--621",
  month =        jul,
  year =         "1989",
  CODEN =        "ATCAA9",
  ISSN =         "0005-1098",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72661",
  catcode =      "G.1.2; G.1.2; G.1.3; G.1.5; H.1.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Linear
                 approximation; G.1.3 Numerical Linear Algebra; G.1.3
                 Linear systems (direct and iterative methods); G.1.5
                 Roots of Nonlinear Equations; H.1.1 Systems and
                 Information Theory; H.1.1 Information theory",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods);
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations; Information Systems, MODELS AND
                 PRINCIPLES, Systems and Information Theory, Information
                 theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-03952",
  jrldate =      "July 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; H.
                 Information Systems; H.1 MODELS AND PRINCIPLES",
}

@TechReport{Dritz:1989:RPS,
  author =       "K. W. Dritz",
  title =        "Rationale for the Proposed Standard for a Generic
                 Package of Elementary Functions for {Ada}",
  type =         "Report",
  number =       "ANL-89/2 Rev. 1",
  institution =  "Argonne National Laboratory, Mathematics and Computer
                 Science Division",
  address =      "Argonne, IL, USA",
  pages =        "????",
  month =        oct,
  year =         "1989",
  bibdate =      "Thu Sep 01 12:08:24 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@InProceedings{Duprat:1989:SRA,
  author =       "J. Duprat and Y. Herreros and J.-M. Muller",
  title =        "Some results about on-line computation of functions",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "112--118",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  acknowledgement = ack-nhfb,
}

@Article{Dyn:1989:PEB,
  author =       "N. Dyn and A. Ron",
  title =        "Periodic exponential box splines on a three direction
                 mesh",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "287--296",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72251",
  catcode =      "G.1.2; F.2.2; G.1.2; G.1.2; G.1.2; G.2.1; G.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Spline and piecewise
                 polynomial approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Geometrical problems and
                 computations; G.1.2 Approximation; G.1.2 Chebyshev
                 approximation and theory; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.2 Approximation;
                 G.1.2 Linear approximation; G.2.1 Combinatorics; G.2.1
                 Recurrences and difference equations; G.3 Statistical
                 computing",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Chebyshev approximation and
                 theory; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Mathematics of
                 Computing, DISCRETE MATHEMATICS, Combinatorics,
                 Recurrences and difference equations; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing",
  genterm =      "algorithms; theory; design",
  guideno =      "1989-07809",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing;
                 G.3 PROBABILITY AND STATISTICS",
}

@Article{Eberlein:1989:SAC,
  author =       "E. Eberlein",
  title =        "Strong approximation of continuous time stochastic
                 processes",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "220--235",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Freiburg, Freiburg, W. Germany",
  bibno =        "69316",
  catcode =      "D.4.8; F.1.2; G.1.2",
  CRclass =      "D.4.8 Performance; D.4.8 Stochastic analysis; F.1.2
                 Modes of Computation; F.1.2 Probabilistic computation;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Software, OPERATING SYSTEMS, Performance, Stochastic
                 analysis; Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Probabilistic
                 computation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; performance; theory",
  guideno =      "1989-08486",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "D. Software; D.4 OPERATING SYSTEMS; F. Theory of
                 Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Egger:1989:PAC,
  author =       "A. Egger and R. Huotari",
  title =        "The {Polya} algorithm on convex sets",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "2",
  pages =        "212--216",
  month =        feb,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72242",
  catcode =      "F.2.2; F.2.2; G.1.2; G.1.2; G.1.5",
  CRclass =      "F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Geometrical problems and computations; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2
                 Computations on discrete structures; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.2 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.5 Roots of Nonlinear Equations; G.1.5
                 Convergence",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations; Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Convergence",
  genterm =      "algorithms; theory",
  guideno =      "1989-07801",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Ehrenmark:1989:ONF,
  author =       "Ulf T. Ehrenmark",
  title =        "Overconvergence of the near-field expansion for
                 linearized waves normally incident on a sloping beach",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "799--815",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "64945",
  catcode =      "G.1.7; G.1.2; F.2.1; G.1.2; F.2.2",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability; G.1.2 Approximation; G.1.2
                 Minimax approximation and algorithms; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Geometrical problems and
                 computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Minimax approximation and algorithms;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computation of transforms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09714",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}

@Article{Einmahl:1989:ERK,
  author =       "U. Einmahl",
  title =        "Extensions of results of {Komlos}, {Major}, and
                 {Tusnady} to the multivariate case",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "1",
  pages =        "20--68",
  month =        jan,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. zu Koln, West Germany",
  bibno =        "66700",
  catcode =      "G.3; G.1.2; F.2.1",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computation of transforms",
  genterm =      "algorithms; theory",
  guideno =      "1989-08456",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Jan. 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY",
}

@Article{Epperson:1989:UIM,
  author =       "J. F. Epperson",
  title =        "On the use of iteration methods for approximating the
                 natural logarithm",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "96",
  number =       "9",
  pages =        "831--835",
  month =        nov,
  year =         "1989",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890",
  MRclass =      "26A06 (26A09)",
  MRnumber =     "91a:26002",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "71703",
  catcode =      "G.1.2; G.1.2; K.3.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation; K.3.2 Computer and
                 Information Science Education",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Computing Milieux, COMPUTERS AND
                 EDUCATION, Computer and Information Science Education",
  genterm =      "algorithms; theory",
  guideno =      "1989-03518",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "Nov. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K.
                 Computing Milieux; K.3 COMPUTERS AND EDUCATION",
}

@Article{Ge:1989:OCL,
  author =       "Renpu Ge",
  title =        "Optimal choice of linear interval extension",
  journal =      j-APPL-MATH-COMP,
  volume =       "30",
  number =       "2",
  pages =        "165--189",
  month =        mar,
  year =         "1989",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "64710",
  catcode =      "G.1.6; G.1.2; G.1.2; G.2.1; F.2.2; G.1.2; G.1.1;
                 G.1.0",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Linear approximation; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.1 Combinatorics; G.2.1 Combinatorial algorithms;
                 F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Computations on discrete structures; G.1.2
                 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.1 Interpolation; G.1.1 Difference
                 formulas; G.1.0 General; G.1.0 Numerical algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Linear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Combinatorial algorithms;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Computations on discrete structures;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Minimax approximation and algorithms;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Difference formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-03670",
  journalabbrev = "Appl. Math. Comput.",
  jrldate =      "March 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.2 DISCRETE MATHEMATICS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Gersch:1989:SPT,
  author =       "W. Gersch and G. Kitagawa",
  title =        "Smoothness priors transfer function estimation",
  journal =      j-AUTOMATICA,
  volume =       "25",
  number =       "4",
  pages =        "603--608",
  month =        jul,
  year =         "1989",
  CODEN =        "ATCAA9",
  ISSN =         "0005-1098",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72658",
  catcode =      "G.1.1; G.1.2; G.1.6",
  CRclass =      "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.6 Optimization; G.1.6 Gradient methods",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Smoothing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Gradient methods",
  genterm =      "algorithms; theory",
  guideno =      "1989-03949",
  jrldate =      "July 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InCollection{Glover:1989:THN,
  author =       "Keith Glover",
  editor =       "Jan C. Willems",
  booktitle =    "From data to model",
  title =        "A tutorial on {Hankel}-norm approximation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "26--48",
  year =         "1989",
  ISBN =         "0-387-51571-2",
  ISBN-13 =      "978-0-387-51571-7",
  LCCN =         "QA279 .F76 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "70545",
  bookpages =    "246",
  catcode =      "G.1.2; F.2.1; F.2.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; F.2.1 Numerical Algorithms and Problems;
                 F.2.1 Computations on matrices; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computation of
                 transforms",
  genterm =      "algorithms; theory",
  guideno =      "1989-01692",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
  waffil =       "Univ. of Groningen, Groningen, The Netherlands",
}

@InProceedings{Glynn:1989:OSS,
  author =       "P. W. Glynn",
  editor =       "Edward A. MacNair and Kenneth J. Musselman and Philip
                 Heidelberger",
  booktitle =    "1989 Winter Simulation Conference proceedings:
                 December 4--6, 1989, the Capital Hilton Hotel,
                 Washington, DC",
  title =        "Optimization of stochastic systems via simulation",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "90--105",
  year =         "1989",
  ISBN =         "0-911801-58-8",
  ISBN-13 =      "978-0-911801-58-3",
  LCCN =         "QA76.9.C65 W56 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  note =         "IEEE order no. 89CH2778-9.",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=5823",
  acknowledgement = ack-nhfb,
  bibno =        "76750",
  bookpages =    "xx + 1139",
  catcode =      "I.6.3; G.1.6; G.3; G.1.2",
  CRclass =      "I.6.3 Applications; G.1.6 Optimization; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Applications; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization; Mathematics of Computing,
                 PROBABILITY AND STATISTICS; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; design; performance",
  guideno =      "1989-12012",
  procdate =     "December 4-6, 1989",
  procloc =      "Washington, D. C.",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY
                 AND STATISTICS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Gomes:1989:GGL,
  author =       "M. I. Gomes",
  title =        "Generalized {Gumbel} and likelihood ratio test
                 statistics in the multivariate {GEV} model",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "7",
  number =       "3",
  pages =        "259--267",
  month =        feb,
  year =         "1989",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "70043",
  catcode =      "G.3; G.1.7; I.5.1; G.1.6; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.7 Ordinary Differential
                 Equations; G.1.7 Convergence and stability; I.5.1
                 Models; I.5.1 Statistical; G.1.6 Optimization; G.1.6
                 Nonlinear programming; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Convergence and stability; Computing Methodologies,
                 PATTERN RECOGNITION, Models, Statistical; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Optimization,
                 Nonlinear programming; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; measurement; reliability; theory",
  guideno =      "1989-04403",
  journalabbrev = "Comput. Stat. Data Anal.",
  jrldate =      "Feb. 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; I. Computing Methodologies; I.5 PATTERN
                 RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@InProceedings{Gonzaga:1989:ASL,
  author =       "Cl{\'o}vis C. Gonzaga",
  title =        "An algorithm for solving linear programming programs
                 in {$O(n^3L)$} operations",
  crossref =     "Megiddo:1989:PMP",
  pages =        "1--28",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "74172",
  catcode =      "G.1.6; G.1.2; F.2.1; I.1.2; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on matrices; I.1.2 Algorithms; I.1.2
                 Algebraic algorithms; I.1.2 Algorithms; I.1.2 Analysis
                 of algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms; Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12474",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}

@Article{Guo:1989:RCS,
  author =       "S.-S. Guo and M. K. Khan",
  title =        "On the rate of convergence of some operators on
                 functions of bounded variation",
  journal =      j-J-APPROX-THEORY,
  volume =       "58",
  number =       "1",
  pages =        "90--101",
  month =        jul,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "69424",
  catcode =      "F.2.1; G.1.2",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on polynomials; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; theory",
  guideno =      "1989-07854",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "July 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS",
}

@Article{Hornik:1989:MFN,
  author =       "K. Hornik and M. Stinchcombe and H. White",
  title =        "Multilayer feedforward networks are universal
                 approximators",
  journal =      j-NEURAL-NETWORKS,
  volume =       "2",
  number =       "5",
  pages =        "359--366",
  year =         "1989",
  CODEN =        "NNETEB",
  ISSN =         "0893-6080",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Technisce Univ. Wien, Vienna, Austria; Univ. of
                 California, San Diego; Univ. of California, San Diego",
  bibno =        "70408",
  catcode =      "F.2.1; G.1.2; F.1.1; I.2.4",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 F.1.1 Models of Computation; F.1.1 Unbounded-action
                 devices; I.2.4 Knowledge Representation Formalisms and
                 Methods",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Models of Computation, Unbounded-action devices;
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Knowledge Representation Formalisms and Methods",
  genterm =      "design; performance",
  guideno =      "1989-09273",
  journalabbrev = "Neural Networks",
  jrldate =      "1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1
                 COMPUTATION BY ABSTRACT DEVICES; I. Computing
                 Methodologies; I.2 ARTIFICIAL INTELLIGENCE",
}

@Article{Jeffries:1989:GFA,
  author =       "John S. Jeffries and Donald R. Smith",
  title =        "A {Green} function approach for a singularly perturbed
                 vector boundary-value problem",
  journal =      j-ADV-APPL-MATH,
  volume =       "10",
  number =       "1",
  pages =        "1--50",
  month =        mar,
  year =         "1989",
  CODEN =        "????",
  ISSN =         "0196-8858",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California at San Diego, La Jolla; Univ. of
                 California at San Diego, La Jolla",
  bibno =        "64833",
  catcode =      "G.1.7; G.1.7; F.2.1; G.1.2; G.1.3; G.1.2; G.1.3",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7 Boundary
                 value problems; G.1.7 Ordinary Differential Equations;
                 G.1.7 Convergence and stability; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; G.1.3 Numerical Linear Algebra; G.1.3
                 Eigenvalues; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; G.1.3 Numerical Linear Algebra;
                 G.1.3 Linear systems (direct and iterative methods)",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computation of transforms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Nonlinear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods)",
  genterm =      "algorithms; theory",
  guideno =      "1989-03271",
  journalabbrev = "Adv. Appl. Math.",
  jrldate =      "March 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Kaishev:1989:SSC,
  author =       "A. I. Kaishev",
  title =        "A sharpened scheme for constructing an a posteriori
                 interval extension of an elementary function.
                 ({Russian})",
  journal =      "Voprosy Kibernet. (Moscow)",
  volume =       "149",
  pages =        "14--18",
  year =         "1989",
  ISBN =         "0134-6388",
  ISBN-13 =      "0134-6388",
  MRclass =      "65G10",
  MRnumber =     "91i:65090",
  MRreviewer =   "I. N. Molchanov",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Kogan:1989:GBF,
  author =       "B. J. Kogan",
  title =        "General background of functional memory algorithms",
  journal =      j-TRANS-SOC-COMP-SIM,
  volume =       "5",
  number =       "4",
  pages =        "285--317",
  month =        oct,
  year =         "1989",
  CODEN =        "TSCSEV",
  ISSN =         "0740-6797",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California, Los Angeles",
  bibno =        "69149",
  catcode =      "C.3; G.1.2; G.1.2; E.4",
  CRclass =      "C.3 Signal processing systems; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; G.1.2
                 Approximation; G.1.2 Linear approximation; E.4 Data
                 compaction and compression",
  descriptor =   "Computer Systems Organization, SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS, Signal processing systems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Data, CODING AND
                 INFORMATION THEORY, Data compaction and compression",
  genterm =      "algorithms; design",
  guideno =      "1989-10680",
  journalabbrev = "Trans. Soc. Comput. Simul.",
  jrldate =      "Oct. 1989",
  subject =      "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
                 AND APPLICATION-BASED SYSTEMS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; E. Data; E.4 CODING
                 AND INFORMATION THEORY",
}

@InProceedings{Kojima:1989:PDI,
  author =       "M. Kojima and S. Mizuno and A. Yoshise",
  title =        "A primal-dual interior point algorithm for linear
                 programming",
  crossref =     "Megiddo:1989:PMP",
  pages =        "29--47",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "74173",
  bookpages =    "x + 158",
  catcode =      "G.1.6; F.2.1; G.1.2; F.2.2; F.2.1; I.1.2; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; F.2.1
                 Numerical Algorithms and Problems; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; F.2.1 Numerical Algorithms
                 and Problems; F.2.1 Computations on matrices; I.1.2
                 Algorithms; I.1.2 Algebraic algorithms; I.1.2
                 Algorithms; I.1.2 Analysis of algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations; Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms; Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12475",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}

@Article{Kraaikamp:1989:SEP,
  author =       "Cor Kraaikamp",
  title =        "Statistic and ergodic properties of {Minkowski}'s
                 diagonal continued fraction",
  journal =      j-THEOR-COMP-SCI,
  volume =       "65",
  number =       "2",
  pages =        "197--212",
  day =          "28",
  month =        jun,
  year =         "1989",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Amsterdam Univ., Amsterdam, The Netherlands and Univ.
                 de Provence, Marseille, France",
  bibno =        "70095",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms; theory",
  guideno =      "1989-10594",
  journalabbrev = "Theor. Comput. Sci.",
  jrldate =      "28 June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Kreider:1989:WSA,
  author =       "K. L. Kreider",
  title =        "A wave splitting approach to time dependent inverse
                 scattering for the stratified cylinder",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "932--943",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "64953",
  catcode =      "G.1.7; G.1.2; J.2; J.2; F.2.2; G.1.3; I.1.1",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7 Initial
                 value problems; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; J.2 Physics; J.2 Electronics;
                 F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Geometrical problems and computations; G.1.3 Numerical
                 Linear Algebra; G.1.3 Linear systems (direct and
                 iterative methods); I.1.1 Expressions and Their
                 Representation; I.1.1 Simplification of expressions",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Initial value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Electronics; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods);
                 Computing Methodologies, ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions",
  genterm =      "algorithms; theory; experimentation; measurement",
  guideno =      "1989-09722",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I.
                 Computing Methodologies; I.1 ALGEBRAIC MANIPULATION",
}

@PhdThesis{Littlestone:1989:MBL,
  author =       "N. Littlestone",
  title =        "Mistake bounds and logarithmic linear-threshold
                 learning algorithms",
  type =         "{Ph.D} Thesis",
  school =       "University of California at Santa Cruz",
  address =      "Santa Cruz, CA, USA",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "76493",
  catcode =      "I.2.6; J.4; H.1.2; G.1.2",
  CRclass =      "I.2.6 Learning; J.4 Psychology; H.1.2 User/Machine
                 Systems; H.1.2 Human information processing; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Learning; Computer Applications, SOCIAL AND BEHAVIORAL
                 SCIENCES, Psychology; Information Systems, MODELS AND
                 PRINCIPLES, User/Machine Systems, Human information
                 processing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; human factors; performance",
  guideno =      "1989-12934",
  source =       "UMI Order No: GAX89-26506",
  subject =      "I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; J. Computer Applications; J.4 SOCIAL AND
                 BEHAVIORAL SCIENCES; H. Information Systems; H.1 MODELS
                 AND PRINCIPLES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Lo:1989:RBP,
  author =       "Shaw-Hwa Lo and Jane-Ling Wang",
  title =        "Representations for the bivariate product limit
                 estimators and the bootstrap versions",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "211--226",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California, Davis; Univ. of California,
                 Davis",
  bibno =        "64339",
  catcode =      "G.3; G.1.2; G.1.4; G.1.7",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.4 Quadrature and
                 Numerical Differentiation; G.1.4 Gaussian quadrature;
                 G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Gaussian quadrature; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Convergence and stability",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08465",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Lorentz:1989:NA,
  author =       "G. G. Lorentz",
  title =        "Notes on approximation",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "360--365",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72258",
  catcode =      "G.1.1; G.1.2; G.1.1",
  CRclass =      "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.1 Interpolation; G.1.1 Spline and piecewise
                 polynomial interpolation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Smoothing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation",
  genterm =      "algorithms; theory",
  guideno =      "1989-07816",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Megiddo:1989:POS,
  author =       "N. Megiddo",
  title =        "Pathways to the optimal set in linear programming",
  crossref =     "Megiddo:1989:PMP",
  pages =        "131--158",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "74179",
  catcode =      "G.1.6; G.1.2; G.2.2; G.1.2; G.1.5; F.2.1; I.1.2; G.4;
                 G.4",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.2 Graph Theory; G.2.2 Path and circuit problems;
                 G.1.2 Approximation; G.1.2 Spline and piecewise
                 polynomial approximation; G.1.5 Roots of Nonlinear
                 Equations; G.1.5 Iterative methods; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computations on
                 matrices; I.1.2 Algorithms; I.1.2 Analysis of
                 algorithms; G.4 Algorithm analysis; G.4 Efficiency",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, DISCRETE MATHEMATICS, Graph Theory, Path and
                 circuit problems; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Spline and piecewise
                 polynomial approximation; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Iterative methods; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
                 Analysis of algorithms; Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Efficiency",
  genterm =      "algorithms; performance; theory",
  guideno =      "1989-12481",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
                 G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing;
                 G.4 MATHEMATICAL SOFTWARE",
}

@PhdThesis{Miler:1989:EEM,
  author =       "T. H. Miler",
  title =        "Error evaluation of microcomputer intrinsic
                 functions",
  type =         "{Ph.D} Thesis",
  school =       "University of Idaho",
  address =      "Moscow, ID",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "76168",
  catcode =      "G.4; G.1.2; J.2",
  CRclass =      "G.4 Reliability and robustness; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; J.2
                 Mathematics and statistics",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Computer Applications, PHYSICAL SCIENCES
                 AND ENGINEERING, Mathematics and statistics",
  genterm =      "algorithms; reliability",
  guideno =      "1989-12941",
  source =       "UMI order no: GAX89-22813",
  subject =      "G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING",
}

@InProceedings{Montuschi:1989:EIH,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "On the efficient implementation of higher radix square
                 root algorithms",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "154--161",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  acknowledgement = ack-nhfb,
}

@Book{Moshier:1989:MPM,
  author =       "Stephen L. B. Moshier",
  title =        "Methods and Programs for Mathematical Functions",
  publisher =    pub-ELLIS-HORWOOD,
  address =      pub-ELLIS-HORWOOD:adr,
  pages =        "vii + 415",
  year =         "1989",
  ISBN =         "0-7458-0289-3",
  ISBN-13 =      "978-0-7458-0289-3",
  LCCN =         "QA331 .M84 1989",
  bibdate =      "Thu Sep 01 10:33:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  price =        "US\pounds 48.00",
  acknowledgement = ack-nj,
}

@Article{Rhee:1989:MII,
  author =       "W. T. Rhee and M. Talagrand",
  title =        "Martingale inequalities, interpolation and
                 {NP}-complete problems",
  journal =      j-MATH-OP-RES,
  volume =       "14",
  number =       "1",
  pages =        "91--96",
  month =        feb,
  year =         "1989",
  CODEN =        "MOREDQ",
  ISSN =         "0364-765X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ., Paris, Paris, France; Ohio State Univ.,
                 Columbus",
  bibno =        "67063",
  catcode =      "G.2.2; H.1.1; G.1.1; G.1.2; G.3; I.6.4; F.1.3",
  CRclass =      "G.2.2 Graph Theory; G.2.2 Path and circuit problems;
                 H.1.1 Systems and Information Theory; H.1.1 General
                 systems theory; G.1.1 Interpolation; G.1.1
                 Interpolation formulas; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.3 Probabilistic
                 algorithms (including Monte Carlo); I.6.4 Model
                 Validation and Analysis; F.1.3 Complexity Classes;
                 F.1.3 Reducibility and completeness",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Path and circuit problems; Information Systems,
                 MODELS AND PRINCIPLES, Systems and Information Theory,
                 General systems theory; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation, Interpolation
                 formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Probabilistic algorithms (including Monte Carlo);
                 Computing Methodologies, SIMULATION AND MODELING, Model
                 Validation and Analysis; Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Classes,
                 Reducibility and completeness",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-09079",
  journalabbrev = "Math. Oper. Res.",
  jrldate =      "Feb. 1989",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 H. Information Systems; H.1 MODELS AND PRINCIPLES; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; I. Computing Methodologies; I.6 SIMULATION
                 AND MODELING; F. Theory of Computation; F.1 COMPUTATION
                 BY ABSTRACT DEVICES",
}

@Article{Ruymgaart:1989:SPB,
  author =       "F. H. Ruymgaart",
  title =        "Some properties of bivariate empirical hazard
                 processes under random censoring",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "271--281",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "64343",
  catcode =      "G.3; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08469",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@InCollection{Saigo:1989:FID,
  author =       "Megumi Saigo",
  title =        "Fractional integrals and derivatives associated with
                 elementary functions and {Bessel} functions",
  crossref =     "Srivastava:1989:UFF",
  pages =        "283--306",
  year =         "1989",
  MRclass =      "26A33 (33C10)",
  MRnumber =     "93h:26011",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  series =       "Ellis Horwood Ser. Math. Appl.",
  acknowledgement = ack-nhfb,
}

@Article{Smith:1989:EMP,
  author =       "David M. Smith",
  title =        "Efficient multiple-precision evaluation of elementary
                 functions",
  journal =      j-MATH-COMP,
  volume =       "52",
  number =       "185",
  pages =        "131--134",
  month =        jan,
  year =         "1989",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D15 (26-04)",
  MRnumber =     "90c:65034",
  MRreviewer =   "Menachem Dishon",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Dept. of Math., Loyola Univ., Los Angeles, CA, USA",
  keywords =     "arithmetic; base b; elementary functions; function
                 evaluation; multiple-precision evaluation",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Tang:1989:TCA,
  author =       "Ping Tak Peter Tang",
  title =        "Testing Computer Arithmetic by Elementary Number
                 Theory",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "????",
  month =        aug,
  year =         "1989",
  bibdate =      "Fri Jun 11 12:38:06 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Tang:1989:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Exponential
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "144--157",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sun Sep 04 22:47:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/;
                 http://doi.acm.org/10.1145/63522.214389",
  abstract =     "Algorithms and implementation details for the
                 exponential function in both single- and
                 double-precision of IEEE 754 arithmetic are presented
                 here. With a table of moderate size, the
                 implementations need only working-precision arithmetic
                 and are provably accurate to within 0.54 ulp as long as
                 the final result does not underflow. When the final
                 result suffers gradual underflow, the error is still no
                 worse than 0.77 ulp.",
  acknowledgement = ack-nj,
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Ubhaya:1989:LAN,
  author =       "V. A. Ubhaya",
  title =        "{$L_p$} approximation from nonconvex subsets of
                 special classes of functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "57",
  number =       "2",
  pages =        "223--238",
  month =        may,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72277",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "verification; theory",
  guideno =      "1989-07833",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "May 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Vaidya:1989:LWB,
  author =       "P. M. Vaidya",
  title =        "A locally well-behaved potential function and a simple
                 {Newton}-type method for finding the center of a
                 polytype",
  crossref =     "Megiddo:1989:PMP",
  pages =        "79--90",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "74176",
  catcode =      "G.1.6; G.1.6; F.2.2; G.1.2; G.1.5; G.1.5; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.6
                 Optimization; G.1.6 Gradient methods; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.5 Roots of
                 Nonlinear Equations; G.1.5 Convergence; G.1.5 Roots of
                 Nonlinear Equations; G.1.5 Iterative methods; I.1.2
                 Algorithms; I.1.2 Nonalgebraic algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Gradient
                 methods; Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Convergence; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Iterative methods; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12478",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
  xxpages =      "131--158",
}

@PhdThesis{Vavasis:1989:CFP,
  author =       "S. A. Vavasis",
  title =        "Complexity of fixed point computations",
  type =         "{Ph.D} Thesis",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "76220",
  catcode =      "J.4; G.1.2; F.1.3; G.1.2; G.2.2",
  CRclass =      "J.4 Economics; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; F.1.3 Complexity Classes; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.2 Graph Theory; G.2.2 Network problems",
  descriptor =   "Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES,
                 Economics; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Nonlinear approximation;
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Graph Theory, Network problems",
  genterm =      "algorithms; theory",
  guideno =      "1989-12859",
  source =       "UMI order no: GAX89-19486",
  subject =      "J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL
                 SCIENCES; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY
                 ABSTRACT DEVICES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
                 DISCRETE MATHEMATICS",
}

@InProceedings{Vial:1989:APP,
  author =       "J.-P. Vial",
  title =        "Approximate projections in a projective method for the
                 linear feasibility problem",
  crossref =     "Megiddo:1989:PMP",
  pages =        "65--78",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "74175",
  bookpages =    "x + 158",
  catcode =      "G.1.6; F.2.2; I.1.2; G.1.6; G.1.2; F.2.1; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; I.1.2 Algorithms; I.1.2
                 Nonalgebraic algorithms; G.1.6 Optimization; G.1.6
                 Constrained optimization; G.1.2 Approximation; G.1.2
                 Elementary function approximation; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computations on
                 matrices; G.1.2 Approximation; G.1.2 Minimax
                 approximation and algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
                 Nonalgebraic algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Optimization, Constrained
                 optimization; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms",
  genterm =      "algorithms; experimentation; measurement; performance;
                 theory",
  guideno =      "1989-12477",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{vonRosen:1989:MLE,
  author =       "D. von Rosen",
  title =        "Maximum likelihood estimators in multivariate linear
                 normal models",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "187--200",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Stockholm, Stockholm, Sweden",
  bibno =        "69314",
  catcode =      "G.1.6; G.1.2; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Linear approximation; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Linear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; theory",
  guideno =      "1989-08484",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Wasilkowski:1989:AIV,
  author =       "G. W. Wasilkowski",
  title =        "On adaptive information with varying cardinality for
                 linear problems with elliptically contoured measures",
  journal =      j-J-COMPLEXITY,
  volume =       "5",
  number =       "3",
  pages =        "363--368",
  month =        sep,
  year =         "1989",
  CODEN =        "JOCOEH",
  ISSN =         "0885-064X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Kentucky, Lexington, KY",
  bibno =        "68756",
  catcode =      "G.1.2; G.1.2; F.1.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; F.1.3 Complexity Classes",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation; Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes",
  genterm =      "algorithms; theory",
  guideno =      "1989-08045",
  journalabbrev = "J. Complexity",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES",
}

@Article{Yortsos:1989:LSI,
  author =       "Y. C. Yortsos and F. J. Hickernell",
  title =        "Linear stability of immiscible displacement in porous
                 media",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "730--748",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "64942",
  catcode =      "G.1.8; G.1.0; J.2; G.1.2; G.1.4; G.1.8",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Parabolic
                 equations; G.1.0 General; G.1.0 Stability (and
                 instability); J.2 Earth and atmospheric sciences; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.4 Quadrature and Numerical Differentiation; G.1.4
                 Finite difference methods; G.1.8 Partial Differential
                 Equations; G.1.8 Difference methods",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Parabolic equations;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Stability (and instability); Computer Applications,
                 PHYSICAL SCIENCES AND ENGINEERING, Earth and
                 atmospheric sciences; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Finite difference methods; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Difference methods",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09711",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Zalik:1989:NIE,
  author =       "R. A. Zalik",
  title =        "A new inequality for entire functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "58",
  number =       "3",
  pages =        "281--283",
  month =        sep,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  acknowledgement = ack-nhfb,
  bibno =        "72294",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "verification; theory",
  guideno =      "1989-07871",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Ziemer:1989:WDF,
  author =       "William P. Ziemer",
  title =        "Weakly differentiable functions: {Sobolev} spaces and
                 functions of bounded variation",
  volume =       "120",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 308",
  year =         "1989",
  ISBN =         "0-387-97017-7",
  ISBN-13 =      "978-0-387-97017-2",
  LCCN =         "QA323 .Z53 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  series =       "Graduate texts in mathematics",
  acknowledgement = ack-nhfb,
  affiliation =  "Indiana Univ., Bloomington",
  bibno =        "69369",
  catcode =      "G.1.2; G.1.8; G.1.5",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.8 Partial Differential Equations;
                 G.1.5 Roots of Nonlinear Equations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations",
  genterm =      "algorithms; theory",
  guideno =      "1989-01732",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Bronstein:1990:IEF,
  author =       "Manuel Bronstein",
  title =        "Integration of elementary functions",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "9",
  number =       "2",
  pages =        "117--173",
  month =        feb,
  year =         "1990",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171",
  MRclass =      "12H05 (68Q40)",
  MRnumber =     "91h:12017",
  MRreviewer =   "Alexandru Buium",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "Theory/cathode.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson
                 Res. Center, Yorktown Heights, NY, USA",
  keywords =     "algebraic extension; algebraic function; decision
                 procedure; elementary function field; elementary
                 functions; exponential; finite terms; indefinite;
                 integration; integration Risch ODEs oderef; logarithm;
                 proof; Trager",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Carre:1990:PEF,
  author =       "C. Carre",
  title =        "Plethysm of elementary functions",
  journal =      "Bayreuth. Math. Schr.",
  volume =       "31",
  pages =        "1--18",
  year =         "1990",
  ISSN =         "0172-1062",
  MRclass =      "20C30 (05E05 22E45)",
  MRnumber =     "91f:20013",
  MRreviewer =   "John R. Stembridge",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Cody:1990:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs for the Error and
                 Complementary Error Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "29--37",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "http://dx.doi.org/10.1145/77626.77628",
  ISSN =         "0098-3500",
  MRclass =      "65-04 (65G05)",
  MRnumber =     "1 073 407",
  bibdate =      "Tue Oct 09 09:29:47 2007",
  bibsource =    "ftp://ftp.math.utah.edu/pub/tex/bib/toms.bib,
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html",
  abstract =     "This paper presents methods for performance evaluation
                 of computer programs for the functions
                 $\textrm{erf}(x)$, $\textrm{erfc}(x)$, and $\e^{x^2}
                 \textrm{erfc}(x)$. Accuracy estimates are based on
                 comparisons using power series expansions and an
                 expansion in the repeated integrals of
                 $\textrm{erfc}(x)$. Some suggestions for checking
                 robustness are also given. Details of a specific
                 implementation of a test program are included.",
  acknowledgement = ack-nhfb,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "B0290F (Interpolation and function approximation);
                 B0290B (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods)",
  keywords =     "FORTRAN; Complementary error functions; Computer
                 programs; Power series expansions; Repeated integrals;
                 Robustness; Test program",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "Error analysis; Function approximation; Performance
                 evaluation",
}

@Article{Dunham:1990:FPF,
  author =       "C. B. Dunham",
  title =        "Feasibility of ``perfect'' function evaluation",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "4",
  pages =        "25--26",
  month =        oct,
  year =         "1990",
  CODEN =        "SNEWD6",
  DOI =          "http://doi.acm.org/10.1145/122272.122276",
  ISSN =         "0163-5778",
  bibdate =      "Tue Apr 12 07:50:19 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nhfb # " and " # ack-nj,
}

@InProceedings{Kiernan:1990:FAE,
  author =       "J. M. Kiernan and T. B. Blachowiak",
  title =        "Fast, Accurate Elementary Functions For the {Cray
                 Y-MP} Computer",
  crossref =     "Cray:1990:PCU",
  pages =        "243--252",
  year =         "1990",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@Article{Koren:1990:EEF,
  author =       "I. Koren and O. Zinaty",
  title =        "Evaluating Elementary Functions in a Numerical
                 Coprocessor Based on Rational Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1030--1037",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

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

@InCollection{Mora:1990:EFI,
  author =       "Gerardo Mora and Edwin Castro and Ioan Muntean",
  booktitle =    "Mathematics in Costa Rica, Vol. 1 (Spanish) (San
                 Jos{\'e}, 1990),",
  title =        "Elementary functions. {I}. ({Spanish})",
  publisher =    "Univ. Costa Rica",
  address =      "San Jos{\'e}, Costa Rica",
  pages =        "76--86",
  year =         "1990",
  MRclass =      "26A09",
  MRnumber =     "1 111 714",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Muller:1990:HCA,
  author =       "Volker M{\"u}ller",
  title =        "{Hochgenaue {CORDIC}-Algorithmen f{\"u}r reelle
                 Standardfunktionen mittels dynamischer
                 Defektberechnung} \toenglish {High-accuracy {CORDIC}
                 Algorithms for Real Elementary Functions by Means of
                 Dynamic Error Computation} \endtoenglish",
  type =         "Diplomarbeit",
  school =       "Institut f{\"u}r angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  month =        dec,
  year =         "1990",
  bibdate =      "Fri Jun 11 12:38:17 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

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

@Book{Swartzlander:1990:CA,
  author =       "Earl E. Swartzlander",
  title =        "Computer arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1990",
  ISBN =         "0-8186-8931-5 (v. 1), 0-8186-5931-9 (v. 1
                 microfiche)",
  ISBN-13 =      "978-0-8186-8931-4 (v. 1), 978-0-8186-5931-7 (v. 1
                 microfiche)",
  LCCN =         "QA76.6.C633 1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  note =         "Two volumes.",
  series =       "IEEE Computer Society Press tutorial",
  acknowledgement = ack-nhfb,
  annote =       "Vol. 1 is a reprint. Originally published:
                 Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980.
                 Originally published in series: Benchmark papers in
                 electrical engineering and computer science; 21. Vol 2
                 is a sequel to the earlier collection. Vol. 1: 2nd ed.
                 Includes bibliographical references and index.
                 Arithmetic operations in a binary computer / R.F. Shaw
                 --- High-speed arithmetic in binary computers / O.L.
                 MacSorley --- Fast carry logic for digital computers /
                 B. Gilchrist, J.H. Pomerene, and S.Y. Wong --- A logic
                 for high-speed addition / A. Weinberger and J.L. Smith
                 --- Conditional-sum addition logic / J. Sklansky --- An
                 evaluation of several two-summand binary adders / J.
                 Sklansky - - Adder with distributed control / A.
                 Svoboda --- Multiple addition by residue threshold
                 functions and their representation by array logic /
                 I.T. Ho and T.C. Chen --- Counting responders in an
                 associative memory / C.C. Foster and F.D. Stockton ---
                 Parallel counters / E.E. Swartzlander, Jr. --- A signed
                 binary multiplication technique / A.D. Booth ---
                 Multiplying made easy for digital assemblies / C.
                 Ghest. A binary multiplication scheme based on squaring
                 / T.C. Chen --- A suggestion for a fast multiplier /
                 C.S. Wallace --- Some schemes for parallel multipliers
                 / L. Dadda --- On parallel digital multipliers / L.
                 Dadda --- A compact high-speed parallel multiplication
                 scheme / W.J. Stenzel, W.J. Kubitz, and G.H. Garcia ---
                 A two's complement parallel array multiplication
                 algorithm / C.R. Baugh and B.A. Wooley --- Comments on
                 ``A two's complement parallel array multiplication
                 algorithm'' / P.E. Blankenship --- The quasi-serial
                 multiplier / E.E. Swartzlander, Jr. --- The two's
                 complement quasi-serial multiplier / T.G. McDaneld and
                 R.K. Guha --- A new class of digital division methods /
                 J.E Robertson --- An algorithm for rapid binary
                 division / J.B. Wilson and R.S. Ledley. Digit-by-digit
                 transcendental-function computation / R.J. Linhardt and
                 H.S.Miller --- A unified algorithm for elementary
                 functions / J.S. Walther --- Some properties of
                 iterative square-rooting methods using high-speed
                 multiplication /C.V. Ramamoorthy, J.R. Goodman, and
                 K.H. Kim --- Radix-16 evaluation of certain elementary
                 functions / M.D. Ercegovac --- On the distribution of
                 numbers / R.W. Hamming --- An analysis of
                 floating-point addition / D.W. Sweeney --- The
                 IBM\ldots{}Model 91: floating-point execution unit /
                 S.F. Anderson \ldots{} [et al.] --Design of large
                 high-speed floating-point-arithmetic units / J.B.
                 Gosling --- Analysis of rounding methods in
                 floating-point arithmetic / D.J. Kuck,D.S. Parker, Jr.,
                 and A.H. Sameh.cos x, tan-p1s x, and cot-p1s x / W.H.
                 Specker.",
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; Computer arithmetic.",
}

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

@TechReport{Tang:1990:PGE,
  author =       "Ping Tak Peter Tang",
  title =        "A Portable Generic Elementary Function Package in
                 {Ada} and an Accurate Test Suite",
  type =         "Technical report",
  number =       "ANL-90/35",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "iii + 35",
  month =        nov,
  year =         "1990",
  bibdate =      "Fri Dec 28 11:36:25 2007",
  URL =          "http://www.osti.gov/bridge/servlets/purl/6310184-4n5sOR/6310184.PDF",
  abstract =     "A comprehensive set of elementary functions has been
                 implemented portably in Ada. The high accuracy of the
                 implementation has been confirmed by rigorous analysis.
                 Moreover, we present new test methods that are
                 efficient and offer a high resolution of 0.005 unit in
                 the last place, Tbese test methods have been
                 implemented portably here and confirm the accuracy of
                 our implemented functions. Reports on the accuracy of
                 other function libraries obtained by our test programs
                 are also presented.",
  acknowledgement = ack-nhfb,
}

@TechReport{Tang:1990:SSI,
  author =       "Ping Tak Peter Tang",
  title =        "Some Software Implementations of the Functions Sine
                 and Cosine",
  type =         "Technical report",
  number =       "ANL-90/3",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  month =        apr,
  year =         "1990",
  bibdate =      "Fri Dec 28 11:21:38 2007",
  URL =          "http://www-fp.mcs.anl.gov/division/publications/abstracts/abstracts90.htm",
  abstract =     "This document presents several software
                 implementations of the elementary functions sin and cos
                 designed to fit a large class of machines.
                 Implementation details are provided. Also provided is a
                 detailed error analysis that bounds the errors of these
                 implementations, over the full range of input
                 arguments, from 0.721 to 0.912 units in the last place.
                 Tests performed on these codes give results that are
                 consistent with the error bounds.",
  acknowledgement = ack-nhfb,
  xxnote =       "Where is this? I can find no electronic version
                 online, other than the abstract at the given URL.",
}

@Article{Tang:1990:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "378--400",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sun Sep 04 23:26:09 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/;
                 http://doi.acm.org/10.1145/98267.98294",
  abstract =     "Algorithms and implementation details for the
                 logarithm functions in both single and double precision
                 of IEEE 754 arithmetic are presented here. With a table
                 of moderate size, the implementation need only working-
                 precision arithmetic and are provably accurate to
                 within 0.57 ulp.",
  acknowledgement = ack-nj,
  keywords =     "algorithms; design; performance; reliability;
                 standardization; theory; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

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

@InProceedings{Bohlender:1991:SEF,
  author =       "G. Bohlender and W. Walter and P. Kornerup and D. W.
                 Matula",
  title =        "Semantics for exact floating point operations",
  crossref =     "Kornerup:1991:PIS",
  pages =        "22--26",
  year =         "1991",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  note =         "IEEE Catalog number 91CH3015-5.",
  abstract =     "Semantics are given for the four elementary arithmetic
                 operations and the square root, to characterize what
                 are termed exact floating point operations. The
                 operands of the arithmetic operations and the argument
                 of the square root are all floating point numbers in
                 one format. In every case, the result is a pair of
                 floating point numbers in the same format with no
                 accuracy lost in the computation. These semantics make
                 it possible to realize the following principle: it
                 shall be a user option to discard any information in
                 the result of a floating point arithmetic operation.
                 The reliability and portability previously associated
                 with only mathematical software implementations in
                 integer arithmetic can thus be attained exploiting the
                 generally higher efficiency of floating point
                 hardware.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  bookpages =    "xiii + 282",
  classification = "C5230 (Digital arithmetic methods); C1160
                 (Combinatorial mathematics)",
  confdate =     "26-28 June 1991",
  conflocation = "Grenoble, France",
  confsponsor =  "IEEE; CNRS; IMAG",
  keywords =     "Exact floating point operations; Elementary arithmetic
                 operations; Square root; Operands; Argument; Floating
                 point numbers; Semantics; Floating point arithmetic;
                 Reliability; Portability; Mathematical software;
                 Integer arithmetic; Floating point hardware",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Number theory",
}

@TechReport{Cody:1991:CPT,
  author =       "W. J. Cody",
  title =        "{CELEFUNT}: {A} Portable Test Package for Complex
                 Elementary Functions",
  type =         "Technical Report",
  number =       "ANL-91/1",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "iii + 21",
  month =        jan,
  year =         "1991",
  bibdate =      "Fri Sep 23 23:39:07 1994",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dritz:1991:IPS,
  author =       "Kenneth W. Dritz",
  title =        "Introduction to the proposed standard for the
                 elementary functions in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "3--8",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Dept. of Math. and Comput. Sci., Argonne Nat. Lab.,
                 IL, USA",
  keywords =     "Ada; committees; elementary functions; generic
                 package; ISO standard; mathematics computing;
                 secondary; standards",
  treatment =    "P Practical",
}

@Article{Dritz:1991:PSGa,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of elementary
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "9--46",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C6110B (Software
                 engineering techniques); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  keywords =     "ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics
                 Working Group; basic; elementary functions;
                 ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package;
                 GENERIC-ELEMENTARY-FUNCTIONS; Group; international
                 standard; joint proposal; mathematical routines;
                 mathematics computing; NRG; Rapporteur Group; reusable
                 applications; SC22; software reusability;
                 specification; standards; WG9 Numerics",
  treatment =    "P Practical",
}

@Article{Dritz:1991:PSGb,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of primitive
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "66--82",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  keywords =     "Ada; compliable Ada; elementary functions; generic
                 package; GENERIC-; mathematical; mathematics computing;
                 primitive functions; primitive operations;
                 PRIMITIVE-FUNCTIONS; software; specification;
                 standards",
  treatment =    "P Practical",
}

@Article{Dritz:1991:RPS,
  author =       "K. W. Dritz",
  title =        "Rationale for the proposed standard for a generic
                 package of elementary functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "47--65",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110 (Systems analysis and programming)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-Europe
                 Numerics; collateral; elementary functions standard;
                 mathematics computing; numerical software; portability;
                 programming; robustness; standards; Working Group",
  treatment =    "P Practical",
}

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

@InProceedings{Ferguson:1991:AMA,
  author =       "W. E. {Ferguson, Jr.} and T. Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  crossref =     "Kornerup:1991:PIS",
  pages =        "237--244",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://ieeexplore.ieee.org/",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/103151.html",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument values.
                 \par

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

@InProceedings{Markstein:1991:WFF,
  author =       "V. Markstein and P. Markstein and T. Nguyen and S.
                 Poole",
  title =        "Wide Format Floating-Point Math Libraries",
  crossref =     "IEEE:1991:PSA",
  pages =        "130--138",
  year =         "1991",
  bibdate =      "Wed Dec 13 18:34:51 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  abstract =     "The authors present the performance and accuracy
                 evaluations of eleven transcendental functions found in
                 64- and 128-bit floating-point formats in math
                 libraries on the Cray Y-MP, the IBM 3090E/VF, the
                 Convex C-240, the Hewlett-Packard 9000/720, and the IBM
                 System/6000. Both architecture and algorithms are shown
                 to impact the results.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "ISQUARE, Inc., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing); C7310
                 (Mathematics)",
  confdate =     "18-22 Nov. 1991",
  conflocation = "Albuquerque, NM, USA",
  confsponsor =  "IEEE; ACM",
  keywords =     "Wide format floating point math libraries;
                 Performance; Accuracy evaluations; Transcendental
                 functions; Floating-point formats; Math libraries; Cray
                 Y-MP; IBM 3090E/VF; Convex C-240; Hewlett-Packard
                 9000/720; IBM System/6000; 64 Bit; 128 Bit",
  language =     "English",
  numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Parallel
                 processing; Performance evaluation",
}

@Article{Midy:1991:CSE,
  author =       "P. Midy and Y. Yakovlev",
  title =        "Computing some elementary functions of a complex
                 variable",
  journal =      j-MATH-COMP-SIM,
  volume =       "33",
  number =       "1",
  pages =        "33--49",
  year =         "1991",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754",
  MRclass =      "65Y10 (65D20)",
  MRnumber =     "MR1122989",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
}

@Article{OGrady:1991:HOA,
  author =       "E. Pearse O'Grady and Baek-Kyu Young",
  title =        "A hardware-oriented algorithm for floating-point
                 function generation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "237--241",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  abstract =     "An algorithm is presented for performing accurate,
                 high-speed, floating-point function generation for
                 univariate functions defined at arbitrary breakpoints.
                 Rapid identification of the breakdown interval, which
                 includes the input argument, is the key operation in
                 the algorithm. A hardware implementation which makes
                 extensive use of read/write memories illustrates the
                 algorithm.",
  acknowledgement = ack-nhfb,
}

@Article{Okabe:1991:LDC,
  author =       "Y. Okabe and N. Takagi and S. Yaima",
  key =          "OTY91",
  title =        "Log-Depth Circuits for Elementary Functions Using
                 Residue Number System",
  journal =      "Electronics and Communications in Japan",
  volume =       "74",
  number =       "8",
  pages =        "31--37",
  year =         "1991",
  bibdate =      "Mon May 19 15:16:09 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
  acknowledgement = ack-nhfb,
}

@Book{Saan:1991:VFP,
  author =       "T. Saan",
  title =        "{\cyr Vychislenie {\`e}lementarnykh funktsi{\u{\i}}s
                 pomoshch'yu drobno-ratsional'nykh priblizheni{\u{\i}}}.
                 ({Russian}) [Calculation of elementary functions by
                 means of rational approximations]",
  publisher =    "{\`E}ston. Nauchno-Proizvod. Ob\cdprime ed. Vychisl.
                 Tekhn. Inform., Tartu,",
  pages =        "139",
  year =         "1991",
  MRclass =      "65-04 (65D15)",
  MRnumber =     "94f:65008",
  MRreviewer =   "W. Govaerts",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "Algorithm 693: {A FORTRAN} Package for Floating-Point
                 Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/108585.html",
  abstract =     "FM is a collection of FORTRAN-77 routines which
                 performs floating-point multiple-precision arithmetic
                 and elementary functions. Results are almost always
                 correctly rounded, and due to improved algorithms used
                 for elementary functions, reasonable efficiency is
                 obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Loyola Marymount Univ., Los Angeles, CA, USA",
  classification = "C7310 (Mathematics); C5230 (Digital arithmetic
                 methods); C4130 (Interpolation and function
                 approximation)",
  keywords =     "Algorithms; Rounding off; Accuracy; Mathematical
                 library; Portable software; Floating-point
                 multiple-precision arithmetic; FM; FORTRAN-77 routines;
                 Elementary functions",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Digital arithmetic; Function approximation;
                 Mathematics computing; Software packages; Subroutines",
}

@Article{Squire:1991:ANS,
  author =       "Jon S. Squire",
  title =        "{Ada} numerics standardization and testing",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  address =      "New York, NY, USA",
  pages =        "1--286",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  acknowledgement = ack-nhfb,
  annote =       "``A special edition from SIGAda \ldots{} presented by
                 SIGAda Numerics Working Group and Ada-Europe Numerics
                 Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
                 Rapporteur Group.''--Cover. Includes bibliographies.
                 Introduction to the proposed standard for the
                 elementary functions in Ada / Kenneth W. Dritz ---
                 Proposed standard for a generic package of elementary
                 functions for Ada / edited by Kenneth W. Dritz ---
                 Rationale for the proposed standard for a generic
                 package of elementary functions for Ada; Proposed
                 standard for a generic package of primitive functions
                 for Ada; Rationale for the proposed standard for a
                 generic package of primitive functions for Ada /
                 Kenneth W. Dritz --- Proposed standard for packages of
                 real and complex type declarations and basic operations
                 for Ada (including vector and matrix types) / edited by
                 Graham S. Hodgson --- Rationale for the proposed
                 standard for packages of real and complex type
                 declarations and basic operations for Ada (including
                 vector and matrix types) / Graham S. Hodgson. Proposed
                 standard for a generic package of complex elementary
                 functions / edited by Jon S. Squire --- Rationale for
                 the proposed standard for a generic package of complex
                 elementary functions / Jon S. Squire --- A portable
                 generic elementary function package in Ada and an
                 accurate test suite / Ping Tak Peter Tang --- Towards
                 validation of generic elementary functions and other
                 standard Ada numerics packages / Jon S. Squire ---
                 Floating point attributes in Ada / Dik T. Winter --- An
                 Ada math library for real-time avionics / Donald A.
                 Celarier and Donald W. Sando --- Predifined floating
                 point type names, uniformity rapporteur group UI-48 /
                 edited by Jon S. Squire.",
  keywords =     "Ada (Computer program language)",
}

@Article{Squire:1991:PSG,
  author =       "J. S. Squire",
  title =        "Proposed standard for a generic package of complex
                 elementary functions (Ada)",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "140--165",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110B (Software engineering techniques)",
  keywords =     "ACM SIGAda; Ada; Ada-Europe Numerics Working Group;
                 applications; complex elementary functions; complex
                 mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS;
                 generic package; GENERIC-; international standard;
                 joint proposal; mathematics computing; Numerics Working
                 Group; portable; reusable; software reusability;
                 standards; WG9 Numerics Rapporteur Group",
  treatment =    "P Practical",
}

@Article{Squire:1991:RPS,
  author =       "J. S. Squire",
  title =        "Rationale for the proposed standard for a generic
                 package of complex elementary functions (Ada)",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "166--179",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110B (Software engineering techniques)",
  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-; basic
                 complex mathematical; complex;
                 COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions;
                 error bounds; Europe Numerics Working Group; generic
                 package; GENERIC-; mathematics computing; proposed
                 standard; reusable applications; routines; software
                 reusability; specification; standards",
  treatment =    "P Practical",
}

@Article{Squire:1991:TVG,
  author =       "J. S. Squire",
  title =        "Towards validation of generic elementary functions and
                 other standard {Ada} numerics packages",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "217--243",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150G (Diagnostic, testing, debugging and evaluating
                 systems); C7310 (Mathematics); C6140D (High level
                 languages)",
  keywords =     "Ada; Ada listings; computing; conformance testing;
                 conformance tests; generic elementary functions;
                 implementors guide; mathematics; program testing;
                 proposed ISO; prototype tests; standard Ada numerics
                 packages; standards; test suite",
  treatment =    "P Practical",
}

@Article{Tang:1991:PGE,
  author =       "Ping Tak Peter Tang",
  title =        "A portable generic elementary function package in
                 {Ada} and an accurate test suite",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "181--216",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics); C6140D (High level languages);
                 C6110B (Software engineering techniques); C6150G
                 (Diagnostic, testing, debugging and evaluating
                 systems)",
  keywords =     "accurate test; Ada; function libraries; mathematics
                 computing; portability; portable generic elementary
                 function package; program testing; resolution; rigorous
                 analysis; software; suite; test programs",
  treatment =    "P Practical",
}

@InProceedings{Tang:1991:TLA,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  crossref =     "Kornerup:1991:PIS",
  pages =        "232--236",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "http://ieeexplore.ieee.org/;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@InProceedings{Wong:1991:FHA,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-based Algorithms for Elementary Function
                 Computations",
  crossref =     "Anonymous:1991:PIS",
  pages =        "56--65",
  year =         "1991",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  acknowledgement = ack-nhfb,
  searchkey =    "ti:elementary function",
}

@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/116813.html",
  acknowledgement = ack-nj,
  keywords =     "algorithms; standardization; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}

@Book{Baker:1992:CMF,
  author =       "Louis Baker",
  title =        "{C} mathematical function handbook",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xviii + 757",
  year =         "1992",
  ISBN =         "0-07-911158-0",
  ISBN-13 =      "978-0-07-911158-6",
  LCCN =         "QA351.B17 1991; QA351 .B17 1992",
  bibdate =      "Fri Aug 31 18:54:02 MDT 2007",
  bibsource =    "melvyl.cdlib.org:210/CDL90",
  series =       "McGraw-Hill programming tools for scientists and
                 engineers",
  acknowledgement = ack-nhfb,
  remark =       "System requirements for computer disk: PC; C or C++
                 compiler.",
  subject =      "Functions, Special; Computer programs; C (Computer
                 program language)",
}

@Article{Baker:1992:LCE,
  author =       "H. G. Baker",
  title =        "Less Complex Elementary Functions",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "11",
  pages =        "15--16",
  month =        nov,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340",
  bibdate =      "Thu Sep 08 08:11:27 1994",
  acknowledgement = ack-nj,
}

@Article{Bohman:1992:FRP,
  author =       "Jan Bohman and Carl-Erik Fr{\"o}berg",
  title =        "The ${\Gamma}$-function revisited: power series
                 expansions and real-imaginary zero lines",
  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "197",
  pages =        "315--322",
  month =        jan,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33B15 (11Y70 65D20)",
  MRnumber =     "92e:33001",
  MRreviewer =   "A. de Castro Brzezicki",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dubois:1992:CFQ,
  author =       "D. Dubois and H. Prade",
  title =        "Calculation with fuzzy quantities",
  crossref =     "EC2:1992:DJN",
  pages =        "24--27",
  year =         "1992",
  bibdate =      "Thu Dec 14 17:22:18 MST 1995",
  abstract =     "In some instances where numerical data are either
                 provisional, incomplete, or variable within a limited
                 range, the classical calculation of confidence
                 intervals can be extended in a fuzzy-set approach,
                 distinguishing between more or less plausible values.
                 The simultaneous use of relatively wide intervals
                 containing all possible values, and generally much
                 narrower intervals covering only the most likely ones,
                 can give sufficiently informative results. Some
                 precautions advisable in arithmetic operations on
                 imprecisely known quantities are outlined. Examples of
                 application include provisional budgeting, resource
                 estimation, evaluation of candidates, and extension of
                 PERT to projects involving precedence among elementary
                 tasks with uncertain durations and/or starting times.
                 Computer-aided engineering design can also benefit from
                 fuzzy specifications for values eventually to be
                 optimised.",
  acknowledgement = ack-nhfb,
  affiliation =  "IRIT, Paul Sabatier Univ., Toulouse, France",
  bookpages =    "384",
  classification = "C7310 (Mathematics); C1160 (Combinatorial
                 mathematics); C4210 (Formal logic)",
  confdate =     "2-3 Nov. 1992",
  conflocation = "Nimes, France",
  keywords =     "Fuzzy quantities; Numerical data; Confidence
                 intervals; Fuzzy-set approach; Arithmetic operations;
                 Imprecisely known quantities; Provisional budgeting;
                 Resource estimation; Candidates; PERT; Engineering
                 design; Fuzzy specifications",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Fuzzy logic; Fuzzy set theory; Statistical analysis",
}

@Article{Feinsilver:1992:BFR,
  author =       "P. Feinsilver and R. Schott",
  title =        "On {Bessel} functions and rate of convergence of zeros
                 of {Lommel} polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "199",
  pages =        "153--156",
  month =        jul,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33C10 (33C45)",
  MRnumber =     "93a:33007",
  MRreviewer =   "Boro D{\"o}ring",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
  affiliation =  "Southern Illinois Univ., Carbondale, IL, USA",
  classcodes =   "B0220 (Analysis); B0290P (Differential equations);
                 B0290F (Interpolation and function approximation);
                 B0210 (Algebra); C1120 (Analysis); C4170 (Differential
                 equations); C4130 (Interpolation and function
                 approximation); C1110 (Algebra)",
  classification = "B0210 (Algebra); B0220 (Analysis); B0290F
                 (Interpolation and function approximation); B0290P
                 (Differential equations); C1110 (Algebra); C1120
                 (Analysis); C4130 (Interpolation and function
                 approximation); C4170 (Differential equations)",
  corpsource =   "Southern Illinois Univ., Carbondale, IL, USA",
  keywords =     "average case analysis; Average case analysis; Bessel
                 function; Bessel functions; convergence of numerical
                 methods; convergence rate; Convergence rate; data
                 structures; differential equations; dynamic; Dynamic
                 data structures; Lommel; Lommel polynomials; Maple
                 program; polynomials; rate of convergence; Rate of
                 convergence; zeros; Zeros",
  thesaurus =    "Bessel functions; Convergence of numerical methods;
                 Differential equations; Polynomials",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Kearfott:1992:IPF,
  author =       "Baker Kearfott and Milind Dawande and Kaisheng Du and
                 Chen-Yi Hu",
  title =        "{INTLIB}: {A} Portable {FORTRAN} 77 Elementary
                 Function Library",
  journal =      j-INTERVAL-COMP,
  volume =       "3",
  number =       "5",
  pages =        "96--105",
  year =         "1992",
  ISSN =         "0135-4868",
  MRclass =      "65G10",
  MRnumber =     "1 253 132",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
  note =         "Interval '92 (Moscow, 1992).",
  acknowledgement = ack-nhfb,
}

@Article{Lang:1992:HRS,
  author =       "T. Lang and P. Montuschi",
  title =        "Higher radix square root with prescaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "996--1009",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A scheme for performing higher radix square root based
                 on prescaling of the radicand is presented to reduce
                 the complexity of the result-digit selection. The
                 scheme requires several steps, namely multiplication
                 for prescaling the radicand, square \ldots{}",
}

@Article{McQuillan:1992:VMH,
  author =       "S. E. McQuillan and J. V. McCanny",
  title =        "{VLSI} module for high-performance multiply, square
                 root and divide",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "139",
  number =       "6",
  pages =        "505--510",
  month =        nov,
  year =         "1992",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A high-performance VLSI architecture to perform
                 multiply-accumulate, division and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control and ean be pipelined
                 right down to the bit level. The system can also
                 \ldots{}",
}

@Article{Mikami:1992:NDO,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "A New {DSP}-Oriented Algorithm for Calculation of the
                 Square Root Using a Nonlinear Digital Filter",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "7",
  pages =        "1663--1669",
  month =        jul,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://ieeexplore.ieee.org/",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  summary =      "A high-speed algorithm for calculating the square root
                 is proposed. This algorithm, which can be regarded as
                 calculation of the step response of a kind of nonlinear
                 IIR filter, requires no divisions. Therefore, it is
                 suitable for a VLSI digital \ldots{}",
}

@Article{Mitchell:1992:VFA,
  author =       "H. B. Mitchell",
  title =        "Very fast accurate square-root algorithm for use with
                 gradient edge operators",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "10",
  pages =        "922--923",
  day =          "7",
  month =        may,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Commonly used gradient edge operators such as the
                 Sobel, Prewitt and Roberts operators all required a
                 square root operation; this is, however,
                 computationally intensive and, consequently, simple but
                 very inaccurate approximations are often used
                 \ldots{}",
}

@Article{Salwin:1992:UPE,
  author =       "A. E. Salwin",
  title =        "Using the Proposed Elementary Functions Standard to
                 Build a Strongly Typed Trig Package",
  journal =      j-SIGADA-LETTERS,
  volume =       "12",
  number =       "5",
  pages =        "59--63",
  month =        sep # "\slash " # oct,
  year =         "1992",
  CODEN =        "AALEE5",
  ISSN =         "0736-721X",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages)",
  corpsource =   "Mitre Corp., McLean, VA, USA",
  keywords =     "Ada; compiler; elementary functions standard;
                 standards; strong typing; strongly typed trig package;
                 trigonometric functions",
  treatment =    "P Practical",
}

@MastersThesis{Schulte:1992:AHD,
  author =       "Michael Joseph Schulte and Function generation",
  title =        "Algorithms and hardware designs for parallel
                 elementary function generation",
  type =         "Thesis (M.S. in Engin.)",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "ix + 73",
  year =         "1992",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  acknowledgement = ack-nhfb,
  keywords =     "Computer science -- Mathematics.; Numerical analysis.;
                 Computer input-output equipment -- Design and
                 construction.; Parallel processing (Electronic
                 computers)",
  searchkey =    "ti:elementary n1 function",
}

@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Expm1 Function in
                 {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "1 167 891",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/;
                 http://doi.acm.org/10.1145/146847.146928",
  abstract =     "Algorithms and implementation details for the function
                 $e^x - 1$ in both single and double precision of IEEE
                 754 arithmetic are presented here. With a table of
                 moderate size, the implementations need only
                 working-precision arithmetic and are provably accurate
                 to within 0.58 ulp.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Temme:1992:AII,
  author =       "N. M. Temme",
  title =        "Asymptotic Inversion of Incomplete Gamma Functions",
  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "198",
  pages =        "755--764",
  month =        apr,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33B20",
  MRnumber =     "93a:33003",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Wong:1992:DSR,
  author =       "W. F. Wong and E. Goto",
  title =        "Division and square-rooting using a split multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "18",
  pages =        "1758--1759",
  day =          "27",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A modification is proposed to the traditional design
                 of a fast floating point multiplication circuit such
                 that instead of just performing A$\times$B where A and
                 B are m bits long, it is also capable of \ldots{}",
}

@InProceedings{Woods:1992:HPD,
  author =       "R. F. Woods and S. E. McQuillan and J. Dowling and J.
                 V. McCanny",
  booktitle =    "Proceedings of Fifth Annual IEEE International ASIC
                 Conference and Exhibit, 1992",
  title =        "High performance {DSP} {ASIC} for multiply, divide and
                 square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "209--213",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "The design of a high-speed ASIC that combines the
                 operations of multiplication, division and square root
                 is described. The chip is based on a systolic array
                 architecture that uses a redundant number system and
                 allows multiplication, division, and \ldots{}",
}

@Article{Alzer:1993:SGF,
  author =       "Horst Alzer",
  title =        "Some gamma function inequalities",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "337--346",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33B15 (26D20)",
  MRnumber =     "93f:33001",
  MRreviewer =   "Aurelio Cannizzo",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  acknowledgement = ack-nhfb,
}

@Article{Bailey:1993:AMT,
  author =       "D. H. Bailey",
  title =        "Algorithm 719: Multiprecision Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Wed Dec 13 18:37:31 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
  abstract =     "The author describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose. The second utility is a
                 translator program, which facilitates the conversion of
                 ordinary Fortran programs to use this package. By means
                 of source directives (special comments) in the original
                 Fortran program, the user declares the precision level
                 and specifies which variables in each subprogram are to
                 be treated as multiprecision. The translator program
                 reads this source program and outputs a program with
                 the appropriate multiprecision subroutine calls. This
                 translator supports multiprecision integer, real, and
                 complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NASA Ames Res. Center, Moffett Field, CA, USA",
  classification = "C7310 (Mathematics); C5230 (Digital arithmetic
                 methods); C6140D (High level languages); C6150C
                 (Compilers, interpreters and other processors); C6120
                 (File organisation)",
  keywords =     "Algorithm 719; Multiprecision translation; Fortran
                 programs; Fortran utilities; Multiprecision
                 computation; Fortran subroutines; Arithmetic
                 operations; Transcendental functions; Floating point
                 numbers; Translator program; Source directives;
                 Multiprecision subroutine calls; Complex data types;
                 Array space; Computational expressions; Operator
                 precedence; Mixed mode operations; Fortran-77
                 intrinsics; Multiprecision data types",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Data structures; Digital arithmetic; FORTRAN;
                 Mathematics computing; Program interpreters;
                 Subroutines",
}

@InCollection{Bohlender:1993:PAF,
  author =       "G. Bohlender and D. Cordes and A. Knofel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for accurate floating-point vector
                 arithmetic",
  crossref =     "Adams:1993:ACA",
  pages =        "87--102",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  abstract =     "Many computers provide accurate and reliable scalar
                 arithmetic for floating point numbers. An accurate
                 definition of the four elementary floating-point
                 operations +, -, *, / is given in the IEEE standards
                 for floating-point arithmetic and was well established
                 long before. An increasing number of computers
                 (especially PC's and workstations) feature IEEE
                 arithmetic. In many numerical algorithms, however,
                 compound operations such as the summation of a sequence
                 of numbers or the dot product of two vectors are highly
                 common. A simulation of these compound operations by
                 means of elementary floating-point operations leads to
                 accumulation of rounding errors and may suffer from
                 catastrophic cancellation of leading digits. Existing
                 standards for floating-point arithmetic do not improve
                 this situation. The goal of the proposal is to define
                 vector operations in a manner consistent with the
                 elementary scalar arithmetic operations. The rounding
                 modes and accuracy requirements as well as the data
                 formats of the operands and results of the vector
                 operations described in the proposal are chosen to be
                 fully consistent with the existing scalar
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  bookpages =    "x + 612",
  classification = "C5230 (Digital arithmetic methods); C7310
                 (Mathematics); C6130 (Data handling techniques)",
  keywords =     "Floating point numbers; Elementary floating-point
                 operations; IEEE standards; IEEE arithmetic; Numerical
                 algorithms; Compound operations; Summation; Sequence;
                 Dot product; Rounding errors; Catastrophic
                 cancellation; Leading digits; Standards; Vector
                 operations; Elementary scalar arithmetic operations;
                 Rounding modes; Accuracy requirements; Data formats;
                 Operands; Scalar floating-point arithmetic",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Roundoff
                 errors; Standards",
}

@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "Algorithm 714: {CELEFUNT}: {A} Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/151272.html",
  abstract =     "This paper discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C7310 (Mathematics); C5230 (Digital arithmetic
                 methods); C4100 (Numerical analysis)",
  keywords =     "CELEFUNT; Portable test package; Complex elementary
                 functions; Fortran programs; Floating-point elementary
                 functions; CABS; CSQRT; CLOG; CEXP; CSIN/CCOS; Complex
                 power function; algorithms; measurement; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "Conformance testing; Digital arithmetic; FORTRAN;
                 Mathematics computing; Numerical analysis; Program
                 testing; Software packages",
}

@Article{Frappier:1993:QFI,
  author =       "Cl{\'e}ment Frappier and Patrick Olivier",
  title =        "A quadrature formula involving zeros of {Bessel}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "303--316",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "41A55 (65D32)",
  MRnumber =     "93d:41025",
  MRreviewer =   "Hans Strauss",
  bibdate =      "Tue Mar 25 15:38:13 MST 1997",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 C4130 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Dept. de Math. Appliqu{\'e}es, Montreal, Que.,
                 Canada",
  keywords =     "Bessel functions; integration; interpolation; poles
                 and; polynomials; quadrature formula; sampling theorem;
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hu:1993:BRS,
  author =       "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad",
  title =        "On Bounding the Range of Some Elementary Functions in
                 {FORTRAN} 77",
  journal =      j-INTERVAL-COMP,
  volume =       "1993",
  number =       "3",
  pages =        "29--39",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10",
  MRnumber =     "1 305 844",
  bibdate =      "Wed Dec 4 11:13:33 1996",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
}

@TechReport{Litvinov:1993:ACR,
  author =       "Grigori L. Litvinov",
  title =        "Approximate construction of rational approximations
                 and the effect of error autocorrection",
  type =         "Technical report",
  number =       "8",
  institution =  "Institute of Mathematics, University of Oslo",
  address =      "Oslo, Norway",
  month =        may,
  year =         "1993",
  bibdate =      "Tue Mar 24 20:51:52 2009",
  note =         "See \cite{Litvinov:1994:ACR}.",
  acknowledgement = ack-nhfb,
}

@Article{Liu:1993:DSC,
  author =       "Hui Min Liu",
  title =        "Determination of several classes of elementary
                 functions by functional inequalities. (Chinese)",
  journal =      "Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)",
  volume =       "11",
  number =       "2",
  pages =        "30--35, 12",
  year =         "1993",
  ISSN =         "1001-6074",
  MRclass =      "26A09 (39B72)",
  MRnumber =     "94g:26003",
  MRreviewer =   "Ling Yau Chan",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InProceedings{Louie:1993:DRS,
  author =       "M. E. Louie and M. D. Ercegovac",
  booktitle =    "Proceedings of the IEEE Workshop on FPGAs for Custom
                 Computing Machines, 5--7 April 1993",
  title =        "A digit-recurrence square root implementation for
                 field programmable gate arrays",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "178--183",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Creating efficient arithmetic processors requires a
                 pairing of high speed arithmetic algorithms with
                 optimal mapping strategies for a given technology. The
                 authors propose bit reduction as key to an efficient
                 pairing process for lookup table based \ldots{}",
}

@InProceedings{Lozier:1993:ABF,
  author =       "Daniel W. Lozier and F. W. J. Olver",
  title =        "{Airy} and {Bessel} Functions by Parallel Integration
                 of {ODEs}",
  crossref =     "Sincovec:1993:PSS",
  pages =        "530--538",
  year =         "1993",
  bibdate =      "Fri Jul 09 06:36:27 2004",
  acknowledgement = ack-nhfb,
}

@InProceedings{McQuillan:1993:NAV,
  author =       "S. E. McQuillan and J. V. McCanny and R. Hamill",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "New algorithms and {VLSI} architectures for {SRT}
                 division and square root",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "80--86",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Radix two algorithms for SRT division and
                 square-rooting are developed. For these schemes, the
                 result digits and the residuals are computed
                 concurrently and the computations in adjacent rows are
                 overlapped. Consequently, their performance should
                 \ldots{}",
}

@Article{Montuschi:1993:RIT,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "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 =       "42",
  number =       "2",
  pages =        "239--246",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  note =         "See remark \cite{Montuschi:1995:RRI}.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "A new architecture is presented for shared radix 2
                 division and square root whose main characteristic is
                 the ability to avoid any addition/subtraction, when the
                 digit 0 has been selected. The solution presented uses
                 a redundant representation of the \ldots{}",
}

@Book{Povolotskii:1993:OFR,
  author =       "A. I. Povolotski{\u{\i}} and G. A. Sviridyuk",
  title =        "{\cyr Odnomerny{\u{\i}}matematicheski{\u{\i}}analiz
                 {\`e}lementarnykh funktsi{\u{\i}}}. ({Russian})
                 [One-dimensional mathematical analysis of elementary
                 functions] {\cyr Nepreryvnye funktsii.
                 Differentsiruemye funktsii. Integriruemye funktsii}.
                 [Continuous functions. Differentiable functions.
                 Integrable functions]",
  publisher =    "Chelyabinsk. Gos. Univ.",
  address =      "Chelyabinsk, USSR",
  pages =        "92",
  year =         "1993",
  ISBN =         "5-230-17764-0",
  ISBN-13 =      "978-5-230-17764-7",
  MRclass =      "26-01 (00A05)",
  MRnumber =     "94e:26001",
  MRreviewer =   "J{\'o}zef Kalinowski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1993:ERC,
  author =       "M. Schulte and E. Swartzlander",
  title =        "Exact rounding of certain elementary functions",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "138--145",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf",
  abstract =     "An algorithm is described which produces exactly
                 rounded results for the functions of reciprocal, square
                 root, 2/sup x/, and log 2/sup x/. Hardware designs
                 based on this algorithm are presented for floating
                 point numbers with 16- and 24-b significands. These
                 designs use a polynomial approximation in which
                 coefficients are originally selected based on the
                 Chebyshev series approximation and are then adjusted to
                 ensure exactly rounded results for all inputs. To
                 reduce the number of terms in the approximation, the
                 input interval is divided into subintervals of equal
                 size and different coefficients are used for each
                 subinterval. For floating point numbers with 16-b
                 significands, the exactly rounded value of the function
                 can be computed in 51 ns on a 20-mm/sup 2/ chip. For
                 floating point numbers with 24-b significands, the
                 functions can be computed in 80 ns on a 98-mm/sup 2/
                 chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Electr. and Comput. Eng., Texas Univ.,
                 Austin, TX, USA",
  bookpages =    "xii + 284",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods)",
  confdate =     "29 June--2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "Elementary functions; Exact rounding; Floating point
                 numbers; Polynomial approximation; Reciprocal; Rounded
                 results; Square root",
  thesaurus =    "Floating point arithmetic; Function evaluation",
}

@Article{Schulte:1993:PHD,
  author =       "Michael J. Schulte and Earl E. {Swartzlander, Jr.}",
  title =        "Parallel hardware designs for correctly rounded
                 elementary functions",
  journal =      j-INTERVAL-COMP,
  volume =       "4",
  pages =        "65--88",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10 (65C20)",
  MRnumber =     "1 305 859",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
}

@TechReport{Schwarz:1993:HRAa,
  author =       "E. Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Technical Report",
  number =       "CSL-TR-93-559",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jan,
  year =         "1993",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@PhdThesis{Schwarz:1993:HRAb,
  author =       "Eric Mark Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "224",
  month =        apr,
  year =         "1993",
  bibdate =      "Mon Jan 07 22:38:06 2008",
  abstract =     "Many common algorithms for high-order arithmetic
                 operations require an initial approximation. The
                 Newton-Raphson algorithm starts with an approximation
                 and then quadratically converges on the solution. The
                 initial approximation determines the number of
                 iterations of the algorithm and is typically
                 implemented as a look-up table in the form of a ROM or
                 PLA. A novel method is suggested which describes
                 high-order arithmetic operations with a partial product
                 array. This method applies to the operations of
                 division, reciprocal, square root, natural logarithm,
                 exponential, and trigonometric functions. The partial
                 product array of Boolean elements which describes the
                 operation can be summed on an existing floating-point
                 multiplier. The hardware needed is only the logic gates
                 to create the Boolean elements in the array and a
                 multiplexor, and the latency is that of the multiplier.
                 Thus, by reusing a floating-point multiplier, a
                 high-precision approximation to a high-order arithmetic
                 operation can be implemented with a low marginal
                 cost.\par

                 This dissertation describes the implementation and
                 shows a method for deriving partial product arrays to
                 approximate arithmetic operations. Then the proposed
                 method is applied and evaluated for several operations.
                 The proposed method yields a minimum approximation of
                 twelve bits correct for the reciprocal operation and
                 sixteen bits for the square root operation. The
                 proposed method is shown to be as small as 0.05\% the
                 size (in gates) of an equivalent precision look-up
                 table and has up to four times the accuracy (in bits)
                 as an equivalent latency polynomial approximation.
                 Also, three new iterative algorithms to increase the
                 precision of the approximations and a theoretical
                 analysis of the partial product array representation
                 are detailed. Thus, high-radix algorithms of many
                 arithmetic operations are possible at low cost.",
  acknowledgement = ack-nhfb,
  keywords =     "division; elementary functions; exponential;
                 logarithm; PPA (partial product array); reciprocal
                 square root; square root",
  remark =       "AAT 9317816. ProQuest document ID 746798521.",
}

@InProceedings{Schwarz:1993:HSA,
  author =       "E. M. Schwarz and M. J. Flynn",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "Hardware starting approximation for the square root
                 operation",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "103--111",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "A method for obtaining high-precision approximations
                 of high-order arithmetic operations is presented. These
                 approximations provide an accurate starting
                 approximation for high-precision iterative algorithms,
                 which translates into few iterations and \ldots{}",
}

@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",
  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",
}

@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",
  bibdate =      "Tue Mar 14 16:17:03 1995",
  note =         "See \cite{Hull:1994:ICE}",
  acknowledgement = ack-rfb,
}

@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",
  ISSN =         "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "1 294 301",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/; OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  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{}",
}

@Article{Damnjanovic:1994:EFL,
  author =       "Zlatan Damnjanovic",
  title =        "Elementary functions and loop programs",
  journal =      "Notre Dame J. Formal Logic",
  volume =       "35",
  number =       "4",
  pages =        "496--522",
  year =         "1994",
  CODEN =        "NDJFAM",
  ISSN =         "0029-4527",
  MRclass =      "03D20 (68Q15)",
  MRnumber =     "96i:03036",
  MRreviewer =   "John P. Helm",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@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",
  MRclass =      "26-01 (33B10)",
  MRnumber =     "1 257 731",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@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",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}

@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",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}

@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",
  ISSN =         "0098-3500",
  bibdate =      "Tue Mar 21 15:10:29 1995",
  note =         "See \cite{Anonymous:1994:C}.",
  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,
  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",
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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",
  bibdate =      "Sat May 20 15:54:18 1995",
  accepted =     "December 1993",
  acknowledgement = ack-rfb,
  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",
}

@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",
  bibdate =      "Tue Mar 24 20:54:11 2009",
  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,
}

@InCollection{Lozier:1994:NES,
  author =       "Daniel W. Lozier and F. W. J. Olver",
  title =        "Numerical evaluation of special functions",
  crossref =     "Gautschi:1994:MCH",
  volume =       "48",
  pages =        "79--125",
  year =         "1994",
  MRclass =      "65D20 (30-04 33-04 41-04)",
  MRnumber =     "95m:65036",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Fri Jul 9 05:44:10 2004",
  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,
  remark =       "The references list contains about 400 entries which
                 should ultimately be incorporated in this BibTeX
                 bibliography collection.",
}

@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",
  note =         "Published in \cite{Lozier:1996:SNS}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps",
  acknowledgement = ack-nhfb,
}

@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",
  acknowledgement = ack-nhfb,
  ZMnumber =     "809.41015",
}

@Article{Merrheim:1994:CEF,
  author =       "X. Merrheim",
  title =        "The computation of elementary functions in radix
                 $2^p$. International Symposium on Scientific Computing,
                 Computer Arithmetic and Validated Numerics (Vienna,
                 1993)",
  journal =      j-COMPUTING,
  volume =       "53",
  number =       "3--4",
  pages =        "219--232",
  year =         "1994",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X",
  MRclass =      "68M07",
  MRnumber =     "95j:68028",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@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",
  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/",
  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",
  journalabr =   "Inf Process Lett",
  keywords =     "Approximation theory; approximation theory; $x^n$
                 approximation; 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",
}

@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",
  acknowledgement = ack-nhfb,
}

@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 =      "Transactions of the Information Processing Society of
                 Japan",
  volume =       "35",
  number =       "5",
  pages =        "926--933",
  month =        may,
  year =         "1994",
  CODEN =        "JSGRD5",
  ISSN =         "0387-5806",
  MRclass =      "65D20",
  MRnumber =     "95f:65045",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  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 = "C5230 (Digital arithmetic methods); C4120
                 (Functional analysis); C6130 (Data handling
                 techniques)",
  keywords =     "Elementary functions evaluation; Numerical evaluation;
                 ATA method; Add/table-lookup/add method; ATA-M method;
                 Add/table-lookup/add/multiply method; Single-precision
                 calculations; Double-precision calculations; Table
                 size; Split parallel multiplication method;
                 Double-precision floating point circuitry; Integrated
                 circuits; Floating-point accelerators; Double-precision
                 division; Uniform pseudo-random number generation;
                 Single-precision complex number multiplication",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Digital arithmetic; Function evaluation; Random number
                 generation; Table lookup",
}

@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",
  ISSN =         "0018-9340",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  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",
  classification = "B2570D (CMOS integrated circuits); B1265B (Logic
                 circuits); B0290F (Interpolation and function
                 approximation); C5230 (Digital arithmetic methods);
                 C5120 (Logic and switching circuits); C4130
                 (Interpolation and function approximation)",
  keywords =     "Hardware designs; Exactly rounded elementary
                 functions; Reciprocal; Square-root; Polynomial
                 approximation; Multi-operand adder; Chebyshev series
                 approximation; Single-precision floating point numbers;
                 Chip area; 1.0-Micron CMOS technology; Computational
                 delay; Computer arithmetic; Exact rounding; Parallel
                 multiplier; Argument reduction; Special-purpose
                 hardware; 1 Micron",
  language =     "English",
  numericalindex = "Size 1.0E-06 m",
  pubcountry =   "USA",
  thesaurus =    "Approximation theory; Chebyshev approximation; CMOS
                 integrated circuits; Digital arithmetic; Multiplying
                 circuits; Polynomials; Summing circuits",
}

@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)",
  MRclass =      "33B15 (30E10 33-04 40-04 65D20)",
  MRnumber =     "95g:33002",
  MRreviewer =   "E. Kaucher",
  bibdate =      "Mon Jan 20 15:27:00 MST 1997",
  acknowledgement = ack-nhfb,
}

@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",
  ISSN =         "0018-9200",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  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); C5230 (Digital arithmetic methods); C5120
                 (Logic and switching circuits); C5220P (Parallel
                 architecture)",
  keywords =     "Double-metal n-well CMOS technology; Floating-point
                 vector-arithmetic unit; CORDIC algorithm;
                 Multiplication; Division; Sine; Cosine; Hyperbolic
                 sine; Square root; Natural logarithm; Inverse tangent;
                 Vector norm; Phase; 1.6 Micron; 220 MFLOPS",
  language =     "English",
  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",
}

@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/",
  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)",
}

@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",
  pages =        "349--358",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  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",
  bookpages =    "xi + 621",
  classification = "C5230 (Digital arithmetic methods); C4130
                 (Interpolation and function approximation)",
  confdate =     "4-7 Jan. 1994",
  conflocation = "Wailea, HI, USA",
  confsponsor =  "IEEE; ACM; Univ. Hawaii; Univ. Hawaii Coll. Bus.
                 Admin",
  keywords =     "Elementary functions; Double precision; Memory
                 density; Memory speed; Numerical computing; ATA-M;
                 Add-Table Lookup-Add with Multiplication; Polynomials;
                 Hyperbolic functions; Floating point multiplication
                 time",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Polynomials; Table lookup",
}

@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",
  ISSN =         "0018-9340",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  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 /sub */,
                 our algorithms to achieve roughly 3.68 tau /sub */,4.56
                 tau /sub */, 5.25 tau /sub */, 3.69 tau /sub */, 7.06
                 tau /sub */, and 6.5 tau /sub */, 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",
  classification = "C5230 (Digital arithmetic methods); C4110 (Error
                 analysis in numerical methods)",
  keywords =     "Hardware-based algorithms; Elementary function
                 computations; Rectangular multipliers; Scientific
                 computations; Common elementary functions; Reciprocal
                 square root; Arc tangent; Sine; Cosine; Microscopic
                 parallelism; Floating point multiplication",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Error analysis",
}

@Article{Xu:1994:VPC,
  author =       "Guo Liang Xu and Jia Kai Li",
  title =        "Variable precision computation of elementary
                 functions. (Chinese)",
  journal =      "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",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal on Numerical Methods and Computer
                 Applications. Shuzhi Jisuan yu Jisuanji Yingyong",
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  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{}",
}

@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",
  MRclass =      "68M07 (68Q20)",
  MRnumber =     "1 390 003",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  acknowledgement = ack-nhfb,
}

@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",
  bibdate =      "Tue Nov 14 09:57:55 1995",
  acknowledgement = ack-rfb,
  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",
}

@Article{Hobson:1995:EMR,
  author =       "R. F. Hobson and M. W. Fraser",
  title =        "An efficient maximum-redundancy radix-$8$ {SRT}
                 division and square-root method",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "1",
  pages =        "29--38",
  month =        jan,
  year =         "1995",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  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)",
  keywords =     "Maximum-redundancy radix-8 SRT algorithm;
                 Multiplication; Division; Square-root method;
                 Integrated control path; Redundant partial-remainder;
                 Parallel iterative multiplier; Partial remainder
                 production; Maximally redundant digit set; IEEE
                 floating point algorithm; Table lookup; CMOS adder
                 cell; CMOS divider; 1.2 Mum",
  language =     "English",
  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",
}

@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 =    "OCLC Proceedings database; http://ieeexplore.ieee.org/",
  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{}",
}

@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 =    "OCLC Proceedings database; http://ieeexplore.ieee.org/",
  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{}",
}

@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 =    "OCLC Proceedings database; http://ieeexplore.ieee.org/",
  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{}",
}

@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 =    "z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html",
  acknowledgement = ack-nhfb,
  subject =      "C (Computer program language)",
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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 =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01732609",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  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",
  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,
  keywords =     "elementary functions",
}

@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 =    "OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf",
  acknowledgement = ack-nhfb,
}

@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 =    "OCLC Proceedings database; http://ieeexplore.ieee.org/",
  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{}",
}

@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",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  note =         "See \cite{Montuschi:1993:RIT}.",
  acknowledgement = ack-nhfb,
  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{}",
}

@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 =    "OCLC Proceedings database; http://ieeexplore.ieee.org/",
  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{}",
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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 =          "http://dx.doi.org/10.1109/12.475133",
  ISSN =         "0018-9340",
  bibdate =      "Fri Dec 08 10:21:28 2006",
  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,
  keywords =     "argument reduction; computer arithmetic; continued
                 fractions; nonlinear optimization; Payne/Hanek radian
                 reduction; range reduction; trigonometric functions",
}

@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",
  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",
  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",
}

@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",
  ISSN =         "0018-9340",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  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",
  classification = "C5230 (Digital arithmetic methods); C4110 (Error
                 analysis in numerical methods)",
  keywords =     "Fast evaluation; Elementary functions; Single
                 precision; Truncated Taylor series; Difference method;
                 Adders; Reciprocal; Square root; Logarithm functions;
                 Inverse trigonometric functions; Floating point
                 multiplies",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Error analysis; Floating point arithmetic",
}

@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",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}

@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",
  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,
  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.",
}

@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 =    "http://ieeexplore.ieee.org/",
  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{}",
}

@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",
  note =         "Published in \cite{Lozier:1997:PST}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps",
  acknowledgement = ack-nhfb,
}

@Article{Lozier:1996:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "66",
  number =       "??",
  pages =        "345--358",
  month =        "????",
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427",
  bibdate =      "Fri Jul 09 05:51:55 2004",
  acknowledgement = ack-nhfb,
  remark =       "See preprint \cite{Lozier:1994:SNS}.",
}

@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",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/;
                 http://doi.acm.org/10.1145/232826.232846",
  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,
  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.",
}

@InProceedings{Rao:1996:RTS,
  author =       "V. M. Rao and B. Nowrouzian",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering. 26--29 May 1996",
  title =        "Rounding techniques for signed binary arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "294--297",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  abstract =     "This paper is concerned with the derivation of the
                 relationship that exists between the number truncation
                 in two's complement (TC) arithmetic and the
                 corresponding truncation in signed-binary (SB)
                 arithmetic. The resulting relationship is subsequently
                 exploited and applied to the development of a pair of
                 novel techniques for SB rounding. These techniques are
                 then translated into algorithm suitable for two-level
                 logic implementation. Finally, the resulting algorithms
                 are applied to the design and implementation of a
                 high-speed SB-kernel based TC multiply-accumulate
                 arithmetic architecture.",
  acknowledgement = ack-nhfb,
}

@Article{Schwarz:1996:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware Starting Approximation Method and Its
                 Application to the Square Root Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "12",
  pages =        "1356--1369",
  month =        dec,
  year =         "1996",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Quadratically converging algorithms for high-order
                 arithmetic operations typically are accelerated by a
                 starting approximation. The higher the precision of the
                 starting approximation, the less number of iterations
                 required for convergence. \ldots{}",
}

@Book{Temme:1996:SFI,
  author =       "N. M. Temme",
  title =        "Special functions: an introduction to the classical
                 functions of mathematical physics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 374",
  year =         "1996",
  ISBN =         "0-471-11313-1",
  ISBN-13 =      "978-0-471-11313-3",
  LCCN =         "QC20.7.F87 T46 1996",
  bibdate =      "Mon Nov 24 21:41:54 MST 2008",
  bibsource =    "z3950.bibsys.no:2100/BIBSYS; z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "functions, special; mathematical physics; boundary
                 value problems",
}

@Article{Williams:1996:TMF,
  author =       "K. B. Williams",
  title =        "Testing Math Functions: When requirements are tight,
                 we must carefully examine all potential sources of
                 error. Make sure your math library isn't the weak link
                 in the chain",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "12",
  pages =        "49--54, 58--65",
  month =        dec,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Thu Nov 14 06:34:33 1996",
  note =         "Describes a package that extends the
                 Cody-Waite-Plauger work on the ELEFUNT package for the
                 testing of the elementary functions, including the
                 inverse hyperbolic functions, cube root, and Bessel
                 functions of the first and second kinds. The C++
                 package implements 192-bit extended precision versions
                 of all of the functions, so that accurate results are
                 available for comparison with the normal
                 double-precision results.",
  acknowledgement = ack-nhfb,
}

@Article{Alzer:1997:SIG,
  author =       "Horst Alzer",
  title =        "On some inequalities for the gamma and psi functions",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "373--389",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33B15 (26D07)",
  MRnumber =     "97e:33004",
  MRreviewer =   "Peter Schroth",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
}

@Article{Alzer:1997:SII,
  author =       "Horst Alzer",
  title =        "On some inequalities for the incomplete gamma
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "218",
  pages =        "771--778",
  month =        apr,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33B20 (26D07)",
  MRnumber =     "97h:33004",
  bibdate =      "Fri Jul 16 10:38:42 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-218",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/",
  acknowledgement = ack-nhfb,
}

@Article{Ghanem:1997:SBF,
  author =       "Riadh Ben Ghanem and Cl{\'e}ment Frappier",
  title =        "Spherical {Bessel} functions and explicit quadrature
                 formula",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "289--296",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "33C10 (41A55 65D32)",
  MRnumber =     "97c:33005",
  MRreviewer =   "N. Hayek Calil",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
}

@Article{Hare:1997:CPB,
  author =       "D. E. G. Hare",
  title =        "Computing the Principal Branch of {log-Gamma}",
  journal =      j-J-ALG,
  volume =       "25",
  number =       "2",
  pages =        "221--236",
  month =        nov,
  year =         "1997",
  CODEN =        "JOALDV",
  DOI =          "http://dx.doi.org/10.1006/jagm.1997.0881",
  ISSN =         "0196-6774",
  bibdate =      "Thu Mar 27 14:31:42 2008",
  abstract =     "The log-Gamma function is an important special
                 function of mathematics, and its principal branch is
                 required in many applications. We develop here the
                 mathematics required to evaluate the principal branch
                 to arbitrary precision, including a new bound for the
                 error in Stirling's asymptotic series. We conclude with
                 a discussion of the implementation of the principal
                 branch of the log-Gamma function in the Maple symbolic
                 algebra system, starting with version Maple V, Release
                 3.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:1997:PAI,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 1997 IEEE International Conference
                 on Computer Design: VLSI in Computers and Processors:
                 ICCD '97",
  title =        "Parallel-array implementations of a non-restoring
                 square root algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "690--695",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "In this paper we present a parallel-array
                 implementation of a new non-restoring square root
                 algorithm (PASQRT). The carry-save adder (CSA) is used
                 in the parallel array. The PASQRT has several features
                 unlike other implementations. First, it does \ldots{}",
}

@InCollection{Lozier:1997:PST,
  author =       "Daniel W. Lozier",
  title =        "A Proposed Software Test Service for Special
                 Functions",
  crossref =     "Boisvert:1997:QNS",
  pages =        "167--178",
  year =         "1997",
  bibdate =      "Fri Jul 09 06:00:46 2004",
  acknowledgement = ack-nhfb,
  remark =       "See preprint \cite{Lozier:1996:PST}.",
}

@TechReport{Lozier:1997:TRN,
  author =       "Daniel W. Lozier",
  title =        "Toward a Revised {NBS} Handbook of Mathematical
                 Functions",
  type =         "Technical Report",
  number =       "NISTIR 6072",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "8",
  month =        sep,
  year =         "1997",
  bibdate =      "Fri Jul 09 06:35:07 2004",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6072.ps.gz",
  acknowledgement = ack-nhfb,
}

@InProceedings{Matsubara:1997:LPZ,
  author =       "G. Matsubara and N. Ide",
  booktitle =    "Proceedings of the Third International Symposium on
                 Advanced Research in Asynchronous Circuits and Systems,
                 7--10 April 1997",
  title =        "A low power zero-overhead self-timed division and
                 square root unit combining a single-rail static circuit
                 with a dual-rail dynamic circuit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "198--209",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "An asynchronous pipeline scheme that combines a low
                 power static circuit with a high-speed dual-rail
                 dynamic circuit is proposed. The scheme utilizes a
                 dual-rail circuit only in the critical path of an SRT
                 division and square root calculation unit. \ldots{}",
}

@Book{Muller:1997:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary functions: algorithms and implementation",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xv + 204",
  year =         "1997",
  ISBN =         "0-8176-3990-X",
  ISBN-13 =      "978-0-8176-3990-7",
  LCCN =         "QA331.M866 1997",
  bibdate =      "Fri Jul 25 12:00:55 1997",
  price =        "US\$59.95",
  URL =          "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
                 http://www.ens-lyon.fr/~jmmuller/book_functions.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1997:AFA,
  author =       "M. J. Schulte and James E. Stine",
  title =        "Accurate Function Approximations by Symmetric Table
                 Lookup and Addition",
  crossref =     "Thiele:1997:IIC",
  pages =        "144--153",
  year =         "1997",
  bibdate =      "Sun Mar 04 10:55:40 2007",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1997:SBT,
  author =       "M. Schulte and J. Stine",
  title =        "Symmetric Bipartite Tables for Accurate Function
                 Approximation",
  crossref =     "Lang:1997:ISC",
  pages =        "175--183",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf",
  acknowledgement = ack-nhfb,
}

@Book{Thompson:1997:ACMa,
  author =       "William J. (William Jackson) Thompson",
  title =        "Atlas for computing mathematical functions: an
                 illustrated guidebook for practitioners: with programs
                 in {C} and {Mathematica}",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 903",
  year =         "1997",
  ISBN =         "0-471-00260-7 (cloth)",
  ISBN-13 =      "978-0-471-00260-4 (cloth)",
  LCCN =         "QA331.T385 1997",
  bibdate =      "Fri May 21 07:11:19 MDT 1999",
  acknowledgement = ack-nhfb,
  annote =       "A Wiley-Interscience publication. Includes CD-ROM.",
  keywords =     "Functions -- Computer programs; Science -- Mathematics
                 -- Computer programs; C (Computer program language);
                 Mathematica (Computer program language)",
}

@Book{Thompson:1997:ACMb,
  author =       "William J. (William Jackson) Thompson",
  title =        "Atlas for computing mathematical functions: an
                 illustrated guide for practitioners with programs in
                 {Fortran 90} and {Mathematica}",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 888",
  year =         "1997",
  ISBN =         "0-471-18171-4 (cloth)",
  ISBN-13 =      "978-0-471-18171-2 (cloth)",
  LCCN =         "QA331.T386 1997",
  bibdate =      "Fri May 21 07:11:19 MDT 1999",
  note =         "Includes CD-ROM.",
  acknowledgement = ack-nhfb,
  annote =       "A Wiley-Interscience publication. System requirements
                 for accompanying computer disc: Windows; Macintosh
                 compatible.",
  keywords =     "Functions -- Computer programs; Science -- Mathematics
                 -- Computer programs; FORTRAN (Computer program
                 language); Mathematica (Computer program language)",
}

@Article{Aberbour:1998:PMF,
  author =       "M. Aberbour and A. Houelle and H. Mehrez and N.
                 Vaucher and A. Guyot",
  title =        "On portable macrocell {FPU} generators for division
                 and square root operators complying to the full
                 {IEEE-754} standard",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "114--121",
  month =        mar,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "1063-8210",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "In this paper, we investigate the design of macrocell
                 generators of division and square root floating-point
                 operators. The number representation used in our
                 operators is the IEEE-754-1985 standard for binary
                 floating-point numbers. The design and \ldots{}",
}

@Article{BenGhanem:1998:QFU,
  author =       "Riadh {Ben Ghanem}",
  title =        "Quadrature formulae using zeros of {Bessel} functions
                 as nodes",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "221",
  pages =        "323--336",
  month =        jan,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D32",
  MRnumber =     "98c:65031",
  MRreviewer =   "Kai Diethelm",
  bibdate =      "Fri Jul 16 10:38:50 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-221",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/",
  acknowledgement = ack-nhfb,
}

@Article{Deleglise:1998:C,
  author =       "Marc Del{\'e}glise and Jo{\"e}l Rivat",
  title =        "Computing $\psi(x)$",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "224",
  pages =        "1691--1696",
  month =        oct,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "11Y35 (11N56)",
  MRnumber =     "1 474 649",
  bibdate =      "Fri Jul 16 10:38:58 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-224",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/",
  acknowledgement = ack-nhfb,
}

@Article{Kiranon:1998:SRV,
  author =       "W. Kiranon and N. Kumprasert",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "145",
  number =       "2",
  pages =        "139",
  month =        apr,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Recently, Lui [1995] presented a square-rooting
                 circuit using CCII, MOS transistors and a buffered
                 unity-gain inverting amplifier. It is interesting since
                 it finds various applications as described in his
                 paper. However, an error occurred in the \ldots{}",
}

@InProceedings{Kuhlmann:1998:FLP,
  author =       "M. Kuhlmann and K. K. Parhi",
  booktitle =    "Proceedings of the 1998 International Conference on
                 Computer Design: VLSI in Computers and Processors. ICCD
                 '98",
  title =        "Fast low-power shared division and square-root
                 architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--135",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "This paper addresses a fast low-power implementation
                 of a shared division and square-root architecture. Two
                 approaches are considered in this paper; these include
                 the SRT (Sweeney, Robertson and Tocher) approach which
                 does not require prescaling and \ldots{}",
}

@Article{Lefevre:1998:TCR,
  author =       "V. Lef{\`e}vre and J.-M. Muller and A. Tisserand",
  title =        "Toward correctly rounded transcendentals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting correctly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that have
                 helped us to solve this problem for the \ldots{}",
}

@Article{Morozov:1998:NWR,
  author =       "D. Kh. Morozov and V. V. Voitsekhovich",
  title =        "A new wide-range approximation of modified {Bessel}
                 functions in terms of elementary functions",
  journal =      "Rev. Mexicana F\'\i s.",
  volume =       "44",
  number =       "3",
  pages =        "231--234",
  year =         "1998",
  CODEN =        "RMXFAT",
  ISSN =         "0035-001X",
  MRclass =      "65D20",
  MRnumber =     "MR1629601",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
  fjournal =     "Revista Mexicana de F\'\i sica",
}

@InProceedings{Agarwal:1999:SAM,
  author =       "R. C. Agarwal and F. G. Gustavson and M. S.
                 Schmookler",
  title =        "Series approximation methods for divide and square
                 root in the {Power3{\TM}} processor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "116--123",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-144.ps;
                 http://euler.ecs.umass.edu/paper/final/paper-144.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; ARITH; IEEE",
  summary =      "The Power3 processor is a 64-bit implementation of the
                 PowerPC TM architecture and is the successor to the
                 Power2 TM processor for workstations and servers which
                 REQUIRE high performance floating point capability. The
                 previous \ldots{}",
}

@Article{Bach:1999:NTS,
  author =       "E. Bach and K. Huber",
  title =        "Note on taking square-roots modulo {N}",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "45",
  number =       "2",
  pages =        "807--809",
  month =        mar,
  year =         "1999",
  CODEN =        "IETTAW",
  ISSN =         "0018-9448",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "In this article it is shown how Gauss' (1981) famous
                 cyclotomic sum formula can be used for extracting
                 square-roots modulo \ldots{}",
}

@InProceedings{Batten:1999:IBO,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and R. Peri and P. D'arcy",
  editor =       "????",
  booktitle =    "Proceedings of the International Conference on Signal
                 Processing Applications and Technologies, Orlando,
                 Florida, November, 1999",
  title =        "Interactions Between Optimizations and a New Type of
                 {DSP} Intrinsic Function",
  publisher =    "????",
  address =      "????",
  year =         "1999",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 11:05:23 2007",
  note =         "Shortened version in \cite{Batten:1999:IFB}.",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Batten:1999:IFB,
  author =       "D. Batten and P. D'arcy",
  title =        "Intrinsic Functions Boost Compilers",
  journal =      "Electrical Engineering Times",
  volume =       "1085",
  pages =        "104--104",
  month =        nov,
  year =         "1999",
  bibdate =      "Sun Mar 04 11:06:22 2007",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bui:1999:DSI,
  author =       "H. Bui and S. Tahar",
  booktitle =    "1999 IEEE Canadian Conference on Electrical and
                 Computer Engineering, 9--12 May 1999",
  title =        "Design and synthesis of an {IEEE-754} exponential
                 function",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "450--455",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "We have designed a floating-point exponential function
                 using the table-driven method. The algorithm was first
                 implemented using sequential VHDL and later translated
                 to Concurrent Verilog. The main part of the work
                 consisted of creating modules that \ldots{}",
}

@Article{Cappuccino:1999:HSS,
  author =       "G. Cappuccino and G. Cocorullo and P. Corsonello and
                 S. Perri",
  title =        "High speed self-timed pipelined datapath for square
                 rooting",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "146",
  number =       "1",
  pages =        "16--22",
  month =        feb,
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "The authors describe a new high-performance self-timed
                 circuit for asynchronous square rooting. The new
                 architecture is based on a modified nonrestoring
                 algorithm. An asynchronous pipelined cellular array
                 without auxiliary system for the \ldots{}",
}

@InProceedings{Cornea-Hasegan:1999:CPO,
  author =       "M. A. Cornea-Hasegan and R. A. Golliver and P.
                 Markstein",
  title =        "Correctness proofs outline for {Newton--Raphson} based
                 floating-point divide and square root algorithms",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "96--105",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-121.ps;
                 http://euler.ecs.umass.edu/paper/final/paper-121.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; ARITH; IEEE",
  summary =      "This paper describes a study of a class of algorithms
                 for the floating-point divide and square root
                 operations, based on the Newton-Raphson iterative
                 method. The two main goals were. (1) Proving the IEEE
                 correctness of these iterative floating-point
                 \ldots{}",
}

@Article{Corsonello:1999:HPS,
  author =       "P. Corsonello and S. Perri",
  title =        "High performance square rooting circuit using hybrid
                 radix-$2$ adders",
  journal =      j-ELECT-LETTERS,
  volume =       "35",
  number =       "3",
  pages =        "185--186",
  day =          "4",
  month =        feb,
  year =         "1999",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A new high performance bit parallel architecture for
                 computing square roots is proposed. The architecture
                 implements a non-restoring algorithm and is structured
                 as a pipelined cellular array. To improve the
                 performance, hybrid radix-$2$ adders are \ldots{}",
}

@Article{Gautschi:1999:NRC,
  author =       "Walter Gautschi",
  title =        "A Note on the Recursive Calculation of Incomplete
                 Gamma Functions",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "101--107",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gautschi:1999:NRC;
                 http://doi.acm.org/10.1145/305658.305717",
  abstract =     "It is known that the recurrence relation for
                 incomplete gamma functions $\Gamma(a + n, x), 0 \le a <
                 1$, $n = 0, 1, 2 \ldots$, when $x$ is positive, is
                 unstable---more so the larger $x$. Nevertheless, the
                 recursion can be used in the range $0 \le n \le x$
                 practically without error growth, and in larger ranges
                 $0 \le n \le N$ with a loss of accuracy that can be
                 controlled by suitably limiting $N$.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; reliability",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Stability (and instability). {\bf
                 G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
}

@TechReport{Gourdon:1999:NCC,
  author =       "Xavier Gourdon and Pascal Sebah",
  title =        "Numbers, constants, and computation",
  institution =  "????",
  address =      "Paris, France",
  year =         "1999",
  bibdate =      "Sat Mar 15 16:28:07 2003",
  note =         "World-Wide Web site.",
  URL =          "http://numbers.computation.free.fr/Constants/home.html",
  acknowledgement = ack-nhfb,
  annote =       "Although this site concentrates mainly on computation
                 of particular mathematical constants, it also treats
                 high-precision computation of inverse and square
                 root.",
}

@Article{Harrison:1999:CTF,
  author =       "John Harrison and Ted Kubaska and Shane Story and Ping
                 Tak Peter Tang",
  title =        "The Computation of Transcendental Functions on the
                 {IA-64} Architecture",
  journal =      j-INTEL-TECH-J,
  number =       "Q4",
  pages =        "7",
  day =          "22",
  month =        nov,
  year =         "1999",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  URL =          "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm;
                 http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hyogo:1999:LVF,
  author =       "A. Hyogo and Y. Fukutomi and K. Sekine",
  booktitle =    "Proceedings of the 1999 IEEE International Symposium
                 on Circuits and Systems: ISCAS '99, 2 June 1999",
  title =        "Low voltage four-quadrant analog multiplier using
                 square-root circuit based on {CMOS} pair",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "274--277",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "We proposed a square-root circuit based on CMOS pairs.
                 In this paper, we propose a low voltage four-quadrant
                 analog multiplier using the square-root circuit. Also
                 we confirmed this operation by PSpice \ldots{}",
}

@InProceedings{Iordache:1999:IPR,
  author =       "C. Iordache and D. W. Matula",
  title =        "On Infinitely Precise Rounding for Division, Square
                 Root, Reciprocal and Square Root Reciprocal",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "233--240",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-164.ps;
                 http://euler.ecs.umass.edu/paper/final/paper-164.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; ARITH; IEEE",
  summary =      "Quotients, reciprocals, square roots and square root
                 reciprocals all have the property that infinitely
                 precise p-bit rounded results for p-bit input operands
                 can be obtained from approximate results of bounded
                 accuracy. We investigate lower bounds \ldots{}",
}

@Article{Lang:1999:VHR,
  author =       "T. Lang and P. Montuschi",
  title =        "Very high radix square root with prescaling and
                 rounding and a combined division\slash square root
                 unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "827--841",
  month =        aug,
  year =         "1999",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "An algorithm for square root with prescaling and
                 selection by rounding is developed and combined with a
                 similar scheme for division. Since division is usually
                 more frequent than square root, the main concern of the
                 combined implementation is to \ldots{}",
}

@InProceedings{Lee:1999:STS,
  author =       "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
                 Seung-Ho Hwang",
  booktitle =    "6th International Conference on VLSI and CAD: ICVC
                 '99",
  title =        "Self-timed shared division and square-root
                 implementation using full redundant signed digit
                 numbers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "541--544",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A radix-$2$ square root implementation for self-timed
                 dividers using redundant signed-digit (RSD) adders is
                 presented. In this method, two self-timed RSD adder
                 stages are used for each result bit selection. A very
                 efficient and simple result bit \ldots{}",
}

@InProceedings{Lozier:1999:DDM,
  author =       "Daniel W. Lozier and B. R. Miller and B. V. Saunders",
  title =        "Design of a Digital Mathematical Library for Science,
                 Technology and Education",
  crossref =     "IEEE:1999:PIF",
  pages =        "118--128",
  year =         "1999",
  bibdate =      "Fri Jul 09 06:33:35 2004",
  URL =          "http://dlmf.nist.gov/about/publications/nistir6297.ps.gz",
  acknowledgement = ack-nhfb,
  remark =       "Preprint: NISTIR 6297, Feb. 1999, 13 pages",
}

@InProceedings{Nannarelli:1999:LPR,
  author =       "A. Nannarelli and T. Lang",
  booktitle =    "(ICCD '99) International Conference on Computer
                 Design",
  title =        "Low-power radix-$4$ combined division and square
                 root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "236--242",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Because of the similarities in the algorithm it is
                 quite common to implement division and square root in
                 the same unit. The purpose of this work is to implement
                 a low-power combined radix-$4$ division and square root
                 floating-point double precision \ldots{}",
}

@InProceedings{Oberman:1999:FPD,
  author =       "S. F. Oberman",
  title =        "Floating point division and square root algorithms and
                 implementation in the {AMD-K7{\TM}} microprocessor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "106--115",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-139.ps;
                 http://euler.ecs.umass.edu/paper/final/paper-139.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; ARITH; IEEE",
  summary =      "This paper presents the AMD-K7 IEEE 754 and $\times$87
                 compliant floating point division and square root
                 algorithms and implementation. The AMD-K7 processor
                 employs an iterative implementation of a series
                 expansion to converge quadratically to the \ldots{}",
}

@InProceedings{Parhami:1999:ALT,
  author =       "B. Parhami",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Analysis of the lookup table size for square-rooting",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1327--1330",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Convergence methods are widely used for division,
                 reciprocation, and square-rooting. With such methods,
                 it is common to use an initial table lookup step for
                 obtaining an approximate result that leads to faster
                 convergence. In the case of division \ldots{}",
}

@Article{Schraudolph:1999:FCA,
  author =       "N. N. Schraudolph",
  title =        "A Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "11",
  number =       "4",
  publisher =    "MIT Press",
  pages =        "853--862",
  day =          "1",
  month =        may,
  year =         "1999",
  CODEN =        "NEUCEB",
  ISSN =         "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "10",
}

@Article{Schulte:1999:AEF,
  author =       "M. Schulte and J. Stine",
  title =        "Approximating Elementary Functions with Symmetric
                 Bipartite Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "842--847",
  year =         "1999",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Fri Jun 24 20:20:58 2005",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1999:ESO,
  author =       "M. J. Schulte and K. E. Wires",
  title =        "Efficient Second Order Approximations for Reciprocals
                 and Square Roots",
  crossref =     "Luk:1999:PSA",
  volume =       "3807",
  pages =        "10--18",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:10:48 2007",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1999:HSI,
  author =       "Michael J. Schulte and Kent E. Wires",
  title =        "High-Speed Inverse Square Roots",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "124--131",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-109.ps;
                 http://euler.ecs.umass.edu/paper/final/paper-109.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; ARITH; IEEE",
  summary =      "Inverse square roots are used in several digital
                 signal processing, multimedia, and scientific computing
                 applications. This paper presents a high-speed method
                 for computing inverse square roots. This method uses a
                 table lookup, operand modification, \ldots{}",
}

@Article{Seidel:1999:HSR,
  author =       "P.-M. Seidel",
  title =        "High-speed redundant reciprocal approximation",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "28",
  number =       "1",
  publisher =    "Elsevier Science",
  pages =        "1--12",
  month =        sep,
  year =         "1999",
  CODEN =        "IVJODL",
  ISSN =         "0167-9260",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "12",
}

@Article{Stine:1999:STA,
  author =       "E. Stine and M. J. Schulte",
  title =        "The Symmetric Table Addition Method for Accurate
                 Function Approximation",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "21",
  number =       "2",
  pages =        "167--177",
  month =        jun,
  year =         "1999",
  CODEN =        "JVSPED",
  ISSN =         "0922-5773",
  bibdate =      "Sun Mar 04 11:02:59 2007",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Story:1999:NAI,
  author =       "S. Story and P. T. P. Tang",
  title =        "New Algorithms for Improved Transcendental Functions
                 on {IA-64}",
  crossref =     "Koren:1999:ISC",
  pages =        "4--11",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "ftp://ftp.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-118.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
}

@Article{Wieder:1999:ANH,
  author =       "Thomas Wieder",
  title =        "{Algorithm 794}: Numerical {Hankel} transform by the
                 {Fortran} program {HANKEL}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "240--250",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/317275.317284;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH;
                 http://www.netlib.org/toms/794;
                 ftp://netlib.bell-labs.com/netlib/toms/794.gz;
                 http://www.netlib.no/netlib/toms/794;
                 http://www.hensa.ac.uk/netlib/toms/794.gz;
                 http://phase.etl.go.jp/netlib/toms/794",
  ISSN =         "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/",
  abstract =     "The numerical evaluation of the Hankel transform poses
                 the problems of both infinite integration and Bessel
                 function calculation. Using the corresponding numerical
                 program routines from the literature, a Fortran program
                 has been written to perform the Hankel transform for
                 real functions, given either in analytical form as
                 subroutines or in discrete form as tabulated data.",
  accepted =     "February 1999",
  acknowledgement = ack-nhfb,
  keywords =     "Hankel transform; numerical analysis",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Theory of
                 Computation --- Analysis of Algorithms and Problem
                 Complexity --- Numerical Algorithms and Problems
                 (F.2.1): Computation of transforms;",
}

@Article{Alhargan:2000:ACA,
  author =       "Fayez A. Alhargan",
  title =        "Algorithms for the Computation of all {Mathieu}
                 Functions of Integer Orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "390--407",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/358407.358420",
  ISSN =         "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "The paper presents methods for the computation of all
                 Mathieu functions of integer order, which cover a large
                 range of $n$ and $h$; previous algorithms were limited
                 to small values of $n$. The algorithms are given in
                 sufficient details to enable straightforward
                 implementation. The algorithms can handle a large range
                 of the order $n$ (0-200) and the parameter $h$
                 (0-4$n$).",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
}

@Article{Alhargan:2000:ASC,
  author =       "Fayez A. Alhargan",
  title =        "{Algorithm 804}: subroutines for the computation of
                 {Mathieu} functions of integer orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "408--414",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/358407.358422",
  ISSN =         "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "Computer subroutines in C++ for computing Mathieu
                 functions of integer orders are described. The core
                 routines for computing Mathieu characteristic numbers
                 and Mathieu coefficients are described in details, the
                 rest of the subroutines are standard implementation of
                 the series summations for each function. The routines
                 can handle a large range of the order $n$ and the
                 parameter $h$.",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
}

@Article{Anderson:2000:RAF,
  author =       "Stuart Anderson",
  title =        "Remark on {Algorithm 723}: {Fresnel} integrals",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "617--617",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/365723.365737",
  ISSN =         "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  accepted =     "16 October 2000",
  acknowledgement = ack-nhfb,
}

@InProceedings{Batten:2000:NAD,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and P. D'arcy",
  title =        "A New Approach to {DSP} Intrinsic Functions",
  crossref =     "Sprague:2000:PAH",
  pages =        "2892--2901",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:18:38 2007",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
  acknowledgement = ack-nhfb,
}

@Book{Bressoud:2000:CCN,
  author =       "David M. Bressoud and S. Wagon",
  title =        "A course in computational number theory",
  publisher =    "Key College Publishers in cooperation with Springer",
  address =      "New York, NY, USA",
  pages =        "xii + 367",
  year =         "2000",
  ISBN =         "1-93019-010-7",
  ISBN-13 =      "978-1-93019-010-8",
  LCCN =         "QA241 .B788 2000",
  bibdate =      "Fri Sep 26 14:29:31 MDT 2008",
  bibsource =    "z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Number theory; Algorithms",
}

@Article{Cawley:2000:FCA,
  author =       "G. C. Cawley",
  title =        "On a Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "12",
  number =       "9",
  publisher =    "MIT Press",
  pages =        "2009--2012",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "NEUCEB",
  ISSN =         "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "4",
}

@Article{Cherri:2000:PCC,
  author =       "A. K. Cherri and M. S. Alam",
  title =        "Parallel computation of complex elementary functions
                 using quaternary signed-digit arithmetic",
  journal =      "Optics and Laser Technology",
  volume =       "32",
  number =       "6",
  publisher =    "Elsevier Science",
  pages =        "391--399",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "0030-3992",
  bibdate =      "Sat Dec 7 09:21:28 MST 2002",
  bibsource =    "Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "9",
}

@InProceedings{Chu:2000:CPT,
  author =       "Wanming Chu and Yamin Li",
  booktitle =    "ACAC 2000: 5th Australasian Computer Architecture
                 Conference",
  title =        "Cost\slash performance tradeoff of $n$-select square
                 root implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "9--16",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Hardware square-root units require large numbers of
                 gates even for iterative implementations. In this paper
                 we present four low-cost high-performance
                 fully-pipelined n-select implementations (nS-Root)
                 based on a non-restoring-remainder square root
                 \ldots{}",
}

@Article{Ercegovac:2000:IGD,
  author =       "Milos D. Ercegovac and Laurent Imbert and David W. Matula and
                 Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "759--763",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/; OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "The aim of this paper is to accelerate division,
                 square root, and square root reciprocal computations
                 when the Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term
                 \ldots{}",
}

@Article{Ercegovac:2000:RSR,
  author =       "Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel
                 Muller and Arnaud Tisserand",
  title =        "Reciprocation, Square Root, Inverse Square Root, and
                 Some Elementary Functions Using Small Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "628--637",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  MRclass =      "68M07 (65B15)",
  MRnumber =     "MR1783602 (2001e:68016)",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/; OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Institute of Electrical and Electronics Engineers.
                 Transactions on Computers",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "This paper deals with the computation of reciprocals,
                 square roots, inverse square roots, and some elementary
                 functions using small tables, small multipliers, and,
                 for some functions, a final ``large'' (almost
                 full-length) multiplication. \ldots{}",
}

@Article{Favati:2000:SAC,
  author =       "P. Favati and G. Lotti and O. Menchi and F. Romani",
  title =        "Separable asymptotic cost of evaluating elementary
                 functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "24",
  number =       "3",
  publisher =    "Kluwer Academic Publishers, Dordrecht, The
                 Netherlands",
  pages =        "255--274",
  year =         "2000",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398",
  MRclass =      "65Y20",
  MRnumber =     "MR1780414 (2001d:65174)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  pagecount =    "20",
}

@InProceedings{Hasan:2000:FPI,
  author =       "M. A. Hasan and A. A. Hasan and S. Rahman",
  booktitle =    "Proceedings of the 39th IEEE Conference on Decision
                 and Control",
  title =        "Fixed point iterations for computing square roots and
                 the matrix sign function of complex matrices",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4253--4258",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this work has been the development of
                 new set of rational iterations for computing square
                 roots and the matrix sign function of complex matrices.
                 Given any positive integer r{\&}ges;2, we presented a
                 systematic way of deriving rth order \ldots{}",
}

@InProceedings{Hassibi:2000:ESR,
  author =       "B. Hassibi",
  booktitle =    "Proceedings. 2000 IEEE International Conference on
                 Acoustics, Speech, and Signal Processing: ICASSP '00,
                 5--9 June 2000",
  title =        "An efficient square-root algorithm for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II737--II740",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}

@InProceedings{Hassibi:2000:FSR,
  author =       "B. Hassibi",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000.",
  title =        "A fast square-root implementation for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1255--1259",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}

@InProceedings{Lefevre:2000:CRF,
  author =       "V. D. Lefevre and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Correctly rounded functions for better arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "875--878",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "The IEEE 754 standard for floating-point arithmetic
                 requires that the four arithmetic operations and the
                 square root should be correctly rounded. This has
                 improved the accuracy, reliability and portability of
                 numerical software. Unfortunately, such \ldots{}",
}

@InProceedings{Lozier:2000:DPN,
  author =       "Daniel W. Lozier",
  title =        "The {DLMF Project}: {A} New Initiative in Classical
                 Special Functions",
  crossref =     "Dunkl:2000:PIW",
  pages =        "207--220",
  year =         "2000",
  bibdate =      "Fri Jul 09 06:31:32 2004",
  acknowledgement = ack-nhfb,
}

@Book{Markstein:2000:IEF,
  author =       "Peter Markstein",
  title =        "{IA-64} and elementary functions: speed and
                 precision",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xix + 298",
  year =         "2000",
  ISBN =         "0-13-018348-2",
  ISBN-13 =      "978-0-13-018348-4",
  LCCN =         "QA76.9.A73 M365 2000",
  bibdate =      "Fri Jan 5 08:00:52 MST 2001",
  bibsource =    "University of California MELVYL catalog.",
  series =       "Hewlett-Packard professional books",
  acknowledgement = ack-nhfb,
  annote =       "Besides recipes for accurate computation of elementary
                 functions, this book also contains algorithms for the
                 correctly-rounded computation of floating-point
                 division and square-root, and of integer division,
                 starting from low-precision reciprocal approximations.
                 There is also a wealth of information on the tradeoffs
                 between integer and floating-point instruction use in a
                 pipelined parallel architecture.",
  keywords =     "IA-64 (computer architecture)",
}

@Article{Paliouras:2000:FPP,
  author =       "V. Paliouras and K. Karagianni and T. Stouraitis",
  title =        "A floating-point processor for fast and accurate
                 sine\slash cosine evaluation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "47",
  number =       "5",
  pages =        "441--451",
  month =        may,
  year =         "2000",
  CODEN =        "ICSPE5",
  ISSN =         "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A VLSI architecture for fast and accurate
                 floating-point sine/cosine evaluation is presented,
                 combining floating-point and simple fixed-point
                 arithmetic. The algorithm implemented by the
                 architecture is based on second order polynomial
                 interpolation \ldots{}",
}

@InProceedings{Takahashi:2000:IMP,
  author =       "D. Takahashi",
  booktitle =    "Proceedings of the 2000 International Workshops on
                 Parallel Processing",
  title =        "Implementation of multiple-precision parallel division
                 and square root on distributed-memory parallel
                 computers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--235",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "We present efficient parallel algorithms for
                 multiple-precision division and square root operation
                 of more than several million decimal digits on
                 distributed-memory parallel computers. It is well known
                 that multiple-precision division and square \ldots{}",
}

@InProceedings{Tchoumatchenko:2000:FBS,
  author =       "V. Tchoumatchenko and T. Vassileva and P. Gurov",
  booktitle =    "Proceedings of the 22nd EUROMICRO Conference EUROMICRO
                 96. 'Beyond 2000: Hardware and Software Design
                 Strategies'.",
  title =        "A {FPGA} based square-root coprocessor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "520--525",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "We present an FPGA implementation of a non-restoring
                 integer square-root algorithm, that uses estimates for
                 result-digit selection and radix-$2$ redundant addition
                 in recurrence. On-the-fly conversion of the
                 result-digit and signed-digit adder/ \ldots{}",
}

@InProceedings{Tommiska:2000:AEI,
  author =       "M. T. Tommiska",
  booktitle =    "Proceedings of the 2000 Third IEEE International
                 Caracas Conference on Devices, Circuits and Systems,
                 15--17 March 2000",
  title =        "Area-efficient implementation of a fast square root
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "S18/1--S18/4",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "An area-efficient implementation of a fast-converging
                 square-root algorithm is presented. The design of
                 special arithmetic operations differs in many ways from
                 the traditional tasks that digital designers are used
                 to, and the role of \ldots{}",
}

@Article{Bashagha:2001:NRS,
  author =       "A. E. Bashagha",
  title =        "Novel radix-$2$ $k$ square root module",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "148",
  number =       "4",
  pages =        "190--196",
  month =        aug,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "The conventional two's complement radix-$2$ k square
                 root algorithm requires a set of 2 k full precision
                 comparisons to generate all the 2 k possible values of
                 the partial remainder. The correct remainder is the
                 minimum \ldots{}",
}

@Article{Berry:2001:WSF,
  author =       "Michael Berry",
  title =        "Why are special functions special?",
  journal =      j-PHYS-TODAY,
  volume =       "54",
  number =       "4",
  pages =        "11--12",
  year =         "2001",
  CODEN =        "PHTOAD",
  ISSN =         "0031-9228",
  bibdate =      "Sat Feb 19 13:23:33 2005",
  acknowledgement = ack-nhfb,
}

@Article{Boisvert:2001:MM,
  author =       "Ronald F. Boisvert and M. J. Donahue and Daniel W.
                 Lozier and R. McMichael and B. W. Rust",
  title =        "Mathematics and Measurement",
  journal =      "NIST Journal of Research",
  volume =       "106",
  number =       "1",
  pages =        "293--313",
  month =        jan # "\slash " # feb,
  year =         "2001",
  bibdate =      "Fri Jul 09 06:26:11 2004",
  acknowledgement = ack-nhfb,
}

@InProceedings{Burgess:2001:DIR,
  author =       "N. Burgess and C. Hinds",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Design issues in radix-$4$ {SRT} square root {\&}
                 divide unit",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1646--1650",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "This paper introduces a number of design issues not
                 covered in the open literature that arose during the
                 design of a radix-$4$ SRT divide/square root unit for a
                 vector processing chip. These include compression of
                 the partial remainder's m.s.b.'s, \ldots{}",
}

@InCollection{Corless:2001:RAE,
  author =       "Robert M. Corless and James H. Davenport and David J.
                 Jeffrey and Gurjeet Litt and Stephen M. Watt",
  booktitle =    "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  volume =       "1930",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "115--126",
  year =         "2001",
  MRclass =      "68W30 (30C35)",
  MRnumber =     "MR1882755 (2002m:68126)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  series =       "Lecture Notes in Comput. Sci.",
  acknowledgement = ack-nhfb,
}

@Article{Eklund:2001:CEF,
  author =       "Neil Eklund",
  title =        "{CORDIC}: elementary function computation using
                 recursive sequences",
  journal =      "College Math. J.",
  volume =       "32",
  number =       "5",
  pages =        "330--333",
  year =         "2001",
  ISSN =         "0746-8342",
  MRclass =      "65D20",
  MRnumber =     "MR1868594",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
  fjournal =     "The College Mathematics Journal",
}

@Unpublished{Godfrey:2001:NCC,
  author =       "P. Godfrey",
  title =        "A Note on the Computation of the Convergent Lanczos
                 Complex Gamma Approximation",
  year =         "2001",
  bibdate =      "Mon Nov 24 21:04:40 2008",
  note =         "Unpublished Web file.",
  URL =          "http://my.fit.edu/?gabdo/gamma.txt",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lang:2001:CRR,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  booktitle =    "Proceedings of the 15th IEEE Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "Correctly Rounded Reciprocal Square-Root by Digit
                 Recurrence and Radix-$4$ Implementation",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "83--93",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "OCLC Proceedings database; http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "We present a reciprocal square-root algorithm by digit
                 recurrence and selection by a staircase function, and
                 the radix-$4$ implementation. As similar algorithms for
                 division and square-root, the results are obtained
                 correctly rounded in a \ldots{}",
}

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

@Article{Loenko:2001:CEF,
  author =       "M. Yu. Loenko",
  title =        "Computation of elementary functions with guaranteed
                 accuracy",
  journal =      j-PROGRAMMIROVANIE,
  volume =       "2",
  pages =        "68--80",
  year =         "2001",
  CODEN =        "PROGD3",
  ISSN =         "0132-3474",
  MRclass =      "65D15 (65G20)",
  MRnumber =     "MR1867584",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi\u\i skaya Akademiya Nauk. Programmirovanie",
}

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

@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Takagi:2001:HAC,
  author =       "N. Takagi",
  booktitle =    "Proceedings of the 15th IEEE Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "A Hardware Algorithm for Computing Reciprocal Square
                 Root",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "94--100",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "OCLC Proceedings database; http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A hardware algorithm for computing the reciprocal
                 square root which appears frequently in multimedia and
                 graphics applications is proposed. The reciprocal
                 square root is computed by iteration of
                 carry-propagation-free additions, shifts, and
                 \ldots{}",
}

@InProceedings{Zheng:2001:ARE,
  author =       "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
  booktitle =    "Proceedings of the 4th International Conference on
                 ASIC",
  title =        "The application of redundant encoding in iterative
                 implementation of division and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--606",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this paper is to discuss the speed
                 improvement in division and square root computation
                 with small area penalty. The digit recurrence SRT
                 algorithm and functional iteration Newton-Raphson
                 algorithm are generally used in modern \ldots{}",
}

@Misc{Ziv:2001:APM,
  author =       "Abraham Ziv and Moshe Olshansky and Ealan Henis and
                 Anna Reitman",
  title =        "Accurate Portable Mathematical Library ({IBM
                 APMathLib})",
  howpublished = "World-Wide Web document",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  day =          "20",
  month =        dec,
  year =         "2001",
  bibdate =      "Wed Nov 24 08:06:54 2004",
  URL =          "http://oss.software.ibm.com/mathlib/;
                 ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz",
  acknowledgement = ack-nhfb,
}

@InCollection{Boisvert:2002:HMF,
  author =       "Ronald F. Boisvert and Daniel W. Lozier",
  title =        "Handbook of Mathematical Functions",
  crossref =     "Lide:2002:CEM",
  pages =        "135--139",
  year =         "2002",
  bibdate =      "Fri Jul 09 06:28:13 2004",
  note =         "Also printed as NIST Special Publication 958, Jan.
                 2001.",
  acknowledgement = ack-nhfb,
}

@Article{Bradford:2002:RAE,
  author =       "Russell Bradford and Robert M. Corless and James H.
                 Davenport and David J. Jeffrey and Stephen M. Watt",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "36",
  number =       "3",
  pages =        "303--318",
  year =         "2002",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443",
  MRclass =      "30-01 (03B35 68W30)",
  MRnumber =     "MR1950025 (2003m:30001)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  note =         "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
}

@InProceedings{Bradford:2002:TBS,
  author =       "Russell Bradford and James H. Davenport",
  booktitle =    "Proceedings of the 2002 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Towards better simplification of elementary
                 functions",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "16--22 (electronic)",
  year =         "2002",
  MRclass =      "68W30 (33B10)",
  MRnumber =     "MR2035228",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
}

@Article{Gil:2002:AAB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77}
                 routines for the computation of complex {Airy}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "325--336",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/569147.569150",
  ISSN =         "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "Two Fortran 77 routines for the evaluation of Airy
                 functions of complex arguments $Ai(z)$, $Bi(z)$ and
                 their derivatives are presented. The routines are based
                 on the use of Gaussian quadrature, Maclaurin series and
                 asymptotic expansions. Comparison with a previous code
                 by D. E. Amos (ACM TOMS 12 (1986)) is provided.",
  acknowledgement = ack-nhfb,
}

@Article{McCluskey:2002:MLF,
  author =       "Glen McCluskey",
  title =        "Math Library Functions in {C9X}",
  journal =      j-LOGIN,
  volume =       "27",
  number =       "2",
  pages =        "8--13",
  month =        apr,
  year =         "2002",
  CODEN =        "LOGNEM",
  ISSN =         "1044-6397",
  bibdate =      "Tue Apr 11 10:52:14 MDT 2006",
  bibsource =    "http://www.usenix.org/publications/login/2002-04/index.html",
  URL =          "http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf",
  acknowledgement = ack-nhfb,
  remark =       "This is a short tutorial on some of the new math
                 library functions in C99.",
}

@InProceedings{Pineiro:2002:HRL,
  author =       "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
  booktitle =    "Application-Specific Systems, Architectures and
                 Processors, 2002. Proceedings. The IEEE International
                 Conference on. 17--19 July 2002",
  title =        "High-radix logarithm with selection by rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "101--110",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A high-radix digit-recurrence algorithm or the
                 computation of the logarithm is presented in this
                 paper. Selection by rounding is used in iterations
                 j/spl ges/2, and selection by table in the first
                 iteration is combined with a restricted digit-set
                 \ldots{}",
}

@Article{Pineiro:2002:HSD,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera",
  title =        "High-Speed Double Precision Computation of Reciprocal,
                 Division, Square Root, and Inverse Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "12",
  pages =        "1377--1388",
  month =        dec,
  year =         "2002",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "A new method for the high-speed computation of
                 double-precision floating-point reciprocal, division,
                 square root, and inverse square root operations is
                 presented in this paper. This method employs a
                 second-degree minimax polynomial approximation to
                 \ldots{}",
}

@InProceedings{Beaumont:2003:BSE,
  author =       "James Beaumont and Russell Bradford and James H.
                 Davenport",
  booktitle =    "Proceedings of the 2003 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Better simplification of elementary functions through
                 power series",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "30--36 (electronic)",
  year =         "2003",
  MRclass =      "33F10 (68W30)",
  MRnumber =     "MR2035192 (2005e:33018)",
  MRreviewer =   "Ekatherina A. Karatsuba",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  acknowledgement = ack-nhfb,
  remark =       "A new algorithm testing the correctness of
                 simplifications of elementary functions in the presence
                 of branch cuts is proposed.",
}

@Article{Dominici:2003:NDS,
  author =       "Diego Dominici",
  title =        "Nested derivatives: a simple method for computing
                 series expansions of inverse functions",
  journal =      j-INT-J-MATH-MATH-SCI,
  volume =       "58",
  pages =        "3699--3715",
  year =         "2003",
  ISSN =         "0161-1712",
  CODEN =        "????",
  MRclass =      "41A58 (33F10)",
  MRnumber =     "MR2031140 (2005f:41079)",
  MRreviewer =   "Tord H. Ganelius",
  URL =          "http://www2.newpaltz.edu/~dominicd/NESTED14.pdf",
  abstract =     "We give an algorithm to compute the series expansion
                 for the inverse of a given function. The algorithm is
                 extremely easy to implement and gives the first $N$
                 terms of the series. We show several examples of its
                 application in calculating the inverses of some special
                 functions.",
  keywords =     "Maple; error function, erf(x); incomplete gamma
                 function, gamma(nu,x); sine integral, Si(x); logarithm
                 integral, li(x); incomplete beta function, B(nu,mu,x)",
}

@InProceedings{Ercegovac:2003:DRA,
  author =       "M. D. Ercegovac and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Seventh Asilomar
                 Conference on Signals, Systems and Computers, 2003",
  title =        "Digit-recurrence algorithms for division and square
                 root with limited precision primitives",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1440--1444",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "We propose a digit-recurrence algorithm for square
                 root using limited-precision multipliers, adders, and
                 table-lookups. The algorithm, except in the
                 initialization, uses the digit-recurrence algorithm for
                 division with limited-precision primitives \ldots{}",
}

@Article{Fabijonas:2003:ACM,
  author =       "B. R. Fabijonas and Daniel W. Lozier and J. M.
                 Rappoport",
  title =        "Algorithms and Codes for the {Macdonald} Function:
                 Recent Progress and Comparisons",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "161",
  number =       "1",
  pages =        "179--192",
  month =        "????",
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427",
  MRclass =      "33F05 (33C10 65D20)",
  MRnumber =     "MR2018582",
  bibdate =      "Fri Jul 09 06:21:51 2004",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps",
  acknowledgement = ack-nhfb,
}

@Article{Gil:2003:CSF,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing Special Functions by Using Quadrature
                 Rules",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "33",
  number =       "1--4",
  pages =        "265--275",
  month =        aug,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398",
  bibdate =      "Mon Sep 29 08:37:11 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Lang:2003:RRS,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "Radix-$4$ Reciprocal Square-root and Its Combination
                 with Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "9",
  pages =        "1100--1114",
  month =        sep,
  year =         "2003",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  abstract =     "In this work, we present a reciprocal square root
                 algorithm by digit recurrence and selection by a
                 staircase function and the radix-$4$ implementation. As
                 in similar algorithms for division and square root, the
                 results are obtained correctly rounded in a
                 straightforward manner (in contrast to existing
                 methods to compute the reciprocal square
                 root). Although, apparently, a single selection
                 function can only be used for $j \geq 2$ (the selection
                 constants are different for $j = 0$, $j = 1$, and $j
                 \geq 2$), we show that it is possible to use a single
                 selection function for all iterations. We perform a
                 rough comparison with existing methods and we conclude
                 that our implementation is a low hardware complexity
                 solution with moderate latency, especially for exactly
                 rounded results. We also extend the unit to support
                 division and square root with the same selection
                 function and with slight modifications in the
                 initialization of the reciprocal square root unit.",
}

@TechReport{Lefevre:2003:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding for the Elementary
                 Functions in Double Precision",
  type =         "Technical report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  day =          "14",
  month =        aug,
  year =         "2003",
  bibdate =      "Thu Jul 08 08:27:53 2004",
  URL =          "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
  abstract =     "We give the results of our search for the worst cases
                 for correct rounding of the major elementary functions
                 in double precision floating-point arithmetic. These
                 results allow the design of reasonably fast routines
                 that will compute these functions with correct
                 rounding, at least in some interval, for any of the
                 four rounding modes specified by the IEEE-754 standard.
                 They will also allow one to easily test libraries that
                 are claimed to provide correctly rounded functions.",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions; floating-point arithmetic;
                 computer arithmetic; Table Maker's Dilemma",
}

@Article{Lozier:2003:NDL,
  author =       "Daniel W. Lozier",
  title =        "{NIST Digital Library of Mathematical Functions}",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "38",
  number =       "1--3",
  pages =        "105--119",
  month =        may,
  year =         "2003",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443",
  bibdate =      "Fri Jul 09 06:23:08 2004",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps",
  acknowledgement = ack-nhfb,
}

@InProceedings{Markstein:2003:FQP,
  author =       "Peter Markstein",
  title =        "A fast quad precision elementary function library for
                 {Itanium}",
  crossref =     "Anonymous:2003:CRN",
  pages =        "5--12",
  year =         "2003",
  bibdate =      "Fri Jun 24 20:14:39 2005",
  abstract =     "This talk will describe Itanium's floating point
                 architecture and how it has been used to produce a high
                 performance, highly accurate quad precision elementary
                 function library.\par

                 Itanium's floating-point features will first be
                 described, from the point of view of a computer
                 architect. Many conflicting requirements vie for
                 consideration during the design of a new computer
                 architecture. These include instruction word size,
                 number of registers, the set of operations, arithmetic
                 precisions supported, and memory access. Some of the
                 trade-offs during the design phase will be
                 discussed.\par

                 One of the objectives of the original Itanium design
                 was to accelerate quad precision arithmetic. The talk
                 will describe how the Itanium elementary function
                 library was constructed, with attention to performance
                 and accuracy. Because a pair of double-extended
                 floating point words are used for internal operations
                 involving quad precision numbers, intermediate results,
                 holding 128 bits, provide 15 guard bits during
                 intermediate calculations, resulting in a very low
                 percentage of misrounded results.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pineiro:2003:LHR,
  author =       "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
  booktitle =    "2003. ISCAS '03. Proceedings of the 2003 International
                 Symposium on Circuits and Systems. 25--28 May 2003",
  title =        "On-line high-radix exponential with selection by
                 rounding",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "IV-121--IV-124",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "An on-line high-radix algorithm for computing the
                 exponential function (e/sup x/) with arbitrary
                 precision n is presented. Selection by rounding and a
                 redundant digit-set for the digits e/sub j/ are used,
                 with selection by table in the first \ldots{}",
}

@InProceedings{Wang:2003:TDF,
  author =       "Xiaojun Wang and B. E. Nelson",
  booktitle =    "FCCM 2003: 11th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines, 9--11
                 April 2003",
  title =        "Tradeoffs of designing floating-point division and
                 square root on {Virtex FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "195--203",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "Low latency, high throughput and small area are three
                 major design considerations of an FPGA (field
                 programmable gate array) design. In this paper, we
                 present a high radix SRT division algorithm and a
                 binary restoring square root algorithm. We \ldots{}",
}

@Article{Berrut:2004:APS,
  author =       "Jean-Paul Berrut and Hans D. Mittelmann",
  title =        "Adaptive Point Shifts in Rational Approximation with
                 Optimized Denominator",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "164--165",
  number =       "??",
  pages =        "81--92",
  day =          "1",
  month =        mar,
  year =         "2004",
  CODEN =        "JCAMDI",
  DOI =          "http://dx.doi.org/10.1016/S0377-0427(03)00485-0",
  ISSN =         "0377-0427",
  bibdate =      "Tue Mar 24 21:10:48 2009",
  note =         "Proceedings of the 10th International Congress on
                 Computational and Applied Mathematics University of
                 Leuven, Belgium, 22--26 July 2002. Edited by M.J.
                 Goovaerts, S. Vandewalle, and L. Wuytack.",
  abstract =     "Classical rational interpolation is known to suffer
                 from several drawbacks, such as unattainable points and
                 randomly located poles for a small number of nodes, as
                 well as an erratic behavior of the error as this number
                 grows larger. In a former article, we have suggested to
                 obtain rational interpolants by a procedure that
                 attaches optimally placed poles to the interpolating
                 polynomial, using the barycentric representation of the
                 interpolants. In order to improve upon the condition of
                 the derivatives in the solution of differential
                 equations, we have then experimented with a conformal
                 point shift suggested by Kosloff and Tal-Ezer. As it
                 turned out, such shifts can achieve a spectacular
                 improvement in the quality of the approximation itself
                 for functions with a large gradient in the center of
                 the interval. This leads us to the present work which
                 combines the pole attachment method with shifts
                 optimally adjusted to the interpolated function. Such
                 shifts are also constructed for functions with several
                 shocks away from the extremities of the interval.",
  acknowledgement = ack-nhfb,
  keywords =     "rational approximation; interpolation; optimal
                 interpolation; point shifts",
}

@Article{Brisebarre:2004:ACR,
  author =       "N. Brisebarre and J.-M. Muller and Saurabh Kumar
                 Raina",
  title =        "Accelerating correctly rounded floating-point division
                 when the divisor is known in advance",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "8",
  pages =        "1069--1072",
  month =        aug,
  year =         "2004",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  abstract =     "We present techniques for accelerating the
                 floating-point computation of $x/y$ when $y$ is known
                 before $x$. The proposed algorithms are oriented toward
                 architectures with available fused-mac operations. The
                 goal is to get exactly the same result as with
                 \ldots{}",
  acknowledgement = ack-nhfb,
  summary =      "We present techniques for accelerating the
                 floating-point computation of x/y when y is known
                 before x. The proposed algorithms are oriented toward
                 architectures with available fused-mac operations. The
                 goal is to get exactly the same result as with
                 \ldots{}",
}

@Article{Defour:2004:PSM,
  author =       "David Defour and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol
                 and Paul Zimmermann",
  title =        "Proposal for a Standardization of Mathematical
                 Function Implementation in Floating-Point Arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "367--375",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm;
                 http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf;
                 http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}

@InProceedings{Doss:2004:FBI,
  author =       "C. C. Doss and R. L. {Riley, Jr.}",
  booktitle =    "FCCM 2004. 12th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "{FPGA}-based implementation of a robust
                 {IEEE-754} exponential unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--238",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "This work explores the feasibility of implementing a
                 floating-point exponentiation unit on reconfigurable
                 computing systems. A table-driven exponentiation unit
                 was implemented using synthesizable VHDL. The project
                 included creating pipelined \ldots{}",
}

@InProceedings{Ercegovac:2004:CSRb,
  author =       "M. D. Ercegovac and J.-M. Muller",
  booktitle =    "Proceedings of the 15th IEEE International Conference
                 on Application-Specific Systems, Architectures and
                 Processors, 2004",
  title =        "Complex square root with operand prescaling",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--62",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "We propose a radix-r digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation. Moreover, the use of digit \ldots{}",
}

@Article{Fabijonas:2004:AAF,
  author =       "B. R. Fabijonas",
  title =        "{Algorithm 838}: {Airy} Functions",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "491--501",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/1039813.1039819",
  ISSN =         "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "We present a Fortran 90 module, which computes the
                 solutions and their derivatives of Airy's differential
                 equation, both on the real line and in the complex
                 plane. The module also computes the zeros and
                 associated values of the solutions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis. The computational methods are
                 numerical integration of the differential equation and
                 summation of asymptotic expansions for large argument.
                 These methods were chosen because they are simple,
                 adaptable to any precision, and amenable to rigorous
                 error analysis. The module can be used to validate
                 other codes or as a component in programs that require
                 Airy functions.",
  acknowledgement = ack-nhfb,
}

@Article{Fabijonas:2004:CCA,
  author =       "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver",
  title =        "Computation of complex {Airy} functions and their
                 zeros using asymptotics and the differential equation",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "471--490",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/1039813.1039818",
  ISSN =         "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "We describe a method by which one can compute the
                 solutions of Airy's differential equation, and their
                 derivatives, both on the real line and in the complex
                 plane. The computational methods are numerical
                 integration of the differential equation and summation
                 of asymptotic expansions for large argument. We give
                 details involved in obtaining all of the parameter
                 values, and we control the truncation errors
                 rigorously. Using the same computational methods, we
                 describe an algorithm that computes the zeros and
                 associated values of the Airy functions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gebali:2004:EAF,
  author =       "Fayez Gebali and Mohamed Watheq El-Kharashi",
  title =        "{ERL}: an algorithm for fast evaluation of
                 exponential, reciprocal, and logarithmic functions",
  crossref =     "Wahdan:2004:IHE",
  pages =        "269--272",
  year =         "2004",
  bibdate =      "Sat Jul 16 18:04:58 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  abstract =     "A fast algorithm (ERL) is proposed for evaluating
                 Exponential, Reciprocal, and Logarithmic functions. The
                 algorithm requires two to three iterations to complete
                 using simple operations such as multiply, accumulate,
                 and table lookup. The algorithm is independent of the
                 number format used by the machine. Thus it can be
                 implemented using the IEEE 754 floating-point standard
                 or any other special format used by special-purpose
                 processors. The dynamic range of the algorithm is
                 limited only by the dynamic range of the machine on
                 which it is implemented Numerical simulations are
                 performed which verifies the speed and accuracy of the
                 algorithm.",
  acknowledgement = ack-nhfb,
}

@Article{Gil:2004:AMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 831}: {Modified} {Bessel} functions of
                 imaginary order and positive argument",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "159--164",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/992200.992204",
  ISSN =         "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "Fortran 77 programs for the computation of modified
                 Bessel functions of purely imaginary order are
                 presented. The codes compute the functions $K_{ia}(x)$,
                 $L_{ia}(x)$ and their derivatives for real $a$ and
                 positive $x$; these functions are independent solutions
                 of the differential equation $x^2 w'' + xw' + (a^2 -
                 x^2)w = 0$. The code also computes exponentially scaled
                 functions. The range of computation is $(x, a) \in
                 (0,1500] \times [-1500, 1500]$ when scaled functions
                 are considered and it is larger than $(0,500] \times
                 [-400, 400]$ for standard IEEE double precision
                 arithmetic. The relative accuracy is better than
                 $10^{-13}$ in the range $(0,200] \times [-200, 200]$
                 and close to $10^{-12}$ in $(0, 1500] \times [-1500,
                 1500]$.",
  acknowledgement = ack-nhfb,
}

@Article{Gil:2004:CSM,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing solutions of the modified {Bessel}
                 differential equation for imaginary orders and positive
                 arguments",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "145--158",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/992200.992203",
  ISSN =         "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "We describe a variety of methods to compute the
                 functions $K_{ia}(x)$, $L_{ia}(x)$ and their
                 derivatives for real $a$ and positive $x$. These
                 functions are numerically satisfactory independent
                 solutions of the differential equation $x^2 w'' + xw' +
                 (a^2 - x^2)w = 0$. In the accompanying paper [Gil et
                 al. 2004], we describe the implementation of these
                 methods in Fortran 77 codes.",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:LTC,
  author =       "W. Kahan",
  title =        "A Logarithm Too Clever by Half",
  howpublished = "World-Wide Web document",
  pages =        "9",
  day =          "9",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:39:08 2005",
  URL =          "http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT",
  acknowledgement = ack-nhfb,
  remark =       "Careful analysis of the problem of computing {\tt
                 log10(x)} accurately from {\tt log(x)}.",
}

@Book{Lau:2004:NLJ,
  author =       "H. T. (Hang Tong) Lau",
  title =        "A numerical library in {Java} for scientists and
                 engineers",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xxiii + 1063",
  year =         "2004",
  ISBN =         "1-58488-430-4",
  ISBN-13 =      "978-1-58488-430-9",
  LCCN =         "QA76.73.J38 L363 2004",
  bibdate =      "Fri Sep 26 14:28:47 MDT 2008",
  bibsource =    "z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0646/2003055149-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Java (Computer program language)",
}

@Article{Marsaglia:2004:END,
  author =       "George Marsaglia",
  title =        "Evaluating the Normal Distribution",
  journal =      j-J-STAT-SOFT,
  volume =       "11",
  number =       "4",
  pages =        "1--7",
  month =        "",
  year =         "2004",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sat Dec 04 09:18:40 2004",
  URL =          "http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1",
  accepted =     "2004-07-18",
  acknowledgement = ack-nhfb,
  remark =       "This article exhibits accurate, compact, and fast
                 algorithms for computation of the normal distribution
                 function and the complementary normal distribution,
                 which have a simple relation to the error function and
                 the complementary error function. They appear to be
                 improvements on almost all previously-published
                 algorithms for these functions. However, closer study
                 shows that the complementary normal distribution
                 function has an unchecked out-of-bounds array access
                 for $|x| >= 17$, and its Taylor series sum has poor
                 convergence because the tabulated intervals are twice
                 too wide. The Taylor series sum for the normal
                 distribution function is expanded around $x = 0$, and
                 thus has poor convergence for large $|x|$. Neither
                 function takes into account the accuracy loss when the
                 computed result is the larger of the two (their sum is
                 one, and their range is $[-\infty,+\infty]$), although
                 the text discusses the problem. The article also
                 discusses the historical origin of the term ``error
                 function'', tracing it to J. W. Glaisher in 1871.",
  submitted =    "2004-06-05",
}

@Article{Mathar:2004:NRI,
  author =       "Richard J. Mathar",
  title =        "Numerical Representations of the Incomplete Gamma
                 Function of Complex-Valued Argument",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "36",
  number =       "3",
  pages =        "247--264",
  month =        jul,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398",
  bibdate =      "Mon Dec 6 07:00:32 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/57/A/4/abstract.htm",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ortiz:2004:SPI,
  author =       "I. Ortiz and M. Jimenez",
  booktitle =    "MWSCAS '04. The 2004 47th Midwest Symposium on
                 Circuits and Systems. 25--28 July 2004",
  title =        "Scalable pipeline insertion in floating-point division
                 and square root units",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-225--II-228",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  abstract =     "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the development of
                 scalable, floating-point (FP) division and square root
                 operators with adjustable precision, range, and
                 pipeline granularity. An algorithm for pipeline
                 insertion was used for both operators, enabling speeds
                 up to 204MFLOPS when implemented on a Xilinx Virtex II
                 FPGA.",
  acknowledgement = ack-nhfb,
  summary =      "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the \ldots{}",
}

@Article{Pineiro:2004:AAL,
  author =       "J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
                 Bruguera",
  title =        "Algorithm and Architecture for Logarithm, Exponential
                 and Powering Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "9",
  pages =        "1085--1096",
  year =         "2004",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Fri Jun 24 10:05:48 2005",
  URL =          "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Pugh:2004:ALG,
  author =       "Glendon Ralpha Pugh",
  title =        "An Analysis of the {Lanczos} Gamma Approximation",
  type =         "Ph.D. thesis",
  school =       "Department of Mathematics, University of British
                 Columbia",
  address =      "Vancouver, BC, Canada",
  pages =        "viii + 154",
  month =        "????",
  year =         "2004",
  ISBN =         "0-612-99536-4",
  ISBN-13 =      "978-0-612-99536-9",
  LCCN =         "AW5 .B7 2005-995364",
  bibdate =      "Mon Nov 24 20:55:30 2008",
  acknowledgement = ack-nhfb,
}

@Article{VanDeun:2004:IAO,
  author =       "J. {Van Deun} and A. Bultheel",
  title =        "An Interpolation Algorithm for Orthogonal Rational
                 Functions",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "164--165",
  number =       "??",
  pages =        "749--762",
  month =        mar,
  year =         "2004",
  CODEN =        "JCAMDI",
  DOI =          "http://dx.doi.org/10.1016/S0377-0427(03)00493-X",
  ISSN =         "0377-0427",
  bibdate =      "Tue Mar 24 21:14:11 2009",
  note =         "Proceedings of the 10th International Congress on
                 Computational and Applied Mathematics University of
                 Leuven, Belgium, 22--26 July 2002. Edited by M.J.
                 Goovaerts, S. Vandewalle, and L. Wuytack.",
  abstract =     "Let $A=\{\alpha_1,\alpha_2,...\}$ be a sequence of
                 numbers on the extended real line $\mathcal{R} =
                 \mathcal{R} \union \{ \infty \}$ and $\mu$ a positive
                 bounded Borel measure with support in (a subset of)
                 $\mathcal{R}$. We introduce rational functions n with
                 poles $\{\alpha_1,\ldots{},\alpha_n\}$ that are
                 orthogonal with respect to $\mu$ (if all poles are at
                 infinity, we recover the polynomial situation). It is
                 well known that under certain conditions on the
                 location of the poles, the system $\{\phi_n\}$ is
                 regular such that the orthogonal functions satisfy a
                 three-term recurrence relation similar to the one for
                 orthogonal polynomials. To compute the recurrence
                 coefficients one can use explicit formulas involving
                 inner products. We present a theoretical alternative to
                 these explicit formulas that uses certain interpolation
                 properties of the Riesz--Herglotz-Nevanlinna transform
                 $\Omega_\mu$ of the measure $\mu$. Error bounds are
                 derived and some examples serve as illustration.",
  acknowledgement = ack-nhfb,
  keywords =     "orthogonal rational functions; orthogonal polynomials;
                 three-term recurrence; interpolation",
}

@Article{Zhu:2004:ISR,
  author =       "Hufei Zhu and Zhongding Lei and F. P. S. Chin",
  title =        "An improved square-root algorithm for {BLAST}",
  journal =      j-IEEE-SIGNAL-PROCESS-LETT,
  volume =       "11",
  number =       "9",
  pages =        "772--775",
  month =        sep,
  year =         "2004",
  CODEN =        "ISPLEM",
  ISSN =         "1070-9908",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/",
  acknowledgement = ack-nhfb,
  summary =      "In this letter, an improved square-root algorithm for
                 Bell Labs Layered Space-Time (BLAST) system is
                 proposed. It speeds up the original square-root
                 algorithm by 36% in terms of the number of
                 multiplications and additions. Compared with the
                 \ldots{}",
}

@InProceedings{Antelo:2005:LLD,
  author =       "Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi
                 and Alberto Nannarelli",
  title =        "Low Latency Digit-Recurrence Reciprocal and
                 Square-Root Reciprocal Algorithm and Architecture",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  URL =          "http://arith17.polito.it/final/paper-116.pdf",
  abstract =     "The reciprocal and square-root reciprocal operations
                 are important in several applications. For the
                 operations, we present algorithms that combine a
                 digit-by-digit module and one iteration of a
                 quadratic-convergence approximation. The latter is
                 implemented by a digit-recurrence, which uses the
                 digits produced by the digit-by-digit part. In this
                 way, both parts execute in an overlapped manner, so
                 that the total number of cycles is about half the
                 number that would be required by the digit-by-digit
                 part alone. Because of the approximation, correct
                 rounding of the result cannot be obtained directly in
                 all cases; we propose a variable-time implementation
                 that produces the correctly rounded result with a small
                 average overhead. Radix-4 implementations are described
                 and have been synthesized. They achieve the same cycle
                 time as the standard digit-by-digit implementation,
                 resulting in a speed-up of about 2 and, because of the
                 approximation part, the area factor is also about 2. We
                 also show a combined implementation for both operations
                 that has essentially the same complexity as that for
                 square-root reciprocal alone.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Article{Brisebarre:2005:NRR,
  author =       "Nicolas Brisebarre and David Defour and Peter Kornerup
                 and Jean-Michel Muller and Nathalie Revol",
  title =        "A New Range-Reduction Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "331--339",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Wed Apr 27 18:04:38 MDT 2005",
  bibsource =    "http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm;
                 http://ieeexplore.ieee.org/",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388197&count=13&index=8;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf?isnumber=30205&prod=JNL&arnumber=1388197&arSt=+331&ared=+339&arAuthor=Brisebarre%2C+N.%3B+Defour%2C+D.%3B+Kornerup%2C+P.%3B+Muller%2C+J.-M.%3B+Revol%2C+N.",
  abstract =     "Range-reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double-precision range.",
  acknowledgement = ack-nhfb,
}

@InProceedings{deDinechin:2005:TPU,
  author =       "Florent de Dinechin and Alexey Ershov and Nicolas
                 Gast",
  title =        "Towards the Post-ultimate {\tt libm}",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  URL =          "http://arith17.polito.it/final/paper-165.pdf",
  abstract =     "This article presents advances on the subject of
                 correctly rounded elementary functions since the
                 publication of the {\tt libultim} mathematical library
                 developed by Ziv at IBM. This library showed that the
                 average performance and memory overhead of correct
                 rounding could be made negligible. However, the
                 worst-case overhead was still a factor 1000 or more. It
                 is shown here that, with current processor technology,
                 this worst-case overhead can be kept within a factor of
                 2 to 10 of current best libms. This low overhead has
                 very positive consequences on the techniques for
                 implementing and proving correctly rounded functions,
                 which are also studied. These results lift the last
                 technical obstacles to a generalisation of (at least
                 some) correctly rounded double precision elementary
                 functions.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Misc{IBM:2005:MAS,
  author =       "{IBM Corporation}",
  title =        "{Mathematical Acceleration Subsystem} for {Linux}",
  howpublished = "World Wide Web document",
  year =         "2005",
  bibdate =      "Mon Dec 05 18:59:35 2005",
  URL =          "http://www-306.ibm.com/software/awdtools/mass/linux/mass-linux.html",
  abstract =     "Mathematical Acceleration Subsystem (MASS) for Linux
                 consists of libraries of mathematical intrinsic
                 functions tuned specifically for optimum performance on
                 POWER architectures.",
  acknowledgement = ack-nhfb,
  keywords =     "Mathematical Acceleration Subsystem (MASS)",
  remark =       "Scalar library functions: atan, atan2, cos, cosh,
                 dnint, exp, log, pow [Fortran **], rsqrt, sin, sinh,
                 sqrt, tan, and tanh.\par

                 Vector library double-precision function: vacos, vasin,
                 vatan2, vcbrt, vcos, vcosh, vcosisin, vdint, vdiv,
                 vdnint, vexp, vexpm1, vlog, vlog10, vlog1p, vpow,
                 vrcbrt, vrec, vrsqrt, vsin, vsincos, vsinh, vsqrt,
                 vtan, and vtanh.\par

                 Vector library single-precision functions: vsacos,
                 vsasin, vsatan2, vscbrt, vscos, vscosh, vscosisin,
                 vsdiv, vsexp, vsexpm1, vslog, vslog10, vslog1p, vspow,
                 vsrcbrt, vsrec, vsrsqrt, vssin, vssincos, vssinh,
                 vssqrt, vstan, and vstanh.",
}

@Article{Kornerup:2005:DSS,
  author =       "Peter Kornerup",
  title =        "Digit Selection for {SRT} Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "294--303",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm;
                 http://ieeexplore.ieee.org/",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194",
  acknowledgement = ack-nhfb,
  summary =      "The quotient digit selection in the SRT division
                 algorithm is based on a few most significant bits of
                 the remainder and divisor, where the remainder is
                 usually represented in a redundant representation. The
                 number of leading bits needed depends on \ldots{}",
}

@Article{Lee:2005:OHF,
  author =       "D.-U. Lee and A. A. Gaffar and O. Mencer and W. Luk",
  title =        "Optimizing hardware function evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "12",
  pages =        "1520--1531",
  month =        dec,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "http://dx.doi.org/10.1109/TC.2005.201",
  ISSN =         "0018-9340",
  bibdate =      "Tue May 30 12:04:26 2006",
  abstract =     "We present a methodology and an automated system for
                 function evaluation unit generation. Our system selects
                 the best function evaluation hardware for a given
                 function, accuracy requirements, technology mapping,
                 and optimization metrics, such as area, throughput, and
                 latency. Function evaluation $f(x)$ typically consists
                 of range reduction and the actual evaluation on a small
                 convenient interval such as $[0, \pi/2)$ for $\sin(x)$.
                 We investigate the impact of hardware function
                 evaluation with range reduction for a given range and
                 precision of $x$ and $f(x)$ on area and speed. An
                 automated bit-width optimization technique for
                 minimizing the sizes of the operators in the data paths
                 is also proposed. We explore a vast design space for
                 fixed-point $\sin(x)$, $\log(x)$, and $\sqrt{x}$
                 accurate to one unit in the last place using MATLAB and
                 ASC, a stream compiler for field-programmable gate
                 arrays (FPGAs). In this study, we implement over 2,000
                 placed-and-routed FPGA designs, resulting in over 100
                 million application-specific integrated circuit (ASIC)
                 equivalent gates. We provide optimal function
                 evaluation results for range and precision combinations
                 between 8 and 48 bits.",
  acknowledgement = ack-nhfb,
  keywords =     "application specific integrated circuits; circuit
                 optimisation; field programmable gate arrays; fixed
                 point arithmetic; logic design; application specific
                 integrated circuits; circuit optimisation; field
                 programmable gate arrays; fixed point arithmetic; logic
                 design; ASC; ASIC; FPGA; MATLAB; application-specific
                 integrated circuit equivalent gates; automated
                 bit-width optimization technique; computer arithmetic;
                 elementary function approximation; field-programmable
                 gate arrays; fixed-point arithmetic; hardware function
                 evaluation optimisation; minimax approximation; stream
                 compiler",
}

@InProceedings{Lefevre:2005:NRD,
  author =       "Vincent Lef{\`e}vre",
  title =        "New Results on the Distance Between a Segment and
                 {$Z^2$}. Application to the Exact Rounding",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  URL =          "http://arith17.polito.it/final/paper-147.pdf",
  abstract =     "This paper presents extensions to Lef{\'e}vre's
                 algorithm that computes a lower bound on the distance
                 between a segment and a regular grid $Z^2$. This
                 algorithm and, in particular, the extensions are useful
                 in the search for worst cases for the exact rounding of
                 unary elementary functions or base-conversion
                 functions. The proof that is presented here is simpler
                 and less technical than the original proof. This paper
                 also gives benchmark results with various optimization
                 parameters, explanations of these results, and an
                 application to base conversion.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@InProceedings{Markstein:2005:FSM,
  author =       "Peter Markstein",
  title =        "A Fast-Start Method for Computing the Inverse
                 Tangent",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  URL =          "http://arith17.polito.it/final/paper-112.pdf",
  abstract =     "In a search for an algorithm to compute $\atan(x)$
                 which has both low latency and few floating point
                 instructions, an interesting variant of familiar
                 trigonometry formulas was discovered that allow the
                 start of argument reduction to commence before any
                 references to tables stored in memory are needed. Low
                 latency makes the method suitable for a closed
                 subroutine, and few floating point operations make the
                 method advantageous for a software-pipelined
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "IA-64; Itanium-2",
  pagecount =    "6",
}

@Article{Pineiro:2005:HSF,
  author =       "Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and
                 Jean-Michel Muller and Javier D. Bruguera",
  title =        "High-Speed Function Approximation Using a Minimax
                 Quadratic Interpolator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "304--318",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm",
  URL =          "http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.;
                 http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf",
  abstract =     "A table-based method for high-speed function
                 approximation in single-precision floating-point format
                 is presented in this paper. Our focus is the
                 approximation of reciprocal, square root, square root
                 reciprocal, exponentials, logarithms, trigonometric
                 functions, powering (with a fixed exponent $p$), or
                 special functions. The algorithm presented here
                 combines table look-up, an enhanced minimax quadratic
                 approximation, and an efficient evaluation of the
                 second-degree polynomial (using a specialized squaring
                 unit, redundant arithmetic, and multioperand addition).
                 The execution times and area costs of an architecture
                 implementing our method are estimated, showing the
                 achievement of the fast execution times of linear
                 approximation methods and the reduced area requirements
                 of other second-degree interpolation algorithms.
                 Moreover, the use of an enhanced minimax approximation
                 which, through an iterative process, takes into account
                 the effect of rounding the polynomial coefficients to a
                 finite size allows for a further reduction in the size
                 of the look-up tables to be used, making our method
                 very suitable for the implementation of an elementary
                 function generator in state-of-the-art DSPs or graphics
                 processing units (GPUs).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stehle:2005:GAT,
  author =       "Damien Stehl{\'e} and Paul Zimmermann",
  title =        "{Gal}'s Accurate Tables Method Revisited",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  URL =          "http://arith17.polito.it/final/paper-152.pdf",
  abstract =     "Gal's accurate tables algorithm aims at providing an
                 efficient implementation of mathematical functions with
                 correct rounding as often as possible. This method
                 requires an expensive pre-computation of the values
                 taken by the function or by several related functions
                 at some distinguished points. Our improvements of Gal's
                 method are two-fold: on the one hand we describe what
                 is the arguably best set of distinguished values and
                 how it improves the efficiency and accuracy of the
                 function implementation, and on the other hand we give
                 an algorithm which drastically decreases the cost of
                 the pre-computation. These improvements are related to
                 the worst cases for the correct rounding of
                 mathematical functions and to the algorithms for
                 finding them. We demonstrate how the whole method can
                 be turned into practice for $2^x$ and $\sin x$ for $x
                 \in [1/2,1)$, in double precision.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Article{Stehle:2005:SWC,
  author =       "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
                 Zimmermann",
  title =        "Searching Worst Cases of a One-Variable Function Using
                 Lattice Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "340--346",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://csdl.computer.org/comp/trans/tc/2005/03/t3toc.htm",
  URL =          "http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388198&count=13&index=9;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388198;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388198.pdf?isnumber=30205&prod=JNL&arnumber=1388198&arSt=+340&ared=+346&arAuthor=Stehle%2C+D.%3B+Lefevre%2C+V.%3B+Zimmermann%2C+P.;
                 http://csdl.computer.org/comp/trans/tc/2005/03/t0340abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0340.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0340.pdf",
  abstract =     "We propose a new algorithm to find worst cases for the
                 correct rounding of a mathematical function of one
                 variable. We first reduce this problem to the real
                 small value problem---i.e., for polynomials with real
                 coefficients. Then, we show that this second problem
                 can be solved efficiently by extending Coppersmith's
                 work on the integer small value problem---for
                 polynomials with integer coefficients---using lattice
                 reduction. For floating-point numbers with a mantissa
                 less than $N$ and a polynomial approximation of degree
                 $d$, our algorithm finds all worst cases at distance
                 less than $N^{\frac{-d^2}{2d+1}}$ from a machine number
                 in time $O(N^{{\frac{d+1}{2d+1}}+\varepsilon})$. For
                 $d=2$, a detailed study improves on the
                 $O(N^{2/3+\varepsilon})$ complexity from Lef{\`e}vre's
                 algorithm to $O(N^{4/7+\varepsilon})$. For larger $d$,
                 our algorithm can be used to check that there exist no
                 worst cases at distance less than $N^{-k}$ in time
                 $O(N^{1/2+\varepsilon})$.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic; correct rounding; multiple
                 precision arithmetic; special function approximations",
}

@InProceedings{Walters:2005:EFA,
  author =       "George Walters and Michael Schulte",
  title =        "Efficient Function Approximation Using Truncated
                 Multipliers and Squarers",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  URL =          "http://arith17.polito.it/final/paper-190.pdf",
  abstract =     "This paper presents a technique for designing linear
                 and quadratic interpolators for function approximation
                 using truncated multipliers and squarers. Initial
                 coefficient values are found using a Chebyshev series
                 approximation, and then adjusted through exhaustive
                 simulation to minimize the maximum absolute error of
                 the interpolator output. This technique is suitable for
                 any function and any precision up to 24-bits (IEEE
                 single precision). Designs for linear and quadratic
                 interpolators that implement the reciprocal function,
                 $f(x) = 1/x,$ are presented and analyzed as an example.
                 We show that a 24-bit truncated reciprocal quadratic
                 interpolator with a design specification of $\pm 1$ ulp
                 error requires 24.1\% fewer partial products to
                 implement than a comparable standard interpolator with
                 the same error specification.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@InProceedings{Anderson:2006:AMF,
  author =       "Cristina S. Anderson and Shane Story and Nikita
                 Astafiev",
  title =        "Accurate Math Functions on the {Intel IA-32}
                 Architecture: {A} Performance-Driven Design",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@InProceedings{deDinechin:2006:STP,
  author =       "Florent de Dinechin and Sergey Maidanov",
  title =        "Software techniques for perfect elementary functions
                 in floating-point interval arithmetic",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Gil:2006:ARP,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 850}: {Real} parabolic cylinder functions
                 {$U(a,x)$, $V(a,x)$}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "102--112",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/1132973.1132978",
  ISSN =         "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "Fortran 90 programs for the computation of real
                 parabolic cylinder functions are presented. The code
                 computes the functions $U(a, x)$, $V(a, x)$ and their
                 derivatives for real $a$ and $x ($x \geq 0)$. The code
                 also computes scaled functions. The range of
                 computation for scaled PCFs is practically
                 unrestricted. The aimed relative accuracy for scaled
                 functions is better than $5 \times 10^{14}$. Exceptions
                 to this accuracy are the evaluation of the functions
                 near their zeros and the error caused by the evaluation
                 of trigonometric functions of large arguments when $|a|
                 > x$. The routines always give values for which the
                 Wronskian relation for scaled functions is verified
                 with a relative accuracy better than $5 \times
                 10^{14}$. The accuracy of the unscaled functions is
                 also better than $5 \times 10^{14}$ for moderate values
                 of $x$ and $a$ (except close to the zeros), while for
                 large $x$ and $a$ the error is dominated by exponential
                 and trigonometric function evaluations. For IEEE
                 standard double precision arithmetic, the accuracy is
                 better than $5 \times 10^{13}$ in the computable range
                 of unscaled PCFs (except close to the zeros).",
  acknowledgement = ack-nhfb,
}

@Article{Gil:2006:CRP,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing the real parabolic cylinder functions
                 {$U(a,x)$, $V(a,x)$}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "70--101",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/1132973.1132977",
  ISSN =         "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "Methods for the computation of real parabolic cylinder
                 functions $U(a, x)$, and $V(a, x)$ and their
                 derivatives are described. We give details on power
                 series, asymptotic series, recursion and quadrature. A
                 combination of these methods can be used for computing
                 parabolic cylinder functions for unrestricted values of
                 the order $a$ and the variable $x$ except for the
                 overflow\slash underflow limitations. By factoring the
                 dominant exponential factor, scaled functions can be
                 computed without practical overflow\slash underflow
                 limitations. In an accompanying article we describe the
                 precise domains for these methods and we present the
                 Fortran 90 codes for the computation of these
                 functions.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parks:2006:UTS,
  author =       "Michael Parks",
  title =        "Unifying Tests for Square Root",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Wires:2006:RRS,
  author =       "Kent E. Wires and Michael J. Schulte",
  title =        "Reciprocal and Reciprocal Square Root Units with
                 Operand Modification and Multiplication",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "42",
  number =       "3",
  pages =        "257--272",
  month =        mar,
  year =         "2006",
  CODEN =        "JVSPED",
  DOI =          "http://dx.doi.org/10.1007/s11265-006-4186-0",
  ISSN =         "0922-5773",
  bibdate =      "Mon Mar 05 08:26:23 2007",
  URL =          "http://springerlink.metapress.com/content/t6027p6713727606/fulltext.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barnett:2007:HPV,
  author =       "Ross Barnett and J. A. Youngman",
  booktitle =    "{1st Joint Meeting of the American Mathematical
                 Society and the New Zealand Mathematical Society,
                 Victoria University of Wellington, Wellington, New
                 Zealand, December 12--15, 2007}",
  title =        "High-Precision Values of the Gamma Function of real
                 argument",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Mon Jul 14 11:57:00 2008",
  URL =          "http://homepages.mcs.vuw.ac.nz/~mathmeet/amsnzms2007/abstracts.pdf",
  abstract =     "A method is described to calculate values of
                 $\Gamma(\nu)$, $0 \leq \nu \leq 1$ to arbitrary
                 precision by combining a Bessel function with a $_0F_1$
                 function. Steed's algorithm is used to compute the
                 regular Bessel function $J_\nu(x)$, for a suitable
                 argument $x$ and real $\nu$, to arbitrary accuracy.
                 Hence the gamma function is obtained. Example values
                 are given to 200D. Verification is by the 80D-results
                 of Frans{\'e}n and Wrigge, by the use of the
                 duplication formula, and by computing the closed form
                 results of Borwein and Zucker. A caveat is offered
                 concerning the coding of the Bessel functions in
                 Numerical Recipes and in the GSL library.",
  acknowledgement = ack-nhfb,
}

@Book{Gil:2007:NMS,
  author =       "Amparo Gil and Javier Segura and N. M. Temme",
  title =        "Numerical methods for special functions",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xvi + 415",
  year =         "2007",
  ISBN-13 =      "978-0-898716-34-4",
  LCCN =         "QA351 .G455 2007",
  bibdate =      "Fri Sep 14 10:24:22 MDT 2007",
  bibsource =    "z3950.loc.gov:7090/Voyager",
  price =        "US\$99.00",
  acknowledgement = ack-nhfb,
  remark =       "To be published October 2007.",
  subject =      "functions, special; data processing; numerical
                 analysis; asymptotic expansions; approximation theory",
}

@Article{Kuliamin:2007:STI,
  author =       "V. V. Kuliamin",
  title =        "Standardization and testing of implementations of
                 mathematical functions in floating point numbers",
  journal =      j-PROG-COMP-SOFT,
  volume =       "33",
  number =       "3",
  pages =        "154--173",
  year =         "2007",
  DOI =          "http://dx.doi.org/10.1134/S036176880703005X",
  ISSN =         "0361-7688",
  bibdate =      "Fri Aug 08 09:01:30 2008",
  abstract =     "Requirements definition and test suites development
                 for implementations of mathematical functions in
                 floating point arithmetic in the framework of the IEEE
                 754 standard are considered. A method based on this
                 standard is proposed for defining requirements for such
                 functions. This method can be used for the
                 standardization of implementations of such functions;
                 this kind of standardization extends IEEE 754. A method
                 for designing test suites for the verification of those
                 requirements is presented. The proposed methods are
                 based on specific properties of the representation of
                 floating point numbers and on some features of the
                 functions under examination.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point function testing and verification",
}

@TechReport{Lefevre:2007:SNP,
  author =       "Vincent Lef{\'e}vre and Jean-Michel Muller",
  title =        "Some notes on the possible under\slash overflow of the
                 most common elementary functions",
  type =         "Report",
  institution =  "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "7",
  year =         "2007",
  bibdate =      "Fri May 25 16:18:32 2007",
  URL =          "http://prunel.ccsd.cnrs.fr/ensl-00149414",
  abstract =     "The purpose of this short note is not to describe when
                 underflow or overflow must be signalled (it is quite
                 clear that the rules are the same as for the basic
                 arithmetic operations). We just want to show that for
                 some of the most common functions and floating-point
                 formats, in many cases, we can know in advance that the
                 results will always lie in the range of the numbers
                 that are representable by normal floating-point
                 numbers, so that in these cases there is no need to
                 worry about underflow or overflow. Note that when it is
                 not the case, an implementation is still possible using
                 a run-time test.",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions; floating-point arithmetic;
                 overflow; underflow",
}

@Article{Neher:2007:CSF,
  author =       "Markus Neher",
  title =        "Complex standard functions and their implementation in
                 the {CoStLy} library",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "??--??",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/1206040.1206042",
  ISSN =         "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "The practical calculation of range bounds for some
                 complex standard functions is addressed in this
                 article. The functions under consideration are root and
                 power functions, the exponential, trigonometric and
                 hyperbolic functions, and their inverse functions. For
                 such a function $f$ and a given rectangular complex
                 interval $z$, some interval $w$ is computed that
                 contains all function values of $f$ in $z$. This is
                 done by expressing the real and the imaginary part of
                 $f$ as compositions of real standard functions and then
                 estimating the ranges of these compositions. In many
                 cases, the inclusions are optimal, such that $w$ is the
                 smallest rectangular interval containing the range of
                 $f$.

                 The algorithms presented in this article have been
                 implemented in a C++ class library called CoStLy
                 (Complex Standard Functions License), which is
                 distributed under the conditions of the GNU General
                 Public License.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
}

@Article{Schmelzer:2007:CGF,
  author =       "Thomas Schmelzer and Lloyd N. Trefethen",
  title =        "Computing the Gamma Function Using Contour Integrals
                 and Rational Approximations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "45",
  number =       "2",
  pages =        "558--571",
  month =        "????",
  year =         "2007",
  CODEN =        "SJNAAM",
  DOI =          "http://dx.doi.org/10.1137/050646342",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  bibdate =      "Mon Nov 24 18:03:07 MST 2008",
  bibsource =    "http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM&Volume=45&Issue=2",
  acknowledgement = ack-nhfb,
}

@Article{Kodama:2008:ASP,
  author =       "Masao Kodama",
  title =        "{Algorithm 877}: {A} Subroutine Package for
                 Cylindrical Functions of Complex Order and Nonnegative
                 Argument",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "22:1--22:21",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/1377596.1377602",
  ISSN =         "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/",
  abstract =     "The algorithm presented provides a package of
                 subroutines for calculating the cylindrical functions
                 $J_\nu(x)$, $N_\nu(x)$, $H_\nu^{1}(x)$, $H_\nu^{2}(x)$
                 where the order $\nu$ is complex and the real argument
                 $x$ is nonnegative. The algorithm is written in Fortran
                 95 and calculates the functions using single, double,
                 or quadruple precision according to the value of a
                 parameter defined in the algorithm. The methods of
                 calculating the functions are based on a series
                 expansion, Debye's asymptotic expansions, Olver's
                 asymptotic expansions, and recurrence methods (Miller's
                 algorithms). The relative errors of the functional
                 values computed by this algorithm using double
                 precision are less than $2.4 \times 10^{-13}$ in the
                 region $0 \leq \mbox{Re}(\nu) \leq 64$, $0 \leq
                 \mbox{Im}(\nu) \leq 63$, $0.024 \leq x \leq 97$.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  keywords =     "Bessel functions; complex order; Cylindrical
                 functions; Debye's asymptotic expansions; Hankel
                 functions; Miller's algorithms; Neumann functions;
                 nonnegative argument; numerical calculation; Olver's
                 asymptotic expansions",
}

@Article{Harris:2009:MIB,
  author =       "Frank E. Harris and J. G. Fripiat",
  title =        "Methods for incomplete {Bessel} function evaluation",
  journal =      j-IJQC,
  volume =       "109",
  number =       "8",
  pages =        "1728--1740",
  month =        feb,
  year =         "2009",
  CODEN =        "IJQCB2",
  DOI =          "http://dx.doi.org/10.1002/qua.21972",
  ISSN =         "0020-7608",
  bibdate =      "Fri Mar 27 07:41:18 2009",
  abstract =     "Presented here are detailed methods for evaluating the
                 incomplete Bessel functions arising when Gaussian-type
                 orbitals are used for systems periodic in one spatial
                 dimension. The scheme is designed to yield these
                 incomplete Bessel functions with an absolute accuracy
                 of $\pm 1 \times 10^{-10}, for the range of integer
                 orders $0 \leq n \leq 12$ [a range sufficient for a
                 basis whose members have angular momenta of up to three
                 units ($s$, $p$, $d$, or $f% atomic functions)]. To
                 reach this accuracy level within acceptable computation
                 times, new rational approximations were developed to
                 compute the special functions involved, namely, the
                 exponential integral $E_1(x)$ and the modified Bessel
                 functions $K_0(x)$ and $K_1(x)$, to absolute accuracy
                 $\pm 1 \time 10^{-15}.",
  acknowledgement = ack-nhfb,
  keywords =     "E1(x); incomplete Bessel function; K0(x); K1(x); leaky
                 aquifer function; modified Bessel function; exponential
                 integral; numerical methods",
}

@Article{Weniger:2009:SHF,
  author =       "Ernst Joachim Weniger",
  title =        "The strange history of {$B$} functions or how
                 theoretical chemists and mathematicians do (not)
                 interact",
  journal =      j-IJQC,
  volume =       "109",
  number =       "8",
  pages =        "1728--1740",
  month =        feb,
  year =         "2009",
  CODEN =        "IJQCB2",
  DOI =          "http://dx.doi.org/10.1002/qua.22014",
  ISSN =         "0020-7608",
  bibdate =      "Fri Mar 27 07:47:31 2009",
  abstract =     "$B$ functions are a class of relatively complicated
                 exponentially decaying basis functions. Because the
                 molecular multicenter integrals of the much simpler
                 Slater-type functions are notoriously difficult, it is
                 not at all obvious why $B$ functions should offer any
                 advantages. However, $B$ functions have Fourier
                 transforms of exceptional simplicity, which greatly
                 simplifies many of their molecular multicenter
                 integrals. This article discusses the historical
                 development of $B$ functions from the perspective of
                 the interaction between mathematics and theoretical
                 chemistry, which traditionally has not been very
                 good. Nevertheless, future progress in theoretical
                 chemistry depends very much on a fertile interaction
                 with neighboring disciplines.",
  acknowledgement = ack-nhfb,
  keywords =     "electronic structure theory; exponentially decaying
                 basis functions; B functions; multicenter integrals;
                 interdisciplinary collaboration",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:

@Book{Ralston:1960:MMD,
  editor =       "Anthony Ralston and Herbert S. Wilf",
  booktitle =    "Mathematical methods for digital computers",
  title =        "Mathematical methods for digital computers",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "various",
  year =         "1960--1977",
  ISBN =         "0-471-70690-6",
  ISBN-13 =      "978-0-471-70690-8",
  LCCN =         "QA39 .R26",
  bibdate =      "Mon Jan 13 10:36:06 1997",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{AFIPS:1969:ACPb,
  key =          "AFIPS FJCC '69",
  title =        "1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada",
  volume =       "35",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "807",
  year =         "1969",
  LCCN =         "TK7885.A1 J6 1969",
  bibdate =      "Sat Sep 24 01:06:00 1994",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nhfb,
}

@Proceedings{AFIPS:1971:ACP,
  key =          "AFIPS SJCC '71",
  booktitle =    "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  title =        "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  volume =       "38",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "631",
  year =         "1971",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:47:01 1994",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj,
}

@Book{Rice:1971:MS,
  author =       "John R. Rice",
  booktitle =    "Mathematical Software",
  title =        "Mathematical Software",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "xvii + 515",
  year =         "1971",
  ISBN =         "0-12-587250-X",
  ISBN-13 =      "978-0-12-587250-8",
  LCCN =         "QA1 .M26",
  bibdate =      "Thu Sep 15 18:56:52 1994",
  note =         "Based on the proceedings of the Mathematical Software
                 Symposium held at Purdue University, Lafayette,
                 Indiana, USA, April 1--3, 1970.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Miller:1975:TNA,
  editor =       "John J. H. Miller",
  booktitle =    "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  title =        "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "various",
  year =         "1975",
  ISBN =         "0-12-496950-X",
  ISBN-13 =      "978-0-12-496950-6",
  LCCN =         "QA297 .R69 1973",
  bibdate =      "Mon Jan 13 10:41:13 1997",
  acknowledgement = ack-nhfb,
}

@Proceedings{Traub:1976:ACC,
  editor =       "J. F. (Joseph Frederick) Traub",
  booktitle =    "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  title =        "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "ix + 239",
  year =         "1976",
  ISBN =         "0-12-697560-4",
  ISBN-13 =      "978-0-12-697560-4",
  LCCN =         "QA297.S9151 1975",
  bibdate =      "Mon Jan 13 10:18:33 1997",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1978:PSC,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the Symposium on Computer Arithmetic
                 (4th: 1978: Santa Monica, CA)",
  title =        "Proceedings of the Symposium on Computer Arithmetic
                 (4th: 1978: Santa Monica, {CA})",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1978",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S919a",
  bibdate =      "Mon May 19 15:22:15 1997",
  note =         "IEEE catalog no. 78 CH1412-6C.",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming ---
                 Congresses.; Floating-point arithmetic --- Congresses.;
                 Computer arithmetic --- Congresses.",
}

@Proceedings{Alefeld:1980:PSE,
  editor =       "G. Alefeld and R. D. Grigorieff and R. Albrecht and U.
                 Kulisch and F. Stummel",
  booktitle =    "Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin",
  title =        "Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin",
  volume =       "2",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "229",
  year =         "1980",
  ISBN =         "0-387-81566-X",
  ISBN-13 =      "978-0-387-81566-4",
  ISSN =         "0344-8029",
  LCCN =         "QA297 .F84",
  bibdate =      "Mon Jan 13 10:20:47 1997",
  series =       "Computing. Supplementum",
  acknowledgement = ack-nhfb,
}

@Proceedings{Lavington:1980:IPP,
  editor =       "Simon Hugh Lavington",
  booktitle =    "Information Processing 80: Proceedings of {IFIP}
                 Congress 80, Tokyo, Japan, October 6--9, 1980,
                 Melbourne, Australia, October 14--17, 1980",
  title =        "Information Processing 80: Proceedings of {IFIP}
                 Congress 80, Tokyo, Japan, October 6--9, 1980,
                 Melbourne, Australia, October 14--17, 1980",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "xiii + 1070",
  year =         "1980",
  ISBN =         "0-444-86034-7",
  ISBN-13 =      "978-0-444-86034-7",
  LCCN =         "QA 75.5 I57 1980",
  bibdate =      "Thu Sep 01 23:09:20 1994",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1981:PIS,
  editor =       "{IEEE}",
  booktitle =    "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18-19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  title =        "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18-19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vii + 278",
  year =         "1981",
  LCCN =         "QA76.9.C62 S95 1981",
  bibdate =      "Mon May 19 13:17:13 1997",
  note =         "IEEE Catalog No. 81CH1630-3. Computer Society Order
                 No. 347.",
  acknowledgement = ack-nhfb,
  xxISBN =       "none",
}

@Proceedings{Mulvey:1982:EMP,
  editor =       "J. M. Mulvey",
  title =        "Evaluating Mathematical Programming Techniques:
                 Proceedings of a Conference Held at the National Bureau
                 of Standards, Boulder, Colorado, January 5--6, 1981",
  volume =       "199",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 379",
  year =         "1982",
  ISBN =         "0-387-11495-5",
  ISBN-13 =      "978-0-387-11495-8",
  LCCN =         "QA402.5 .E94 1982",
  bibdate =      "Thu Nov 17 06:36:49 1994",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib",
  series =       "Lecture Notes in Economics and Mathematical Systems",
  acknowledgement = ack-nhfb,
}

@Book{Bultheel:1999:ORF,
  editor =       "Adhemar Bultheel and Pablo Gonzales-Vera and Erik
                 Hendriksen and Olav Njastad",
  booktitle =    "Orthogonal Rational Functions",
  title =        "Orthogonal Rational Functions",
  volume =       "5",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiv + 407",
  year =         "1999",
  ISBN =         "0-521-65006-2 (hardcover)",
  ISBN-13 =      "978-0-521-65006-9 (hardcover)",
  LCCN =         "QA404.5 .O75 1999",
  bibdate =      "Tue Mar 24 21:04:21 MDT 2009",
  bibsource =    "z3950.loc.gov:7090/Voyager",
  series =       "Cambridge monographs on applied and computational
                 mathematics",
  URL =          "http://www.loc.gov/catdir/toc/cam024/98011646.html;
                 http://www.loc.gov/catdir/description/cam029/98011646.html",
  acknowledgement = ack-nhfb,
  subject =      "functions, orthogonal; functions of complex
                 variables",
}

@Proceedings{Marron:1985:FEP,
  editor =       "J. S. Marron",
  title =        "Function estimates: proceedings of a conference held
                 July 28--August 3, 1985",
  volume =       "59",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "ix + 178",
  year =         "1985",
  ISBN =         "0-8218-5062-8",
  ISBN-13 =      "978-0-8218-5062-6",
  ISSN =         "0271-4132",
  LCCN =         "QA276.8 .C651 1985",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  note =         "Held at Humboldt State University, Arcata,
                 California.",
  series =       "Contemporary mathematics (American Mathematical
                 Society)",
  acknowledgement = ack-nhfb,
  bibno =        "18241",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms; theory",
  guideno =      "1986-12215",
  procdate =     "July 28--Aug. 3, 1985",
  procloc =      "Arcata, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Proceedings{Miranker:1985:ASC,
  editor =       "Willard L. Miranker and Richard A. Toupin",
  booktitle =    "Accurate Scientific Computations: Symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
  title =        "Accurate Scientific Computations: Symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
  volume =       "235",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 205",
  year =         "1985",
  ISBN =         "0-387-16798-6",
  ISBN-13 =      "978-0-387-16798-5",
  LCCN =         "QA76.95 .A231 1986",
  bibdate =      "Mon May 19 12:34:16 1997",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
}

@Proceedings{Miranker:1986:ASC,
  editor =       "Willard L. Miranker and Richard A. Toupin",
  booktitle =    "Accurate scientific computations: symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: proceedings",
  title =        "Accurate scientific computations: symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: proceedings",
  volume =       "235",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 205",
  year =         "1986",
  CODEN =        "LNCSD9",
  ISBN =         "0-387-16798-6 (USA: paperback)",
  ISBN-13 =      "978-0-387-16798-5 (USA: paperback)",
  ISSN =         "0302-9743",
  LCCN =         "QA76.95 .A231 1986",
  bibdate =      "Fri Apr 12 07:14:49 1996",
  note =         "Symposium sponsored by IBM Deutschland.",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "mathematics --- data processing --- congresses;
                 numerical calculations --- congresses",
}

@Proceedings{ACM:1987:UAA,
  editor =       "{ACM}",
  booktitle =    "Using Ada: ACM SIGAda international conference,
                 Boston, Massachusetts, December 8--11, 1987",
  title =        "Using Ada: {ACM} {SIGA}da international conference,
                 Boston, Massachusetts, December 8--11, 1987",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 240",
  year =         "1987",
  ISBN =         "0-89791-243-8",
  ISBN-13 =      "978-0-89791-243-3",
  LCCN =         "QA 76.73 A35 U85 1987",
  bibdate =      "Mon May 19 13:18:54 1997",
  acknowledgement = ack-nhfb,
}

@Proceedings{Iserles:1987:SAN,
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  title =        "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xiv + 719",
  year =         "1987",
  ISBN =         "0-19-853614-3",
  ISBN-13 =      "978-0-19-853614-7",
  LCCN =         "QA297 .S781 1987",
  bibdate =      "Thu Sep 08 00:41:24 1994",
  price =        "UK\pounds55.00, US\$77.50",
  acknowledgement = ack-nj,
}

@Proceedings{Mason:1987:AA,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "Algorithms for approximation: based on the proceedings
                 of the IMA Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985",
  title =        "Algorithms for approximation: based on the proceedings
                 of the {IMA} Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985",
  volume =       "10",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xvi + 694",
  year =         "1987",
  ISBN =         "0-19-853612-7",
  ISBN-13 =      "978-0-19-853612-3",
  LCCN =         "QA221 .A5361 1987",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991)",
  price =        "US\$90",
  series =       "The Institute of Mathematics and Its Applications
                 conference series, new series",
  acknowledgement = ack-nhfb,
  bibno =        "39820",
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory; algorithms",
  guideno =      "1987-16080",
  procdate =     "The Institute of mathematics and its applications
                 conference series; 10 July 1985",
  procloc =      "Shrivenham, UK",
  sub =          "Proceedings of the IMA Conference on Algorithms for
                 the approximation of functions",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Proceedings{USENIX:1988:UPC,
  editor =       "{USENIX Association}",
  booktitle =    "{USENIX} proceedings: {C++} Conference, Denver, {CO},
                 October 17--21, 1988",
  title =        "{USENIX} proceedings: {C++} Conference, Denver, {CO},
                 October 17--21, 1988",
  publisher =    pub-USENIX,
  address =      pub-USENIX:adr,
  pages =        "362",
  year =         "1988",
  bibdate =      "Sun Feb 18 07:46:09 MST 1996",
  acknowledgement = ack-nhfb,
  keywords =     "C++ (Computer program language) --- Congresses.",
}

@Proceedings{ACM:1989:PAI,
  editor =       "{ACM}",
  booktitle =    "Proceedings of the ACM-SIGSAM 1989 International
                 Symposium on Symbolic and Algebraic Computation, ISSAC
                 '89",
  title =        "Proceedings of the {ACM}-{SIGSAM} 1989 International
                 Symposium on Symbolic and Algebraic Computation,
                 {ISSAC} '89",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "399",
  year =         "1989",
  ISBN =         "0-89791-325-6",
  ISBN-13 =      "978-0-89791-325-6",
  LCCN =         "QA76.95.I59 1989",
  bibdate =      "Tue Sep 17 06:46:18 MDT 1996",
  acknowledgement = ack-nhfb,
  confdate =     "17--19 July 1989",
  conflocation = "Portland, OR, USA",
  confsponsor =  "ACM",
  pubcountry =   "USA",
}

@Proceedings{Ercegovac:1989:PSC,
  editor =       "Milo{\v{s}} D. Ercegovac and Earl E. {Swartzlander,
                 Jr.}",
  booktitle =    "Proceedings: 9th Symposium on Computer Arithmetic:
                 September 6--8, 1989, Santa Monica, California, {USA}",
  title =        "Proceedings: 9th Symposium on Computer Arithmetic:
                 September 6--8, 1989, Santa Monica, California, {USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 247",
  year =         "1989",
  ISBN =         "0-8186-8963-3 (case), 0-8186-5963-7 (microfiche)",
  ISBN-13 =      "978-0-8186-8963-5 (case), 978-0-8186-5963-8
                 (microfiche)",
  LCCN =         "QA 76.9 C62 S95 1989",
  bibdate =      "Thu Sep 01 22:36:52 1994",
  note =         "IEEE catalog no. 89CH2757-3.",
  acknowledgement = ack-nhfb,
  confdate =     "6-8 Sept. 1989",
  conflocation = "Santa Monica, CA, USA",
  confsponsor =  "IEEE; IFIP; Univ. California",
  pubcountry =   "USA",
}

@Proceedings{Megiddo:1989:PMP,
  editor =       "N. Megiddo",
  booktitle =    "Progress in Mathematical Programming: Interior-Point
                 and Related Methods",
  title =        "Progress in Mathematical Programming: Interior-Point
                 and Related Methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 158",
  year =         "1989",
  ISBN =         "0-387-96847-4",
  ISBN-13 =      "978-0-387-96847-6",
  LCCN =         "QA402.5 .P7851 1989",
  bibdate =      "Sat Nov 09 07:07:37 2002",
  note =         "Proceedings of the conference held at the Asilomar
                 conference center in Pacific Grove, California, March
                 1--4, 1987.",
  acknowledgement = ack-nhfb,
}

@Book{Srivastava:1989:UFF,
  editor =       "H. M. Srivastava and Shigeyoshi Owa",
  booktitle =    "Univalent functions, fractional calculus, and their
                 applications (K\=oriyama, 1988)",
  title =        "Univalent functions, fractional calculus, and their
                 applications ({K}\=oriyama, 1988)",
  publisher =    pub-ELLIS-HORWOOD,
  address =      pub-ELLIS-HORWOOD:adr,
  pages =        "404",
  year =         "1989",
  ISBN =         "0-470-21630-1, 0-7458-0701-0 (??invalid ISBN
                 checksum??)",
  ISBN-13 =      "978-0-470-21630-9, 978-0-7458-0701-0 (??invalid
                 ISBN-13 checksum??)",
  LCCN =         "QA331 .U55 1989",
  bibdate =      "Mon Jan 13 09:52:29 1997",
  price =        "UK\pounds 39.95",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cray:1990:PCU,
  editor =       "????",
  key =          "Cray UG '90",
  booktitle =    "Proceedings Cray User Group",
  title =        "Proceedings Cray User Group",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  month =        "Spring",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Sep 08 08:56:01 1994",
  acknowledgement = ack-nj,
}

@Proceedings{Anonymous:1991:PIS,
  editor =       "Anonymous",
  booktitle =    "Proceedings of the International Symposium on
                 Supercomputing: Fukuoka, Japan, November 6--8, 1991",
  title =        "Proceedings of the International Symposium on
                 Supercomputing: Fukuoka, Japan, November 6--8, 1991",
  publisher =    "Kyushu University Press",
  address =      "Fukuoka, Japan",
  pages =        "iv + 261",
  year =         "1991",
  ISBN =         "4-87378-284-8",
  ISBN-13 =      "978-4-87378-284-3",
  LCCN =         "QA76.88.I 1991",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  acknowledgement = ack-nhfb,
  searchkey =    "ti:elementary function",
}

@Proceedings{IEEE:1991:PSA,
  editor =       "{IEEE}",
  booktitle =    "Proceedings, Supercomputing '91: Albuquerque, New
                 Mexico, November 18--22, 1991",
  title =        "Proceedings, Supercomputing '91: Albuquerque, New
                 Mexico, November 18--22, 1991",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxiii + 917",
  year =         "1991",
  ISBN =         "0-8186-9158-1 (IEEE case), 0-8186-2158-3 (IEEE paper),
                 0-8186-6158-5 (IEEE microfiche), 0-89791-459-7 (ACM)",
  ISBN-13 =      "978-0-8186-9158-4 (IEEE case), 978-0-8186-2158-1 (IEEE
                 paper), 978-0-8186-6158-7 (IEEE microfiche),
                 978-0-89791-459-8 (ACM)",
  LCCN =         "QA76.5 .S894 1991",
  bibdate =      "Fri Aug 30 08:01:51 MDT 1996",
  bibsource =    "University of California MELVYL catalog.",
  note =         "ACM order number 415913. IEEE Computer Society Press
                 order number 2158. IEEE catalog number 91CH3058-5.",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques); C5470
                 (Performance evaluation and testing); C6110P (Parallel
                 programming)",
  keywords =     "combinatorial algorithms; data dependence; distributed
                 memory code generation; high school environment;
                 latency tolerance; memory access; numerical algorithms;
                 parallel processing; parallel programming; performance
                 evaluation; performance tools; processor design;
                 program analysis; storage hierarchy optimization;
                 supercomputer benchmarks; supercomputer congresses;
                 supercomputing; system issues",
}

@Proceedings{Kornerup:1991:PIS,
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proceedings: 10th {IEEE} Symposium on Computer
                 Arithmetic: June 26--28, 1991, Grenoble, France",
  title =        "Proceedings: 10th {IEEE} Symposium on Computer
                 Arithmetic: June 26--28, 1991, Grenoble, France",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 282",
  year =         "1991",
  ISBN =         "0-8186-9151-4 (case), 0-8186-6151-8 (microfiche),
                 0-7803-0187-0 (library binding)",
  ISBN-13 =      "978-0-8186-9151-5 (case), 978-0-8186-6151-8
                 (microfiche), 978-0-7803-0187-0 (library binding)",
  LCCN =         "QA76.9.C62 S95 1991",
  bibdate =      "Thu Sep 01 23:18:52 1994",
  acknowledgement = ack-nhfb,
}

@Proceedings{EC2:1992:DJN,
  key =          "AEF'92",
  title =        "Deuxi{\`e}mes journ{\'e}es nationales: Les
                 applications des ensembles flous, en l'honneur du
                 {Professeur A. Kaufmann}, {Nimes}, 2--3 novembre 1992,
                 conference scientifique ({English}: Second national
                 conference: Application of Fuzzy Sets, in honor of
                 {Professor A. Kaufman}, {Nimes}, 2--3 {November} 1992,
                 scientific conference)",
  publisher =    "EC2",
  address =      "Nanterre Cedex, France",
  pages =        "384",
  year =         "1992",
  ISBN =         "2-906899-78-X",
  ISBN-13 =      "978-2-906899-78-0",
  LCCN =         "????",
  bibdate =      "Wed Jan 10 07:40:53 1996",
  acknowledgement = ack-nhfb,
}

@Book{Adams:1993:ACA,
  editor =       "E. Adams and U. Kulisch",
  booktitle =    "Scientific computing with automatic result
                 verification",
  title =        "Scientific computing with automatic result
                 verification",
  volume =       "189",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "x + 612",
  year =         "1993",
  ISBN =         "0-12-044210-8",
  ISBN-13 =      "978-0-12-044210-2",
  LCCN =         "QA76.S368 1993",
  bibdate =      "Mon Jan 13 09:58:58 1997",
  series =       "Mathematics in science and engineering",
  acknowledgement = ack-nhfb,
}

@Proceedings{Sincovec:1993:PSS,
  editor =       "Richard F. Sincovec and others",
  title =        "Proceedings of the Sixth {SIAM} Conference on Parallel
                 Processing for Scientific Computing, held March 22--24,
                 1993, in Norfolk, {VA}, {USA}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xix + 1041 + iv",
  year =         "1993",
  ISBN =         "0-89871-315-3",
  ISBN-13 =      "978-0-89871-315-2",
  LCCN =         "QA76.58 .S55 1993 v.1-2",
  bibdate =      "Tue Oct 11 12:21:40 1994",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib",
  note =         "Two volumes.",
}

@Proceedings{Swartzlander:1993:SCA,
  editor =       "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
                 Graham Jullien",
  booktitle =    "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  title =        "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 284",
  year =         "1993",
  ISBN =         "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
                 0-8186-3861-3 (microfiche)",
  ISBN-13 =      "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
                 (casebound), 978-0-8186-3861-9 (microfiche)",
  ISSN =         "0018-9340",
  LCCN =         "QA 76.9 C62 S95 1993",
  bibdate =      "Thu Sep 01 22:58:49 1994",
  note =         "IEEE Transactions on Computers {\bf 43(8)}, 1994",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cuyt:1994:NNM,
  editor =       "Annie Cuyt",
  booktitle =    "Nonlinear numerical methods and rational approximation
                 {II}",
  title =        "Nonlinear numerical methods and rational approximation
                 {II}",
  volume =       "296",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xviii + 446",
  year =         "1994",
  ISBN =         "0-7923-2967-8",
  LCCN =         "QA297 .N642 1994",
  bibdate =      "Wed Nov 3 09:30:14 MST 1999",
  note =         "Proceedings of an international conference held at the
                 University of Antwerp, Belgium, Sept. 5--11, 1993.",
  series =       "Mathematics and its applications",
  acknowledgement = ack-nhfb,
  keywords =     "approximation theory -- congresses; numerical analysis
                 -- congresses",
}

@Proceedings{Gautschi:1994:MCH,
  editor =       "Walter Gautschi",
  booktitle =    "{Mathematics of Computation} 1943--1993: a
                 half-century of computational mathematics",
  title =        "{Mathematics of Computation} 1943--1993: a
                 half-century of computational mathematics",
  volume =       "48",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xx + 643",
  year =         "1994",
  ISBN =         "0-8218-0291-7",
  ISBN-13 =      "978-0-8218-0291-5",
  MRclass =      "00B25 (11-06 65-06)",
  MRnumber =     "95j:00014",
  note =         "Papers from the Symposium on Numerical Analysis and
                 the Minisymposium on Computational Number Theory held
                 in Vancouver, British Columbia, August 9--13, 1993",
  series =       "Proceedings of Symposia in Applied Mathematics",
}

@Proceedings{Mudge:1994:PTS,
  editor =       "Trevor N. Mudge and Bruce D. Shriver",
  booktitle =    "Proceedings of the Twenty-Seventh Hawaii International
                 Conference on System Sciences Vol. I: Architecture",
  title =        "Proceedings of the Twenty-Seventh Hawaii International
                 Conference on System Sciences Vol. {I}: Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1994",
  ISBN =         "0-8186-5050-8 (paper), 0-8186-5051-6 (microfiche)",
  ISBN-13 =      "978-0-8186-5050-5 (paper), 978-0-8186-5051-2
                 (microfiche)",
  LCCN =         "????",
  bibdate =      "Mon Jan 13 10:02:18 1997",
  note =         "First of five volumes. IEEE Catalog No. 94TH0607-2.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Knowles:1995:PSC,
  editor =       "Simon Knowles and William H. McAllister",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England",
  title =        "Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 252",
  year =         "1995",
  ISBN =         "0-8186-7089-4 (paperback), 0-8186-7089-4 (case),
                 0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound),
                 0-7803-2949-X (casebound)",
  ISBN-13 =      "978-0-8186-7089-3 (paperback), 978-0-8186-7089-3
                 (case), 978-0-8186-7149-4 (microfiche),
                 978-0-8186-7089-3 (softbound), 978-0-7803-2949-2
                 (casebound)",
  LCCN =         "QA 76.9 C62 S95 1995",
  bibdate =      "Sun Mar 29 08:48:20 1998",
  acknowledgement = ack-nhfb,
}

@Proceedings{Singh:1995:CRT,
  editor =       "Avtar Singh",
  booktitle =    "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  title =        "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1995",
  ISBN =         "0-8186-7370-2",
  ISBN-13 =      "978-0-8186-7370-2",
  LCCN =         "TK7801 .A83 1995",
  bibdate =      "Sun Mar 29 08:51:26 1998",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Boisvert:1997:QNS,
  editor =       "Ronald F. Boisvert",
  booktitle =    "Quality of Numerical Software: Assessment and
                 Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
                 Conference on the Quality of Numerical Software,
                 Assessment and Enhancement, Oxford, United Kingdom,
                 8--12 July 1996}",
  title =        "Quality of Numerical Software: Assessment and
                 Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
                 Conference on the Quality of Numerical Software,
                 Assessment and Enhancement, Oxford, United Kingdom,
                 8--12 July 1996}",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "vii + 384",
  year =         "1997",
  ISBN =         "0-412-80530-8",
  ISBN-13 =      "978-0-412-80530-1",
  LCCN =         "QA297 .I35 1996",
  bibdate =      "Fri Jul 09 05:58:30 2004",
  acknowledgement = ack-nhfb,
}

@Proceedings{Lang:1997:ISC,
  editor =       "Tomas Lang and Jean-Michel Muller and Naofumi Takagi",
  booktitle =    "13th IEEE Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 USA",
  title =        "13th {IEEE} Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 {USA}",
  volume =       "13",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 291",
  year =         "1997",
  ISBN =         "0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8",
  ISBN-13 =      "978-0-8186-7846-2, 978-0-8186-7847-9,
                 978-0-8186-7848-6",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 1997",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  note =         "IEEE Computer Society order number PR07846. IEEE Order
                 Plan catalog number 97CB36091.",
  series =       "Symposium on Computer Arithmetic",
  acknowledgement = ack-nhfb,
  sponsor =      "IEEE.",
}

@Proceedings{Thiele:1997:IIC,
  editor =       "Lothar Thiele and others",
  booktitle =    "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  title =        "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 540",
  year =         "1997",
  ISBN =         "0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1",
  ISBN-13 =      "978-0-8186-7959-9, 978-0-8186-7960-5,
                 978-0-8186-7958-2",
  LCCN =         "TK7874.6 .I57 1997eb; TK7874.6 .I57 1997; TK7874.6
                 .I58 1997",
  bibdate =      "Sun Mar 4 21:13:29 MST 2007",
  bibsource =    "melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (11th : 1997 :
                 Z{\"u}rich, Switzerland)",
  remark =       "IEEE Computer Society Press order number PR07958. IEEE
                 catalog number 97TB100177",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application-specific integrated
                 circuits",
}

@Proceedings{IEEE:1999:PIF,
  editor =       "IEEE",
  booktitle =    "Proceedings of the IEEE Forum on Research and
                 Technology Advances in Digital Libraries, May 19--21,
                 1999, Baltimore, Maryland",
  title =        "Proceedings of the {IEEE} Forum on Research and
                 Technology Advances in Digital Libraries, May 19--21,
                 1999, Baltimore, Maryland",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 217",
  year =         "1999",
  ISBN =         "0-7695-0219-9",
  ISBN-13 =      "978-0-7695-0219-9",
  LCCN =         "ZA4080 .F67 1999",
  bibdate =      "Fri Jul 09 06:32:32 2004",
  acknowledgement = ack-nhfb,
  xxeditor =     "Frances M. Titsworth",
}

@Proceedings{Koren:1999:ISC,
  editor =       "Israel Koren and Peter Kornerup",
  booktitle =    "14th IEEE Symposium on Computer Arithmetic:
                 proceedings: April 14--16, 1999, Adelaide, Australia",
  title =        "14th {IEEE} Symposium on Computer Arithmetic:
                 proceedings: April 14--16, 1999, Adelaide, Australia",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1999",
  ISBN =         "0-7803-5609-8, 0-7695-0116-8, 0-7695-0118-4",
  ISBN-13 =      "978-0-7803-5609-2, 978-0-7695-0116-1,
                 978-0-7695-0118-5",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S887 1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  note =         "IEEE Computer Society Order Number PR00116. IEEE Order
                 Plan Catalog Number 99CB36336.",
  URL =          "http://computer.org/conferen/home/arith/;
                 http://www.ecs.umass.edu/ece/arith14/program.html",
  acknowledgement = ack-nhfb,
  annote =       "Also known as ARITH-14.",
  source =       "Computer arithmetic",
  sponsor =      "IEEE.",
}

@Proceedings{Luk:1999:PSA,
  editor =       "Franklin T. Luk",
  booktitle =    "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations IX:
                 19--21 July, 1999, Denver, Colorado}",
  title =        "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations IX:
                 19--21 July, 1999, Denver, Colorado}",
  volume =       "3807",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "ix + 648",
  year =         "1999",
  ISBN =         "0-8194-3293-8",
  ISBN-13 =      "978-0-8194-3293-3",
  LCCN =         "TK5102.5 .A3325 1999; TK5102.5 .A3173 1999eb; TK5102.9
                 .A37 1999; TK5102.5; TS510 .S63",
  bibdate =      "Mon Mar 5 07:43:43 MST 2007",
  bibsource =    "melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Signal processing; Digital techniques; Congresses;
                 Algorithms; Computer architecture",
}

@Proceedings{Dunkl:2000:PIW,
  editor =       "Charles Dunkl and Mourad Ismail and Roderick Wong",
  booktitle =    "Proceedings of the international workshop, special
                 functions: {Hong Kong, 21--25 June 1999}",
  title =        "Proceedings of the international workshop, special
                 functions: {Hong Kong, 21--25 June 1999}",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xi + 438",
  year =         "2000",
  ISBN =         "981-02-4393-6",
  ISBN-13 =      "978-981-02-4393-7",
  LCCN =         "QA351 .P76 2000",
  bibdate =      "Fri Jul 09 06:30:25 2004",
  acknowledgement = ack-nhfb,
}

@Proceedings{Sprague:2000:PAH,
  editor =       "Ralph H. Sprague",
  booktitle =    "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  title =        "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "liv + 259",
  year =         "2000",
  ISBN =         "0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7",
  ISBN-13 =      "978-0-7695-0493-3, 978-0-7695-0494-0, 978-0-7695-0495-7",
  LCCN =         "TA168 .H37 2000; TA168 .H37 2000xeb; TA168",
  bibdate =      "Sun Mar 4 21:23:42 MST 2007",
  bibsource =    "melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Hawaii International Conference on System Sciences
                 (33rd : 2000 : Maui, Hawaii)",
  remark =       "IEEE Computer Society Order Number: PR00493",
  subject =      "Systems engineering; Congresses; Information theory;
                Electronic data processing; System design",
}

@Proceedings{Burgess:2001:ISC,
  editor =       "N. Burgess and L. Ciminiera",
  booktitle =    "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  title =        "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 285",
  year =         "2001",
  ISBN =         "0-7695-1150-3; 0-7695-1152-X",
  ISBN-13 =      "978-0-7695-1150-4; 978-0-7695-1152-8",
  ISSN =         "1063-6889",
  LCCN =         "????",
  bibdate =      "Fri May 03 14:20:49 2002",
  note =         "IEEE order no. PR01150.",
  price =        "US\$145",
  acknowledgement = ack-nhfb,
  xxnote =       "Check dates: 11--13 or 11--17??",
  xxtitle =      "Computer Arithmetic: Papers presented at the {15th
                 IEEE Symposium on Computer Arithmetic (Arith-15 2001),
                 11--17 June, 2001, Vail, CO}",
}

@Book{Lide:2001:CEM,
  editor =       "David R. Lide",
  booktitle =    "A Century of Excellence in Measurements, Standards,
                 and Technology",
  title =        "A Century of Excellence in Measurements, Standards,
                 and Technology",
  volume =       "958",
  publisher =    pub-NIST,
  address =      pub-NIST:adr,
  pages =        "ix + 386",
  year =         "2001",
  bibdate =      "Fri Jul 09 06:29:11 2004",
  series =       "NIST special publication",
  acknowledgement = ack-nhfb,
}

@Book{Lide:2002:CEM,
  editor =       "David R. Lide",
  booktitle =    "A Century of Excellence in Measurements, Standards,
                 and Technology",
  title =        "A Century of Excellence in Measurements, Standards,
                 and Technology",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "ix + 386",
  year =         "2002",
  ISBN =         "0-8493-1247-7",
  ISBN-13 =      "978-0-8493-1247-2",
  LCCN =         "QC100.U6 .C46 2002",
  bibdate =      "Fri Jul 09 06:29:11 2004",
  note =         "Republication of \cite{Lide:2001:CEM}.",
  URL =          "http://www.loc.gov/catdir/toc/fy031/2002283707.html",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:2003:CRN,
  editor =       "Anonymous",
  booktitle =    "5th Conference on Real Numbers and Computers 2003 ---
                 RNC5, Lyon, France, September 2003",
  title =        "5th Conference on Real Numbers and Computers 2003 ---
                 {RNC5}, Lyon, France, September 2003",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 14:57:33 2005",
  acknowledgement = ack-nhfb,
}

@Book{Wahdan:2004:IHE,
  editor =       "Abdel-Moniem Wahdan",
  booktitle =    "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  title =        "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xlv + 954",
  year =         "2004",
  bibdate =      "Tue Jul 19 08:01:02 MDT 2005",
  bibsource =    "melvyl.cdlib.org:210/CDL90",
  note =         "IEEE catalog number 04EX893.",
  acknowledgement = ack-nhfb,
  subject =      "Electric engineering; Congresses; Electronics;
                 Congresses; Computer engineering; Congresses",
}

@Proceedings{IEEE:2005:PIS,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  title =        "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 21 19:02:16 2005",
  bibsource =    "http://arith17.polito.it/",
  acknowledgement = ack-nhfb,
  xxnote =       "Not yet published: check editor??",
}

@Proceedings{Anonymous:2006:PCR,
  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  title =        "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 27 10:26:43 2006",
  bibsource =    "http://rnc7.loria.fr/",
  acknowledgement = ack-nhfb,
}