Tools for Evaluating Mathematical and Statistical Software
Special Functions Focus Area
This area of numerical computation has the property that input to its software
is of small dimension.
Accordingly, high accuracy reference software that produces test data with
guaranteed error bounds is feasible.
Recent research is providing algorithms for new functions which are being used
to extend library functionality.
Library developers need illustrations of anomalous behavior to improve
robustness of research algorithms, and library users need a simple mechanism
that they can use to tailor tests to their own specific applications.
To address these issues we are experimenting with the development of a
Webbased interactive software testing service for special functions.
This project is part of a larger effort to develop
tools for evaluating mathematical and
statistical software (this link available only within National Institute
of Standards and Technology).
 Principal Results and Services

Numerical Evaluation of Special Functions. This is the current Web version of Published Paper 1 below, updated to December 2000. Its purpose is to assist in locating useful approximations and software for the numerical generation of higher transcendental functions.

The Mathematical Function Evaluator (available only within the National Institute of Standards and Technology). This Web page is under construction. It will illustrate some of the concepts described in Published Paper 3 below by supplying numerical values of mathematical functions on demand.
 Published Papers
 D. W. Lozier and F. W. J. Olver, Numerical Evaluation of Special Functions, in Mathematics of Computation 19431993: A HalfCentury of Computational Mathematics, (W. Gautschi, ed.), Proceedings of Symposia in Applied Mathematics 48, American Mathematical Society, Providence, Rhode Island, 1994, pp. 79125. For a reprint send mail to dlozier@nist.gov.
 D. W. Lozier, Software Needs in Special Functions, Journal of Computational and Applied Mathematics 66 (1996) 345358. For a reprint send mail to dlozier@nist.gov. Preprint: NISTIR 5490, August 1994. [Postscript, 0.33mb, 15 pages].
 D. W. Lozier, A Proposed Software Test Service for Special Functions, in Quality of Numerical Software: Assessment and Enhancement, (R. Boisvert, ed.), Chapman and Hall, London, 1997, pp. 167178. Preprint: NISTIR 5916, October 1996 [Postscript, 0.430mb, 11 pages].
 Informal Papers
 D. W. Lozier, Software Testing Service for Special Functions: A Proposal and Request for Comments, Informal White Paper 1, October 19, 1995. [Postscript, 0.103mb, 9 pages]
 D. W. Lozier, A Methodology for Testing Mathematical Special Functions, Informal White Paper 2, May 9, 1996. [Postscript, 0.166mb, 3 pages]
 Technical Presentations
 F. W. J. Olver, Numerical Evaluation of Special Functions, Mathematics of Computation 50th Anniversary Symposium, Vancouver, BC, August 10, 1993.
 D. W. Lozier, Software Needs in Special Functions, International Congress on Computational and Applied Mathematics, Leuven, Belgium, July 26, 1994.
 D. W. Lozier, Software Testing Service for Special Functions: A Proposal and Request for Comments, SIAM Annual Meeting, Minisymposium on Computational Aspects of Special Functions and Orthogonal Polynomials, October 25, 1995.
 D. W. Lozier, A Proposed Software Testing Service for Special Functions, IFIP Working Group 2.5 Conference on the Quality of Numerical Software, Oxford, England, July 15, 1996.
 Staff
Dan Lozier (Task Leader),
Marje McClain,
Bruce Miller,
Bonita Saunders,
Frank Olver
 External Collaborators
SIAM Activity Group on Orthogonal Polynomials and Special Functions
Last change in this page: January 23, 2004. This project has been dormant in recent years. Resumption is anticipated but not scheduled at this time. Comments about the proposed Software Testing Service for Special Functions are welcome. Please send them to daniel.lozier@nist.gov