Performance evaluation of programs related to the real gamma function

ABSTRACT

Methods are presented for evaluating the performance of programs for the functions &Ggr;(x), ln &Ggr;(x), and &psgr;(x). Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.

REFERENCES

• 1: Milton Abramowitz, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,, Dover Publications, Incorporated, 1974
• 2: COD~, W.J. SPECFUN--A portable special function package. In New Computing Environ~ ments: Microcomputers ~n Large-Scale Scient~fw Computing, A. Wouk (Ed.), SIAM, Phfiadelphia, Pa., 1987, pp. 1-12.
• 3: W. J. Cody, Algorithm 665: Machar: a subroutine to dynamically determined machine parameters, ACM Transactions on Mathematical Software (TOMS), v.14 n.4, p.303-311, Dec. 1988 [doi>10.1145/50063.51907]
• 4: W. J. Cody , L. Stoltz, Performance evaluation of programs for certain Bessel functions, ACM Transactions on Mathematical Software (TOMS), v.15 n.1, p.41-48, March 1989 [doi>10.1145/62038.62039]
• 5: William James Cody, Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics), Prentice-Hall, Inc., Upper Saddle River, NJ, 1980
• 6: NAg FORTRAN Library Manual, Mark 11, Voh 6. Numerical Algorithms Group, Ltd., Oxford, England, 1984.
• 7: SFUN/LIBRARY User's Manual. IMSL, Inc., Houston, Tex , 1987.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms

Additional Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing

General Terms:
Measurement, Performance, Reliability

Keywords:
&psgr; function, accuracy, digamma function, gamma function, performance evaluation, robustness