W. J. Cody
Abstract
This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applicaitons include testing of programs for certain Bessel functions, Dawson's integral, and error functions.
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Index Terms
- The use of Taylor series to test accuracy of function programs
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Reviews
Ian Gladwell
Local Taylor series expansions are recommended for determining the accuracy of special function routines. The authors emphasize using exact machine numbers as arguments in the Taylor series, special action to deal with large relative errors near zeros of the special function, and calibration using correctly rounded results of higher-precision calculations. The main example considered is the exponential integral, for which tests of several existing subroutines are described. The success of these tests depends on obtaining accurate values for the leading terms in the Taylor expansion. This approach is implemented in the package SPECFUN, which also tests the accuracy of Dawson's integral and of various Bessel functions.
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