/tmp/sp

[David G. Hough at validgh]

ACM Trans on Math Software, Volume 20 #2, June 1994

Implementing Complex Elementary Functions Using Exception Handling

T. E. Hull, T. F. Fairgrieve, P. T. P. Tang

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,
(tffacs.toronto.edu).