IMPLEMENTING THE COMPLEX ARCSINE AND ARCCOSINE FUNCTIONS USING EXCEPTION HANDLING

We develop efficient algorithms for reliable and accurate evaluations of the complex arcsine and arccosine functions. A tight error bound is derived for each algorithm; the results are valid for all machine-rep resentable points in the complex plane. The algorithms are presented i n a pseudocode that has a convenient exception-handling facility. Corr esponding Fortran 77 programs for an IEEE environment have also been d eveloped to illustrate the practicality of the algorithms, and these p rograms have been tested very carefully to help confirm the correctnes s of the algorithms and their error bounds. The results of these tests are included in the article, but the Fortran 77 programs are not (the se programs are available from Fairgrieve). Tests of other widely avai lable programs fail at many points in the complex plane, and otherwise are slower and produce much less accurate results.