references:
THE STATE OF THE ART IN NUMERICAL ANALYSIS
edited by ISERLES and POWELL:
Chapter 7 contains an artical on branch cuts and numerical algorithms for complex multivalued elementary
functions: sqrt, ln, arcsin, arcos, arctan ,arcsinh, arccosh, arctanh, z exp w
by W. KAHAN of U.C. Berkeley (415-642-6000)
HANDBOOK OF MATHEMATICAL FUNCTIONS WITH FORMULAS, GRAPHS, AND MATHEMATICAL TABLES
edited by ABRAMOWITZ and STEGUN
APPROXIMATIONS FOR DIGITAL COMPUTERS
by CECIL HASTINGS:
contains mostly polynomial aproximations of functions in limited real domains
The speed and accuracy of multivalued complex functions depends on the speed and accuracy of log,
sqrt, and arctan of real numbers.
Arcsin is currently implemented using a polynomial approximation for 0<|x|<1 (found in APPROXIMATIONS FOR DIGITAL COMPUTERS)
and the logarithm definition for the rest of the complex plane. The algorithms in Kahan's article on branch cuts are
different from those implemented in numer.lisp