  We present an efficient multi-accuracy algorithm for the computations of a
set of special functions of a complex argument, z=x+iy. These functions include
the complex probability function w(z), and closely related functions such as
the error function erf(z), complementary error function erfc(z), imaginary
error function erfi(z), scaled complementary error function, erfcx(z), the
plasma dispersion function Z(z), Dawson s function Daw(z), and Fresnel
integrals S(z) and C(z). Computational results from the present algorithm are
compared with results from competitive algorithms and widely used software
packages showing superior accuracy and efficiency of the present algorithm. In
particular, the present results highlight concerns about the accuracy of
evaluating such special functions using commercial packages like Mathematica
and free/open source packages like the MIT-C++ package.
