Remark on Algorithm 680: evaluation of the complex error function: Cause and Remedy for the Loss of Accuracy Near the Real Axis

In this remark we identify the cause of the loss of accuracy in the computation of the Faddeyeva function, w(z), near the real axis when using Algorithm 680. We provide a simple correction to this problem which allows us to restore this code as one of the important reference routines for accuracy comparisons

Efficient Multi-Accuracy Computations of Complex Functions with Complex Arguments

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