A FORTRAN Package for Efficient Multi-Accuracy Computations of the Faddeyeva Function and Related Functions of Complex Arguments
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We present a Fortran package for efficient multiaccuracy computations of the Faddeyeva function w(z), and related functions of the complex argument z=x+iy 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), Dawsons function Daw(z), and Fresnel integrals S(z) and C(z). Depending on the case studied, targeted accuracy, and the precision used, efficiency improvements up to more than a factor of five, compared to the Fortran version of Algorithm 916 are obtained. Compared to the free/open source package developed in C++ at the Massachusetts Institute of Technology (MIT) and depending on the case studied, the present algorithm can be up to a factor of two faster for the 13 significant-digits accuracy and up to a factor of five faster for the four significant figures accuracy. The accuracy of computing other related special functions is assessed through comparison with results obtained from the Mathematica software package and the Matlab Special Functions of Applied Mathematics (SFAM) in the symbolic toolbox.
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