Remark on "Algorithm 916: Computing the Faddeyeva and Voigt functions": Efficiency Improvements and Fortran Translation

TL;DR

This paper presents efficiency improvements and a Fortran translation of Algorithm 916 for computing Faddeyeva and Voigt functions, enabling faster evaluations with adjustable accuracy for large-scale practical applications.

Contribution

It introduces significant speed enhancements, a flexible accuracy trade-off scheme, and a Fortran implementation of Algorithm 916 for practical, large-scale computations.

Findings

Execution time improved by more than a factor of two at highest accuracy.

A user-defined accuracy trade-off maintains reliability and efficiency.

Fortran version enables large-scale, low-accuracy computations in real-world problems.

Abstract

This remark describes efficiency improvements to Algorithm 916 [Zaghloul and Ali 2011]. It is shown that the execution time required by the algorithm, when run at its highest accuracy, may be improved by more than a factor of two. A better accuracy vs efficiency trade off scheme is also implemented; this requires the user to supply the number of significant figures desired in the computed values as an extra input argument to the function. Using this trade-off, it is shown that the efficiency of the algorithm may be further improved significantly while maintaining reasonably accurate and safe results that are free of the pitfalls and complete loss of accuracy seen in other competitive techniques. The current version of the code is provided in Matlab and Scilab in addition to a Fortran translation prepared to meet the needs of real-world problems where very large numbers of function evaluations would require the use of a compiled language. To fulfill this last requirement, a recently proposed reformed version of Humlicek's w4 routine, shown to maintain the claimed accuracy of the algorithm over a wide and fine grid is implemented in the present Fortran translation for the case of 4 significant figures. This latter modification assures the reliability of the code to be employed in the solution of practical problems requiring numerous evaluation of the function for applications tolerating low accuracy computations (<10-4).