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Accurate yet efficient computation of the Voigt and complex error function isa challenge since decades in astrophysics and other areas of physics. Rationalapproximations have attracted considerable attention and are used in manycodes, often in combination with other techniques. The 12-term code "cpf12" ofHuml\'i\v{c}ek (1979) achieves an accuracy of five to six significant digitsthroughout the entire complex plane. Here we generalize this algorithm to alarger (even) number of terms. The $n=16$ approximation has a relative accuracybetter than $10^{-5}$ for almost the entire complex plane except for very smallimaginary values of the argument even without the correction term required forthe cpf12 algorithm. With 20 terms the accuracy is better than $10^{-6}$. Inaddition to the accuracy assessment we discuss methods for optimization andpropose a combination of the 16-term approximation with the asymptoticapproximation of Huml\'i\v{c}ek (1982) for high efficiency.

The Voigt and complex error function: Huml\'i\v{c}ek's rational approximation generalized