Accurate yet efficient computation of the Voigt and complex error function is
a challenge since decades in astrophysics and other areas of physics. Rational
approximations have attracted considerable attention and are used in many
codes, often in combination with other techniques. The 12-term code "cpf12" of
Huml\'i\v{c}ek (1979) achieves an accuracy of five to six significant digits
throughout the entire complex plane. Here we generalize this algorithm to a
larger (even) number of terms. The n=16 approximation has a relative accuracy
better than 10−5 for almost the entire complex plane except for very small
imaginary values of the argument even without the correction term required for
the cpf12 algorithm. With 20 terms the accuracy is better than 10−6. In
addition to the accuracy assessment we discuss methods for optimization and
propose a combination of the 16-term approximation with the asymptotic
approximation of Huml\'i\v{c}ek (1982) for high efficiency.Comment: 9 pages, 5 figure
