Rapid and accurate calculation of the Voigt function

Two general techniques significantly improve both the accuracy and speed of spectral line shapes that use only the complex Voigt function. Such line shape functions include the Voigt line profile, which is closely related to the real part of this function. The first technique is a new algorithm, which trades a small amount of RAM (at most 1.49 megabytes) for a considerable gain in speed and accuracy. The accuracy is one part in 106 of the function itself. In addition, the derivatives of the function with respect to x and y are returned with an accuracy of 0.5%. The algorithm is up to nine times faster than the Drayson or Humlíček algorithms and about two orders of magnitude more accurate. A second independent improvement is a set of simple criteria to decide when an evaluation is required and when a value of zero can be assumed. This section alone can reduce the computation time by three orders of magnitude or more and it can be applied to algorithms using any Voigt approximation.