Review of CPU and GPU Faddeeva Implementations

The Faddeeva error function is frequently used when computing electric fields generated by two-dimensional Gaussian charge distributions. Numeric evaluation of the Faddeeva function is particularly challenging since there is no single expansion that converges rapidly over the whole complex domain. Various algorithms exist, even in the recent literature there have been new proposals. The many different implementations in computer codes offer different trade-offs between speed and accuracy. We present an extensive benchmark of selected algorithms and implementations for accuracy, speed and memory footprint, both for CPU and GPU architectures.