Minimization of rounding errors in WFTA programs
Ryszard Stasiński, Ewa Łukasik · 2003
Two ideas linked with high-precision computation of WFTAs (Winograd-Fourier transform algorithm) using fixed-point arithmetic are analyzed. Use of the best, optimized small-N DFT (discrete Fourier transform) modules is considered. The sizes of these modules appear to be equal to Fermat prime numbers, and powers of two. The computation of WFTAs with full accuracy of intermediate result is studied. The properties of the received algorithms seem to be comparable to those of FFTs (fast Fourier transforms) in the former case, while similar to those of DFT computed directly, or using an RNS (residue number system) in the latter case.>