Design of a modern fast Fourier transform and cache effective bit-reversal algorithm

ABSTRACT This article deals with efficient vectorization of the fast Fourier transform algorithm while focusing on Cooley–Tukey versions with power-of-two radixes. Aside from examples of optimizations for 256 and 512-bit vectors, this work also discusses relations between individual radix-based versions, vectorization and OpenMP threading. Ideas are progressing into a timeless design of the FFT algorithm, which can work with any vector size and radix version through conversion into radix-2 output permutation. Furthermore, the implementation of the Cache Optimized Bit-Reversal algorithm, which doubles the performance of its predecessor, is introduced.