SIMD Vectorization of Non-Two-Power Sized FFTs

Abstract

SIMD (single instruction multiple data) vector instructions, such as Intel's SSE family, are available on most architectures, but are difficult to exploit for speed-up. In many cases, such as the fast Fourier transform (FFT), signal processing algorithms have to undergo major transformations to map efficiently. Using the Kronecker product formalism, we rigorously derive a novel variant of the general-radix Cooley-Tukey FFT that is structured to map efficiently for any vector length v and radix. Then, we include the new FFT into the program generator spiral to generate actual C implementations. Benchmarks on Intel's SSE show that the new algorithms perform better on practically all sizes than the best available libraries Intel's MKL and FFTW.