Architecture independent short vector FFTs

This paper introduces a SIMD vectorization for FFTW—the “fastest Fourier transform in the west” by Matteo Frigo and Steven Johnson. The new method leads to an architecture independent short vector SIMD FFT vectorization that utilizes the architecture adaptivity of FFTW. It is based on special FFT kernels (up to size 64 and more) that are utilized by FFTW to compute the whole transform. This vectorization supports all features of complex transforms in FFTW (arbitrary size, dimension and stride of the data vector; in-place and out-of-place transforms) and is fully transparent to the user. It is suitable for arbitrary vector sizes of the underlying hardware.