Fast Fourier Transform using compiler auto-vectorization

Abstract

The purpose of this thesis is to develop a fast Fourier transformation algorithm written in C with the use of GCC (GNU Compiler Collection) auto-vectorization in the multiplicative group of integers modulo n, where n is a word sized odd integer. The specific Fourier transform algorithm employed is the cache-friendly version of the Truncated Fourier Transform. The algorithm was implemented by modifying an existing library for modular arithmetic written in C called zn poly. The majority of the thesis work consisted of changing the code in a way to make integration into FLINT possible. FLINT is a versatile library, written in C, aimed at fast arithmetic of different kinds. The results show that auto-vectorization is possible with a potential speedup factor of 3. The performance increase is however entirely dependent on the task at hand and the nature of the computation being made.