Performance Models and Search Methods for Optimal FFT Implementations

This thesis considers systematic methodologies for finding optimized implementations for the fast Fourier transform (FFT). By employing rewrite rules (e.g., the CooleyTukey formula), we obtain a divide and conquer procedure (decomposition) that breaks down the initial transform into combinations of different smaller size sub-transforms, which are graphically represented as breakdown trees. Recursive application of the rewrite rules generates a set of algorithms and alternative codes for the FFT computation. The set of "all" possible implementations (within the given set of the rules) results in pairing the possible breakdown trees with the code implementation alternatives. To evaluate the quality of these implementations, we develop analytical and experimental performance models. Based on these models, we derive methods dynamic programming, soft decision dynamic programming and exhaustive search to find the implementation with minimal runtime. Our test results demonstrate that good algorithms and codes, accurate performance evaluation models, and effective search methods, combined together provide a system framework (library) to derive automatically fast FFT implementations.