DFT Performance Prediction in FFTW

Fastest Fourier Transform in the West (FFTW) is an adaptive FFT library that generates highly efficient Discrete Fourier Transform (DFT) implementations. It is one of the fastest FFT libraries available and it outperforms many adaptive or hand-tuned DFT libraries. Its success largely relies on the huge search space spanned by several FFT algorithms and a set of compiler generated C code (called codelets) for small size DFTs. FFTW empirically finds the best algorithm by measuring the performance of different algorithm combinations. Although the empirical search works very well for FFTW, the search process does not explain why the best plan found performs best, and the search overhead grows polynomially as the DFT size increases. The opposite of empirical search is model-driven optimization. However, it is widely believed that model-driven optimization is inferior to empirical search and is particularly powerless to solve problems as complex as the optimization of DFT. In this paper, we propose a model-driven DFT performance predictor that can replace the empirical search engine in FFTW. Our technique adapts to different architectures and automatically predicts the performance of DFT algorithms and codelets (including SIMD codelets). Our experiments show that this technique renders DFT implementations that achieve more than 95% of the performance with the original FFTW and uses less than 5% of the search overhead on four test platforms. More importantly, our models give insight on why different combinations of DFT algorithms perform differently on a processor given its architectural features.