Code Generators for Automatic Tuningof Numerical Kernels : Experiences with FFTWPosition

Achieving peak performance in important numerical kernels such as dense matrix multiply or sparse-matrix vector multiplication usually requires extensive, machine-dependent tuning by hand. In response, a number automatic tuning systems have been developed which typically operate by (1) generating multiple implementations of a kernel, and (2) empirically selecting an optimal implementation. One such system is FFTW (Fastest Fourier Transform in the West) for the discrete Fourier transform. In this paper, we review FFTW's inner workings with an emphasis on its code generator, and report on our empirical evaluation of the system on two diierent hardware and compiler platforms. We then describe a number of our own extensions to the FFTW code generator that compute eecient discrete cosine transforms and show promising speed-ups over a vendor-tuned library. We also comment on current opportunities to develop tuning systems in the spirit of FFTW for other widely-used kernels.