The Fastest Fourier Transform in the West (MIT-LCS-TR-728)

This paper describes FFTW, a portable C package for computing the oneand multidimensional complex discrete Fourier transform (DFT). FFTW is typically faster than all other publicly available DFT software, including the well-known FFTPACK and the code from Numerical Recipes. More interestingly, FFTW is competitive with or better than proprietary, highly-tuned codes such as Sun’s Performance Library and IBM’s ESSL library. FFTW implements the Cooley-Tukey fast Fourier transform, and is freely available on the Web at http://theory.lcs.mit.edu/ ̃fftw. Three main ideas are the keys to FFTW’s performance. First, the computation of the transform is performed by an executor consisting of highly-optimized, composable blocks of C code called codelets. Second, at runtime, a planner finds an efficient way (called a ‘plan’) to compose the codelets. Through the planner, FFTW adapts itself to the architecture of the machine it is running on. Third, the codelets are automatically generated by a codelet generator written in the Caml Light dialect of ML. The codelet generator produces long, optimized, unreadable code, which is nevertheless easy to modify via simple changes to the generator.