The Design and Implementation of FFTW3 （FFTW3的设计和实现）.pdf

1 The Design and Implementation of FFTW3 Matteo Frigo and Steven G. Johnson (Invited Paper) Abstract— FFTW is an implementation of the discrete Fourier of a multi-dimensional array. (Most implementations sup- transform (DFT) that adapts to the hardware in order to port only a single DFT of contiguous data.) maximize performance. This paper shows that such an approach • FFTW supports DFTs of real data, as well as of real can yield an implementation that is competitive with hand- optimized libraries, and describes the software structure that symmetric/antisymmetric data (also called discrete co- makes our current FFTW3 version flexible and adaptive. We sine/sine transforms). further discuss a new algorithm for real-data DFTs of prime size, The interaction of the user with FFTW occurs in two a new way of implementing DFTs by means of machine-specific stages: planning, in which FFTW adapts to the hardware, “SIMD” instructions, and how a special-purpose compiler can and execution, in which FFTW performs useful work for the derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm. user. To compute a DFT, the user first invokes the FFTW planner , specifying the problem to be solved. The problem is Index Terms— FF