FFTW Fast Fourier Transform Library

FFTW (Fastest Fourier Transform in the West) is a software library for computing discrete Fourier transforms (DFT) developed by Matteo Frigo and Steven G. Johnson at MIT. First released in 1997, FFTW is widely recognized as the fastest free FFT implementation, often matching or exceeding the performance of vendor-optimized libraries. Key features: computes 1D, 2D, and multi-dimensional DFT of arbitrary size including both complex-to-complex and real-to-complex transforms. Planahead architecture: FFTW first plans the optimal algorithm by measuring execution time of various strategies, then executes the transform using the fastest discovered method, adapting to the specific hardware and problem size. Support for arbitrary input sizes including prime sizes, powers of two, and composite sizes, using a combination of Cooley-Tukey, Rabiner-Winograd, Bluestein, and Rader algorithms. SIMD optimization with automatic detection and utilization of SSE, SSE2, SSE3, AVX, AVX2, AVX-512, Altivec, and NEON vector instructions for maximum throughput. Multi-threaded transforms using OpenMP or pthreads for parallel computation of large transforms. Transforms of real input data producing complex output (r2c) and vice versa (c2r), as well as discrete cosine transforms (DCT) and discrete sine transforms (DST) of types I-IV. Wisdom mechanism for saving and reusing optimal plans across program runs. Fortran, C++, and Python (via pyFFTW) interfaces. MPI support for distributed computation of very large transforms across clusters. Arbitrary-dimensional transforms with strided and non-contiguous memory layouts. Precision variants for single, double, and long double floating-point arithmetic. Open source under GPL and commercial license options.