The 2DECOMP&FFT library is a software framework in Fortran to build large-scale parallel applications. It is designed for applications using three-dimensional structured mesh and spatially implicit numerical algorithms. At the foundation, it implements a general-purpose 2D pencil decomposition for data distribution on distributed-memory platforms. On top, it provides a highly scalable and efficient interface to perform three-dimensional distributed FFTs.
PFFFT is a very small 1D Fast Fourier Transform library based on the venerable FFTPACK v4. It handles single precision real and complex transforms. Computations take advantage of SSE1 instructions on x86, Altivec on PowerPC, and NEON on ARM, allowing it to achieve a performance level that is not too far from the very best FFTs (FFTW, Intel MKL, Apple vDSP).