Fourier transform and convolution subroutines for the IBM 3090 Vector facility
IBM Journal of Research and Development
Array Permutation by Index-Digit Permutation
Journal of the ACM (JACM)
Cache-efficient numerical algorithms using graphics hardware
Parallel Computing
Recursion-driven parallel code generation for multi-core platforms
Proceedings of the Conference on Design, Automation and Test in Europe
Using GPUs to compute large out-of-card FFTs
Proceedings of the international conference on Supercomputing
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Conventional algorithms for computing large one-dimensional fast Fourier transforms (FFTs), even those algorithms recently developed for vector and parallel computers, are largely unsuitable for systems with external or hierarchical memory. The principal reason for this is the fact that most FFT algorithms require at least m complete passes through the data set to compute a 2m-point FFT.This paper describes some advanced techniques for computing an ordered FFT on a computer with external or hierarchical memory. These algorithms (1) require as few as two passes through the external data set, (2) employ strictly unit stride, long vector transfers between main memory and external storage, (3) require only a modest amount of scratch space in main memory, and (4) are well suited for vector and parallel computation.Performance figures are included for implementations of some of these algorithms on Cray supercomputers. Of interest is the fact that a main memory version outperforms the current Cray library FFT routines on the Cray-2, the Cray X-MP, and the Cray Y-MP systems. Using all eight processors on the Cray Y-MP, this main memory routine runs at nearly two gigaflops.