Efficient FFT on Torus Multicomputers: A Performance Study

In this paper, the problem of computing a one-dimensional FFT on a c-dimensional torus multicomputer is focused. Different approaches are proposed which differ in the way they use the interconnection network of the torus. One of the approaches is based on the multidimensional index mapping technique for FFT computation. A second approach is based on embedding on the torus a hypercube algorithm for computing the radix-2 Cooley-Tukey FFT. The third approach reduces the communication cost of the hypercube algorithm through the communication pipelining technique. Analytical models are presented to compare the different approaches. Finally, some performance estimates are given to illustrate the comparison.