Ordered fast fourier transforms on a massively parallel hypercube multiprocessor

Charles Tong, Paul N. Swarztrauber
1991 Journal of Parallel and Distributed Computing  
We examine design alternatives for ordered FFT algorithms on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end we combine the order and computational phases of the FFT and also use sequence to processor maps that reduce communication. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as
more » ... hat of the input sequence. Two such orderings are examined, namely, "standard-order" and "A-order" which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 r elements and the hypercube has P = 2 d processors then a standard-order FFT can be implemented with d +r ⁄2+1 parallel transmissions. An Aorder sequence can be transformed with 2d −r ⁄2 parallel transmissions which is r −d +1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine. interests are parallel numerical solution of partial differential equations, parallel algorithms for numerical linear algebra, parallel computer architectures, and systolic arrays for numerical solutions of sparse linear systems. Paul N. Swarztrauber is a Senior Scientist at the National Center for Atmospheric Research and a Adjoint Professor in the Computer Science Department at the University of Colorado. His research interests are in computational mathematics including the numerical solution of partial differential equations, parallel algorithms for numerical linear algebra, harmonic analysis, parallel and vector algorithms for the fast Fourier transform and numerical software.
doi:10.1016/0743-7315(91)90028-8 fatcat:vf3icvow4vgalkfha3co35wb3e