Array Permutation by Index-Digit Permutation

Authors:
Donald Fraser
Affiliations:
Commonwealth Scientific and Industrial Research Organization, Division of Computing Research, P.O. Box 1800, Canberra City, A.C.T. 2601, Australia and University of Sydney, Sydney, Australia
Venue:
Journal of the ACM (JACM)
Year:
1976

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Abstract

An array may be reordered according to a common permutation of the digits of each of its element indices. The digit-reversed reordering which results from common fast Fourier transform (FFT) algorithms is an example. By examination of this class of permutation in detail, very efficient algorithms for transforming very long arrays are developed.