Parallel Fast Fourier Transforms for Non Power of Two Data

This report deals with parallel algorithms for computing discrete Fourier transforms of real sequences of length N not equal to a power of two. The method described is an extension of existing power of two transforms to sequences with N a product of small primes. In particular, this implementation requires N = 2 p 3 q 5 r. The communication required is the same as for a transform of length N = 2 p. The algorithm presented is intended for use in the solution of partial diierential equations, or in any situation in which a large number of forward and backward transforms must be performed and in which the Fourier Coeecients need not be ordered. This implementation is a one dimensional FFT but the techniques are applicable to multidimensional transforms as well. The algorithm has been implemented on a 128 node Intel Ipsc/860.