Many versions of the fast Fourier transform require a reordering of either the input or the output data that corresponds to reversing the order of the bits in the array index. There has been a surprisingly large number of papers on this subject in the recent literature. This paper collects 30 methods for bit reversing an array. Each method was recoded into a uniform style in Fortran and its performance measured on several different machines, each with a different memory system. This paper includes a description of how the memories of the machines operate to motivate two new algorithms that perform substantially better than the others.
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Alan H. Karp (1996) studied this question.
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