A fast recursive bit-reversal algorithm

A novel fast recursive O(N) algorithm for bit-reversal permutation of a data array is presented. Exploiting regularity in the bit-reversal and eliminating redundant computations, this new method provides a considerable improvement in computational time. This computational efficiency results from the fact that every permutation index is basically computed by a single logical or arithmetic operation between a previous index and a proper offset. Experiments show that it is faster than any other bit-reversal algorithms that seem to be available. The performance of this method is compared to that of other bit-reversal method. Extension of the method to general digit reversal is described. Bit-reversal permutation of two-dimensional arrays is also discussed