Fast bit-reversal algorithms

A novel fast algorithm for computing a sequence of bit-reversed integers is presented. In finding a mapping function from a sequence of integers to a sequence of their bit-reverse, a recursive approach is taken to overcome the logarithmic factor burdening the standard scheme. The associated constant for the timing factor is shown to be very low even at the register level. The method generalizes to radix-r and mixed-radix cases and provides an efficient vectorizable scheme with the same low constant