A new superfast bit reversal algorithm

In this paper we present a new bit reversal algorithm which outperforms the existing ones. The bit reversal technique is involved in the fast Fourier transform technique (FFT), which is widely used in computer-based numerical techniques for solving numerous problems. The new approach for computing the bit reversal is based upon a pseudo-semi-group homomorphism property. The surprise is that this property is almost trivial to prove but at the same time it also leads to a very efficient algorithm which we believe to be the best with only (N) operations and optimal constant, i.e. unity. Copyright © 2002 John Wiley & Sons, Ltd.