A second improved digit-reversal permutation algorithm for fast transforms

Based on three previously published theorems and an algorithm for the digit-reversal permutation required by fast transform algorithms, a fourth theorem is given, indicating an alternate order of generating the index pairs for swapping, and a second permutation algorithm results. This algorithm uses the same principles as the first and differs principally in that in its innermost loop, one of the pair of indexes is usually generated by an integer increment (i:=i+n). This will result in slightly faster execution on most computers.< >