On inherent in-place and in-order features of the prime factor algorithm

For the computation of the prime factor algorithm (PFA), an in-place and in-order approach is always desirable because it reduces the memory requirement for the storage of the temporary results, and the computation time which is required to unscramble the output sequence to a proper order. In fact, the processing time required for this unscrambling process can take up as much as 50% of the overall computation time. It is shown that the PFA has an intrinsic property that allows it to be easily realized in an in-place and in-order form. No extra operation is required as in the previous propositions. Nevertheless, the sequence length of the PFA computation must be carefully selected. The conditions under which a particular sequence length is possible for a natural in-place and in-order PFA computation are analyzed. The result is useful to both the hardware and software realization of the PFA