Bounds on the minimum number of data transfers in WFTA and FFT programs

Bounds on the minimum number of data transfers (i.e., loads, stores, and copies) required by WFTA and FFT programs are presented. The analysis is applicable to those general-purpose computers with M general processor registers (e.g., the IBM 370, PDP-11, etc.) where
4 \leq M \ll
transform length. It is shown that the 1008- point WFTA requires about 21 percent more data transfers than the 1024-point radix-4 FFT; on the other hand, the 120-point WFTA has about the same number of data transfers as the mixed radix (4 × 4 × 4 × 2) version of the 128-point FFT and 22 percent fewer than the radix-2 version. Finally, comparisons of the "total" program execution times (multiplications, additions, and data transfers, but not indexing or permutations) are presented.