A comparative study of time efficient FFT and WFTA programs for general purpose computers

Time efficient autogen software implementations of the fast Fourier transform (FFT) and the Winograd Fourier transform algorithm (WFTA) are examined and compared in detail. Both high-level language (optimized Fortran IV) and assembler implementations are considered on two general purpose computers, the DEC PDP-11/55 and the IBM- 370/168, both having floating-point multiply/add time ratios of about 1.17. It is shown that although the WFTA reduces the number of multiplications relative to the FFT, a substantial increase in data transfer, both memory/register and register/register, together with a smaller increase in additions and data reordering overhead, combine to give WFTA execution times about 20-40 percent longer than those for the FFT. These results are explained by examining the internal computational kernel structure for both algorithms and relating the arithmetic operation sequencing to the computer instructions necessary to implement the software. It is concluded that for floating-point software implementations on the class of general purpose computers considered, the WFTA offers neither time nor space advantages over the radix-4 FFT.