Nesting strategies for prime factor FFT algorithms

Abstract

Several nesting techniques for the prime factor FFT algorithm are examined. These include the full nesting strategy of Winograd's algorithm, which gives a very low multiplication count; a split nesting technique, which requires the same number of multiplications as Winograd's FFT, but fewer additions; and a partial nesting technique, which further reduces the addition count at the cost of some extra multiplications and requires the lowest total number of floating-point operations. Applications to large multidimensional transforms, as well as to 1-dimensional transforms, are discussed. On large scientific computers where the multiplications can be overlapped with the additions, the prime factor algorithm without nesting remains the fastest and is the easiest to implement.