Optimum Complexity FFT Algorithms for RISC Processors

Modern RISC processors provide a special instruction { the fused multiplyadd (FMA) instruction a b c { to perform both a multiplication and an addition operation at the same time. In this paper newly developed radix-2, radix-4, and split-radix FFT algorithms that optimally take advantage of this powerful instruction are presented. All oating-point operations of these algorithms are executed as FMA instructions. If a processor is provided with FMA instructions, the radix-2 FFT algorithm introduced has the lowest complexity of all Cooley-Tukey radix-2 algorithms. The new radix-4 algorithm requires 15% fewer oating-point operations and 10% fewer memory accesses than conventional Cooley-Tukey radix-4 algorithms. In general, the advantages of the FFT algorithms presented in this paper are their low complexity, their high e ciency, and their striking simplicity.