Automated Formula Generation and Performance Learning for the FFT

Abstract : A single signal processing algorithm can be represented by many different but mathematically equivalent formulas. When these formulas are implemented in actual code, they often have very different running times. Thus, an important problem is finding a formula that implements the signal processing algorithm as efficiently as possible. In this paper we present three major results toward this goal: (1) Different but mathematically equivalent formulas can be generated automatically in a principled way, (2) Simple features describing formulas can be used to distinguish formulas with significantly different running times, and (3) A function approximator can learn to accurately predict the running time of a formula given a limited set of training data.