Automated Formula Generation and Performance Learning for the FFT

A single signal processing algorithm can be represented by many di erent but mathematically equivalent formulas. When these formulas are implemented in actual code, they often have very di erent running times. Thus, an important problem is nding a formula that implements the signal processing algorithm as e ciently as possible. In this paper we present three major results toward this goal: (1) Di erent but mathematically equivalent formulas can be generated automatically in a principled way, (2) Simple features describing formulas can be used to distinguish formulas with signi cantly di erent 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. This research was sponsored by the DARPA Grant No. DABT63-98-1-0004. The rst author, Bryan Singer, is partly supported by a National Science Foundation Graduate Fellowship. The content of the information in this publication does not necessarily re ect the position or the policy of the Defense Advanced Research Projects Agency (DARPA), the National Science Foundation (NSF), or the US Government, and no o cial endorsement should be inferred.