Statistical Modeling of Feedback Data in an Automatic Tuning System

Achieving peak performance from library subroutines usually requires extensive, machine-dependent tuning by hand. Automatic tuning systems have been developed in response which typically operate, at compiletime, by (1) generating a large number of possible implementations of a subroutine, and (2) selecting a fast implementation by an exhaustive, empirical search. In this paper, we show how statistical modeling of the performance feedback data collected during the search phase can be used in two novel and important ways. First, we develop a heuristic for stopping an exhaustive compile-time search early if a near-optimal implementation is found. Second, we show how to construct run-time decision rules, based on run-time inputs, for selecting from among a subset of the best implementations. We apply our methods to actual performance data collected by the PHiPAC tuning system for matrix multiply on a variety of hardware and compiler platforms.