Autotuning divide‐and‐conquer stencil computations

Abstract

Summary This paper explores autotuning strategies for serial divide‐and‐conquer stencil computations, comparing the efficacy of traditional “heuristic” autotuning with that of “pruned‐exhaustive” autotuning. We present a pruned‐exhaustive autotuner called Ztune that searches for optimal divide‐and‐conquer trees for stencil computations. Ztune uses three pruning properties—space‐time equivalence, divide subsumption, and favored dimension—that greatly reduce the size of the search domain without significantly sacrificing the quality of the autotuned code. We compared the performance of Ztune with that of a state‐of‐the‐art heuristic autotuner called OpenTuner in tuning the divide‐and‐conquer algorithm used in Pochoir stencil compiler. Over a nightly run on ten application benchmarks across two machines with different hardware configurations, the Ztuned code ran 5% –12% faster on average, and the OpenTuner tuned code ran from 9% slower to 2% faster on average, than Pochoir's default code. In the best case, the Ztuned code ran 40% faster, and the OpenTuner tuned code ran 33% faster than Pochoir's code. Whereas the autotuning time of Ztune for each benchmark could be measured in minutes, to achieve comparable results, the autotuning time of OpenTuner was typically measured in hours or days. Surprisingly, for some benchmarks, Ztune actually autotuned faster than the time it takes to perform the stencil computation once.

Fast Option Pricing using Nonlinear Stencils

“…The first category is standard algorithms that perform stencil computations by repeatedly applying the stencil operator iteratively on the evolving data. The class includes looping algorithms, tiled looping algorithms [13,19,129,127,128,130,18,6,49,133,73,72], and recursive divide-and-conquer algorithms [40,41,115,84,102,61]. All these algorithms work for both linear and nonlinear stencils in arbitrary dimensions under periodic and boundary conditions, but differ in the way to apply the stencil.…”

Special issue: Advanced stencil‐code engineering

“…There is one, sixth, paper that describes work that was presented at the seminar but not the result of a cooperation launched there. “Autotuning divide‐and‐conquer stencil computations,” authored by Ekanathan Palamadai Natarajan, Maryam Mehri Dehnavi and Charles E. Leiserson, compares traditional, heuristic autotuning with an approach that the authors call pruned‐exhaustive autotuning and that leverages knowledge of the particular recursion of the stencil computation. The result is a speedup of sequential stencil computations of up to 40%.…”