Loop transformations: convexity, pruning and optimization

  • Authors:

  • Louis-Noël Pouchet;Uday Bondhugula;Cédric Bastoul;Albert Cohen;J. Ramanujam;P. Sadayappan;Nicolas Vasilache

  • Affiliations:

  • The Ohio State University, Columbus, OH, USA;IBM T.J. Watson Research Center, White Plains, OH, USA;University of Paris-sud 11, Saclay, OH, USA;INRIA, Saclay, OH, USA;Louisiana State University, Baton Rouge, OH, USA;The Ohio State University, Columbus, OH, USA;Reservoir Labs, Inc., New York, NY, USA

  • Venue:
  • Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 2011

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Abstract

High-level loop transformations are a key instrument in mapping computational kernels to effectively exploit the resources in modern processor architectures. Nevertheless, selecting required compositions of loop transformations to achieve this remains a significantly challenging task; current compilers may be off by orders of magnitude in performance compared to hand-optimized programs. To address this fundamental challenge, we first present a convex characterization of all distinct, semantics-preserving, multidimensional affine transformations. We then bring together algebraic, algorithmic, and performance analysis results to design a tractable optimization algorithm over this highly expressive space. Our framework has been implemented and validated experimentally on a representative set of benchmarks running on state-of-the-art multi-core platforms.