A case study in mechanically deriving dense linear algebra code

  • Authors:

  • Bryan Marker;Don Batory;Robert Van De Geijn

  • Affiliations:

  • Department of Computer Science, The University of Texas at Austin, USA;Department of Computer Science, The University of Texas at Austin, USA;Department of Computer Science, The University of Texas at Austin, USA

  • Venue:
  • International Journal of High Performance Computing Applications
  • Year:
  • 2013

  • Interfaces are key

    SE-HPCCSE '13 Proceedings of the 1st International Workshop on Software Engineering for High Performance Computing in Computational Science and Engineering

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Abstract

Design by Transformation (DxT) is a top-down approach to mechanically derive high-performance algorithms for dense linear algebra. We use DxT to derive the implementation of a representative matrix operation, two- sided Trmm. We start with a knowledge base of transformations that were encoded for a simpler set of operations, the level-3 BLAS, and add only a few transformations to accommodate the more complex two- sided Trmm. These additions explode the search space of our prototype system, DxTer, requiring the novel techniques defined in this paper to eliminate large segments of the search space that contain suboptimal algorithms. Performance results for the mechanically optimized implementations on 8192 cores of a BlueGene/P architecture are given.