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Detection of linear algebra operations in polyhedral programs

Guillaume Iooss 1, 2
2 CASH - CASH - Compilation and Analysis, Software and Hardware
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Writing a code which uses an architecture at its full capability has become an increasingly difficult problem over the last years. For some key operations, a dedicated accelerator or a finely tuned implementation exists and delivers the best performance. Thus, when compiling a code, identifying these operations and issuing calls to their high-performance implementation is attractive. In this dissertation, we focus on the problem of detection of these operations. We propose a framework which detects linear algebra subcomputations within a polyhedral program. The main idea of this framework is to partition the computation in order to isolate different subcomputations in a regular manner, then we consider each portion of the computation and try to recognize it as a combination of linear algebra operations.We perform the partitioning of the computation by using a program transformation called monoparametric tiling. This transformation partitions the computation into blocks, whose shape is some homothetic scaling of a fixed-size partitioning. We show that the tiled program remains polyhedral while allowing a limited amount of parametrization: a single size parameter. This is an improvement compared to the previous work on tiling, that forced us to choose between these two properties.Then, in order to recognize computations, we introduce a template recognition algorithm. This template recognition algorithm is built on a state-of-the-art program equivalence algorithm. We also propose several extensions in order to manage some semantic properties.Finally, we combine these two previous contributions into a framework which detects linear algebra subcomputations. A part of this framework is a library of template, based on the BLAS specification. We demonstrate our framework on several applications.
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https://tel.archives-ouvertes.fr/tel-01370553
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Submitted on : Thursday, September 22, 2016 - 6:47:09 PM
Last modification on : Wednesday, November 20, 2019 - 3:20:27 AM

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Guillaume Iooss. Detection of linear algebra operations in polyhedral programs. Other [cs.OH]. Université de Lyon; Colorado state university, 2016. English. ⟨NNT : 2016LYSEN019⟩. ⟨tel-01370553⟩

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