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Index Set Splitting

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Abstract

There are many algorithms for the space-time mapping of nested loops. Some of them even make the optimal choices within their framework. We propose a preprocessing phase for algorithms in the polytope model, which extends the model and yields space-time mappings whose schedule is, in some cases, orders of magnitude faster. These are cases in which the dependence graph has small irregularities. The basic idea is to split the index set of the loop nests into parts with a regular dependence structure and apply the existing space-time mapping algorithms to these parts individually. This work is based on a seminal idea in the more limited context of loop parallelization at the code level. We elevate the idea to the model level (our model is the polytope model), which increases its applicability by providing a clearer and wider range of choices at an acceptable analysis cost. Index set splitting is one facet in the effort to extend the power of the polytope model and to enable the generation of competitive target code.

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Authors and Affiliations

  1. Universität Passau, FMI, D-94030, Passau, Germany

    Martin Griebl & Christian Lengauer

  2. Université de Versailles, PRiSM, 45 avenue des États-Unis, F-78035, Versailles, France

    Paul Feautrier

Authors
  1. Martin Griebl
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  2. Paul Feautrier
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  3. Christian Lengauer
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Griebl, M., Feautrier, P. & Lengauer, C. Index Set Splitting. International Journal of Parallel Programming 28, 607–631 (2000). https://doi.org/10.1023/A:1007516818651

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