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Optimal Fine and Medium Grain Parallelism Detection in Polyhedral Reduced Dependence Graphs

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Abstract

This paper presents an optimal algorithm for detecting line or medium grain parallelism in nested loops whose dependences are described by an approximation of distance vectors by polyhedra. In particular, this algorithm is optimal for the classical approximation by direction sectors. This result generalizes, to the case of several statements. Wolf and Lam's algorithm which is optimal for a single statement. Our algorithm relies on a dependence uniformization process and on parallelization techniques related to system of uniform recurrence equations. It can also be viewed as a combination of both Allen and Kennedy's algorithm and Wolf and Lam's algorithm.

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  1. Laboratoire LIP, URA CNRS 1398, École Normale Supérieure de Lyon, F-69364, Lyon Cedex 07

    Alain Darte & Frédéric Vivien

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  1. Alain Darte
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  2. Frédéric Vivien
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Darte, A., Vivien, F. Optimal Fine and Medium Grain Parallelism Detection in Polyhedral Reduced Dependence Graphs. International Journal of Parallel Programming 25, 447–496 (1997). https://doi.org/10.1023/A:1025168022993

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