Integer Affine Transformations of Parametric Z-polytopes and Applications to Loop Nest Optimization

Abstract : The polyhedral model is a well-known compiler optimization framework for the analysis and transformation of affine loop nests. We present a new method concerning a difficult geometric operation that is raised by this model: the integer affine transformation of parametric Z-polytopes. The result of such a transformation is given by a worst-case exponential union of Z-polytopes. We also propose a polynomial algorithm (for fixed dimension), to count points in arbitrary unions of a fixed number of parametric Z-polytopes. We implemented these algorithms and compared them to other existing algorithms, for a set of applications to loop nest analysis and optimization.
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ACM Transactions on Architecture and Code Optimization, Association for Computing Machinery, 2012, 9 (2), pp.8.1-8.27. 〈10.1145/2207222.2207224〉
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Contributeur : Vincent Loechner <>
Soumis le : vendredi 1 avril 2011 - 12:17:10
Dernière modification le : jeudi 11 janvier 2018 - 06:23:13

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Rachid Seghir, Vincent Loechner, Benoit Meister. Integer Affine Transformations of Parametric Z-polytopes and Applications to Loop Nest Optimization. ACM Transactions on Architecture and Code Optimization, Association for Computing Machinery, 2012, 9 (2), pp.8.1-8.27. 〈10.1145/2207222.2207224〉. 〈inria-00582388〉

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