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Published in:
2007 | OriginalPaper | Chapter
Loop Parallelization in Multi-dimensional Cartesian Space
Authors : Saeed Parsa, Shahriar Lotfi
Published in: Perspectives of Systems Informatics
Publisher: Springer Berlin Heidelberg
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Loop parallelization is of great importance to automatic translation of sequential into parallel code. We have applied Diophantine equations to compute the basic dependency vector sets covering all possible non-uniform dependencies between loop iterations. To partition the resultant dependencies space into multi-dimensional tiles of suitable shape and size, a new genetic algorithm is proposed in this article. Also, a new scheme based on multi-dimensional wave-fronts is developed to convert the multi-dimensional parallelepiped tiles into parallel loops. The problem of determining optimal tiles is NP-hard. Presenting a new constraint genetic algorithm in this paper the tiling problem is for the first time solved, in Cartesian spaces of any dimensionality.