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Partitioning and labeling of loops by unimodular transformations

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1 Author(s)
E. H. D'Hollander ; Dept. of Electr. Eng., State Univ. of Ghent, Belgium

A general method for the identification of the independent subsets in loops with constant dependence vectors is presented. It is shown that the dependence relation remains invariant under a unimodular transformation. Then a unimodular transformation is used to bring the dependence matrix into a form where the independent subsets are obtained by a direct and inexpensive partitioning algorithm. This leads to a procedure for the automatic conversion of a serial loop into a nest of parallel DO-ALL loops. Another unimodular transformation results in an algorithm to label the dependent iterations of an n-fold nested loop in O(n2) time. This provides a multithreaded dynamic scheduling scheme requiring only one fork and one join primitive

Published in:

IEEE Transactions on Parallel and Distributed Systems  (Volume:3 ,  Issue: 4 )