Partitioning and Labeling of Loops by Unimodular Transformations

  • Authors:
  • E. H. D'Hollander

  • Affiliations:
  • -

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1992

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Abstract

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 bya 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(n/sup 2/) time. This provides a multithreaded dynamic scheduling scheme requiring only one fork and one join primitive.