The Power Test for Data Dependence
IEEE Transactions on Parallel and Distributed Systems
Dependence Uniformization: A Loop Parallelization Technique
IEEE Transactions on Parallel and Distributed Systems
A Loop Parallelization Method for Nested Loops with Non-uniform Dependences
ICPADS '97 Proceedings of the 1997 International Conference on Parallel and Distributed Systems
(R) Unique Sets Oriented Partitioning of Nested Loops with Non-Uniform Dependences
ICPP '96 Proceedings of the Proceedings of the 1996 International Conference on Parallel Processing - Volume 3
Parallel Region Execution of Loops with Irregular Dependencies
ICPP '94 Proceedings of the 1994 International Conference on Parallel Processing - Volume 02
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Loop parallelization is an important optimization issue in the execution of scientific programs. This paper proposes loop transformation techniques for finding parallel regions within nested loops with non-uniform dependences in order to improve parallelism. By parallelizing anti dependence region using variable renaming, there remains only flow dependence in the loop. We then divide the iteration space into FDT (Flow Dependence Tail set) and FDH (Flow Dependence Head set). By two given equations, we show how to determine whether the intersection of FDT and FDH is empty or not. So, we can find two parallel regions for doubly nested loops with non-uniform dependences. In the case that FDT does not overlap FDH, we will divide the iteration space into two parallel regions by a line.