Data dependence and its application to parallel processing
International Journal of Parallel Programming
Selected papers of the second workshop on Languages and compilers for parallel computing
Efficient and exact data dependence analysis
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International Journal of Parallel Programming
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Most current data dependence tests cannot handle loop bounds or array subscripts that are symbolic, nonlinear expressions (e.g. A (n*i+j), where 0 ≤ j ≤ n). In this paper, we describe a dependence test, called the range test, that can handle such expressions. Briefly, the range test proves independence by determining whether certain symbolic inequalities hold for a permutation of the loop nest. Powerful symbolic analyses and constraint propagation techniques were developed to prove such inequalities. The range test has been implemented in Polaris, a parallelizing compiler being developed at the University of Illinois.