Monotonic Evolution: an Alternative to Induction Variable Substitution for Dependence Analysis
Résumé
We present a new approach to dependence testing in
the presence of induction variables. Instead of looking for closed form expressions, our method computes
monotonic evolution which captures the direction in
which the value of a variable changes. This information is then used in the dependence test to help determine whether array references are dependence-free.
Under this scheme, closed form computation and induction variable substitution can be delayed until after
the dependence test and be performed on-demand. To
improve computational efficiency, we also propose an optimized (non-iterative) data-flow algorithm to compute
evolution. Experimental results show that dependence
tests based on evolution information matches the accuracy of that based on closed-form computation (implemented in Polaris), and when no closed form expressions can be calculated, our method is more accurate
than that of Polaris.
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