Dependence Testing without Induction Variable Substitution

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 used for dependence testing of array references. Under this scheme, closed form computation and induction variable substitution can be delayed until after the dependence test and be performed on-demand. The technique can be extended to dynamic data structures, using either pointer-based implementations or standard object-oriented containers. To improve efficiency, we also propose an optimized (non-iterative) data-flow algorithm to compute evolution. Experimental results show that dependence tests based on evolution information match 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