The Direction Vector I Test

The GCD and Banerjee tests are the standard data dependence tests used to determine whether a loop may be parallelized/vectorized. In an earlier work, we presented a new data dependence test, the I test, which extends the accuracy of the GCD and the Banerjee tests. In the original presentation, only the case of general dependence was considered, i.e., the case of dependence with a direction vector of the form (*, *, …, *). In the present work, we generalize the I test to check for data dependence subject to an arbitrary direction vector.