The Banerjee-Wolfe and GCD Tests on Exact Data Dependence Information

The GCD test and the Banerjee?Wolfe test are the two tests traditionally used to determine statement data dependence, subject to direction vectors, in automatic vectorization/parallelization of loops. In an earlier study, a sufficient condition for the accuracy of the Banerjee?Wolfe test was stated and proved. In that work, we only considered the case of general data dependence, i.e., the case of data dependence without direction vector information. In this paper, we extend the previous result to the case of data dependence subject to an arbitrary direction vector. We also state and prove a sufficient condition for the accuracy of a combination of the GCD and Banerjee?Wolfe tests. Furthermore, we show that the sufficient conditions, for the accuracy of the Banerjee?Wolfe test and the accuracy of a combination of the GCD and Banerjee?Wolfe tests are necessary conditions as well. Finally, we demonstrate how these results can be used in actual practice to obtain exact data dependence information.

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