The power test for data dependence

A data dependence decision algorithm called the power test is introduced. The power test is a combination of the extended GCD algorithm and the Fourier-Motzkin method to eliminate variables in a system of inequalities. This is the first test that can generate the information needed for some advanced transformations, and that can handle complex simultaneous loop limits. Previous work in data dependence decision algorithms is reviewed. Some examples which motivated the development of this test are examined, including those which demonstrate the additional power of the power test. Although it may be too expensive for use as a general-purpose dependence test in a compiler, the power test has proved useful in an interactive program restructuring environment