The extension of the I test

The I test is an efficient and precise data dependence method to ascertain whether integer solutions exist for one-dimensional arrays with constant bounds. For one-dimensional arrays with variable limits, the I test assumes that there may exist integer solutions. In this paper, we extend the I test. The extended I test can be applied towards determining whether integer solutions exist for one-dimensional arrays with variable limits, improving the applicable range of the I test. Experiments with benchmark cited from EISPACK, LINPACK, Parallel loops, etc. showed that among 1189 pairs of one-dimensional arrays tested, 183 had their data dependence analysis amended by the extended I test. That is, the extended I test increases the success rate of the I test by approximately 15.4%. Comparing with the Power test and the Omega test, the extended I test has higher accuracy than the Power test and shares the same accuracy with the Omega test for these 1189 pairs of arrays, but has much better efficiency over these two well-known tests.