The I+ test

Abstract

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 propose the I+ test|an extended version of the I test. The I+ test can be applied towards determining whether integer solutions exist for onedimensional arrays with either variable or constant limits, improving the applicable range of the I test. Experiments with benchmark cited from EISPACK, LINPACK, Parallel loops, Livermore loops and Vector loops showed that among 1189 pairs of one-dimensional arrays tested, 183 had their data dependence analysis amended by the I+ test. That is, the I+ test increases the success rate of the I test by approximately 15:4 percent. Comparing with the Power test and the Omega test, the I+ test has higher accuracy than the Power test and shares the same accuracy with the Omega test when determining integer solutions for these 1189 pairs of one-dimensional arrays, but has much better efficiency over them.