QP test: a dependence test for quadratic array subscripts

Traditional dependence tests detect dependences with linear array subscripts, but only give passive results to those with non-linear expressions. It may result in a multitude of pseudo-dependences. To maximise the parallelism of applications and improve an optimising compiler´s ability of detecting dependences between program statements, it is necessary to develop a non-linear dependence test to eliminate these pseudo-dependences. This study presents a new non-linear dependence test by analysing the optimal solution of the quadratic subscripts with the index bounds constraints. The authors prove that the non-linear dependences caused by subscripts, which can be written in the form of quadratic programming model, are able to be detected, and introduce a non-linear dependence testing algorithm based on quadratic programming. The effectiveness of this algorithm is verified. The authors developed a prototype implementation of the test with the Open64 compiler and evaluated it using some real world applications from Perfect Club benchmarks and Spec2006 benchmark suites. The experimental results indicate that, compared to existing testing methods, the quadratic programming (QP) test is more efficient for quadratic cases.