The infinity Lambda test: A multi-dimensional version of Banerjee infinity test (Q1575624)

The Banerjee infinity test accurately determines data dependence for one linear equation under symbolic limits and any given direction vectors [\textit{U. Banerjee}, Depence Analysis for Supercomputing (Kluwer Academic Publishers, Norwell, MA, 1988); \textit{P. M. Petersen}, Evaluation of programs and parallelizing compilers using dynamic analysis techniques, Ph. D. Thesis, University of Illinois at Urbana-Champaign (January 1993)]. For \(m\) linear equations with the same constraints, as each linear equation has to be tested separately, the Banerjee infinity test may generally lose the accuracy. In this paper, we proposed the infinity Lambda test -- a multi-dimensional version of the Banerjee infinity test. The infinity Lambda test can be applied to deal with data dependence of coupled arrays with symbolic (unknown at compile time) bounds. Experiments with benchmark showed that the infinity Lambda test increases the success rate of the Lambda test by approximately 12\%.