Dependence analysis with direction vector for array references

Abstract

We presented a new scheme for exact data dependence analysis, called interval reduction (IR) test in J. Sys. Software [2000;52(1):55–65]. This scheme reduces the solution interval of each constraint variable in the dependence equation by repeated projection. Once the effective solution interval of any constraint variable shrinks to empty, this linear diophantine equation contains no integer solution and the memory accesses subject to this constraint are then independent. Otherwise, all the integer solutions can be enumerated. IR test is an efficient and exact data dependence test method. In the original presentation, only general dependence is considered. If there exists a dependence, we do not care what the direction vector is. In this paper, we extend the IR test to check the data dependence subject to an arbitrary direction vector. Experimental results are presented to show its effectiveness compared to the omega test and power test.