Dependence analysis with direction vector for array references

We presented a new scheme for exact data dependence analysis, called interv al 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 a ny constraint variable shrinks to empty, this linear diophantine equation c ontains no integer solution and the memory accesses subject to this constra int are then independent. Otherwise, all the integer solutions can be enume rated. IR test is an efficient and exact data dependence test method. In th e original presentation, only general dependence is considered. If there ex ists a dependence, we do not care what the direction vector is. In this pap er, we extend the IR test to check the data dependence subject to an arbitr ary direction vector. Experimental results are presented to show its effect iveness compared to the omega test and power test. (C) 2001 Elsevier Scienc e Ltd. All rights reserved.