The range test: a dependence test for symbolic, non-linear expressions

Most current data dependence tests cannot handle loop bounds or array subscripts that are symbolic, nonlinear expressions (e.g. A(n*i+j), where 0⩽j⩽n). We describe a dependence test, called the range test, that can handle such expressions. Briefly, the range test proves independence by determining whether certain symbolic inequalities hold for a permutation of the loop nest. Powerful symbolic analyses and constraint propagation techniques were developed to prove such inequalities, The range test has been implemented in Polaris, a parallelizing compiler being developed at the University of Illinois