Nonlinear and Symbolic Data Dependence Testing

One of the most crucial qualities of an optimizing compiler is its ability to detect when different data references access the same storage location. Such references are said to be data-dependent and they impose constraints on the amount of program modifications the compiler can apply for improving the program's performance. For parallelizing compilers, the most important program constructs to investigate are loops and the array references they contain. In previous work, we have found a serious limitation of current data dependence tests to be that they cannot handle loop bounds or array subscripts that are symbolic, nonlinear expressions. In this paper, 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 developed at the University of Illinois. We present measurements of the range test's performance and compare it with state-of-the-art tests.