Symbolic range propagation

Many analyses and transformations in a parallelizing compiler can bene t from the ability to compare arbitrary symbolic expressions. In this paper, we describe how one can compare expressions by using symbolic ranges of variables. A range is a lower and upper bound on a variable. We will also describe how these ranges can be e ciently computed from the program text. Symbolic range propagation has been implemented in Polaris, a parallelizing compiler being developed at the University of Illinois, and is used for symbolic dependence testing, detection of zero-trip loops, determining array sections possibly referenced by an access, and loop iteration-count estimation.