Efficient Manipulation of Disequalities During Dependence Analysis

Abstract

Constraint-based frameworks can provide a foundation for efficient algorithms for analysis and transformation of regular scientific programs. For example, we recently demonstrated that constraint-based analysis of both memory- and value-based array dependences can often be performed in polynomial time. Many of the cases that could not be processed with our polynomial-time algorithm involved negated equality constraints (also known as disequalities).

In this report, we review the sources of disequality constraints in array dependence analysis and give an efficient algorithm for manipulating certain disequality constraints. Our approach differs from previous work in that it performs efficient satisfiability tests in the presence of disequalities, rather than deferring satisfiability tests until more constraints are available, performing a potentially exponential transformation, or approximating. We do not (yet) have an implementation of our algorithms, or empirical verification that our test is either fast or useful, but we do provide a polynomial time bound and give our reasons for optimism regarding its applicability.