Abstract
Symbolic analysis is of paramount importance for parallelizing compilers and performance estimators to examine symbolic expressions with program unknowns such as machine and problem sizes and to solve queries based on systems of constraints (equalities and inequalities). This paper describes novel techniques for counting the number of solutions to a system of constraints, simplifying systems of constraints, computing lower and upper bounds of symbolic expressions, and determining the relationship between symbolic expressions. All techniques target wide classes of linear and non-linearsymbolic expressions and systems of constraints. Our techniques have been implemented and are used as part of a parallelizing compiler and a performance estimator to support analysis and optimization of parallel programs. Various examples and experiments demonstrate the effectiveness of our symbolic analysis techniques.
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