Efficient Symbolic Analysis for Parallelizing Compilers and Performance Estimators

摘要

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.