Counting solutions to Presburger formulas: how and why
Counting solutions to Presburger formulas: how and why
Concrete Math
Estimation of Nested Loops Execution Time by Integer Arithmetic in Convex Polyhedra
Proceedings of the 8th International Symposium on Parallel Processing
Efficient Symbolic Analysis for Parallelizing Compilers and Performance Estimators
The Journal of Supercomputing
A Unified Symbolic Evaluation Framework for Parallelizing Compilers
IEEE Transactions on Parallel and Distributed Systems
Advanced symbolic analysis for compilers: new techniques and algorithms for symbolic program analysis and optimization
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Critical analyses in performance estimators for parallel programs require an algorithm that count the number of integer solutions to a set of inequalities. Most current performance estimators are restricted to linear inequalities for this analysis. In this paper we describe a symbolic algorithm which can estimate the number of integer solutions to a set of both linear and non-linear inequalities. The result is either an integer value or a symbolic expression depending on whether the inequalities contain non-loop variables. We have implemented this algorithm and use it as part of P3T, a performance estimator for data parallel programs. We demonstrate the usefulness of this algorithm by predicting the work load of all processors for a parallel program and compare it to measurements taken on an iPSC/860 hypercube system.