Toward symbolic performance prediction of parallel programs

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