$\pi$ Abstraction: Parallelism-Aware Array Data Flow Analysis for OpenMP

Abstract

Array data flow analysis (ADFA) is a classical method for collecting array section information in sequential programs. When applying ADFA to parallel OpenMP programs, array access information needs to be analyzed in loops whose iteration spaces are partitioned across threads. The analysis involves symbolic expressions that are functions of the original loop iteration spaces, subscript expressions and thread numbers. Adequate representations of, and operations on, these expressions can be critical for the accuracy of the analysis. This paper presents a new ADFA compiler framework for OpenMP programs. We introduce the $\pi$ operator to abstractly represent the parallelism effects in array section expressions and improve the accuracy of the cross-thread analysis during data flow computation. We also present a novel delayed symbolic evaluation technique that enables all array section operations in the data flow computation to be performed fully accurately. Using four NAS OpenMP benchmarks, we show that the $\pi$ operator improves array section operations’ accuracy (i.e., reduces conservative operations) during data flow computation by $66$ %, on average, compared to the best alternative. In addition, it reduces the number of terms, and thus the complexity of computed array sections by $33$ %, on average. We also show that delayed symbolic evaluation eliminates conservative operations and does so without significant increase in complexity when combined with $\pi$ operators.

This work was supported, in part, by the National Science Foundation under grants No. 0720471-CNS, 0707931-CNS, 0833115-CCF, 0916817-CCF and 1346896-CCF.