Toward Advanced Symbolic Analysis

Bae, Hansang. M.S.E.C.E., Purdue University, May, 2003. Toward Advanced Symbolic Analysis. Major Professor: Rudolf Eigenmann. Automatic parallelization of programs at the loop level requires advanced program analysis techniques. The goal of these techniques is supporting other parallelization techniques by providing as much compile-time information as possible. Evaluation of symbolic expressions is one of such techniques, including expression propagation and range analysis. However, these techniques may not be sufficient for best result of loop parallelization – finding as much parallelism as possible. A comprehensive performance study on the current advanced symbolic analysis techniques was performed to see how important they are in automatic program parallelization. Range analysis, expression propagation, and expression manipulation techniques in the Polaris parallelizing compiler were evaluated in this study. The result showed that all of them made the parallelizer find more parallel loops, and sometimes affected the performance of resulting parallel programs significantly. However, it turned out that more advanced techniques are required to find more fine-grain parallelism resident in programs. Those techniques should understand certain variables’ behaviors in recurrence relations, and should make better decisions when comparing two symbolic expressions. Sequence variable analysis is proposed as a tool for analyzing the behavior of a variable in a recurrence relation. This technique could be useful in data dependence analysis and array privatization as well as in removing some complex recurrence relations. Also, a simple property of integer division could strengthen existing data dependence analysis.