A unified symbolic evaluation framework for parallelizing compilers

The quality of many optimizations and analyses of parallelizing compilers depends significantly on the ability to evaluate symbolic expressions and on the amount of information available about program variables at arbitrary program points. In this paper, we describe an effective and unified symbolic evaluation framework that statically determines the values of variables and symbolic expressions, assumptions about and constraints between variable values, and the condition under which control flow reaches a program statement. We introduce the program context, a novel representation for comprehensive and compact control and data flow analysis information. Program contexts are described as first order logic formulas, which allows us to use public domain software for standard symbolic manipulation. Computations are represented as algebraic expressions defined over a program's problem size. Our symbolic evaluation techniques comprise accurate modeling of assignment and input/output statements, branches, loops, recurrences, arrays, and procedures. All of our techniques target both linear, as well as nonlinear, expressions and constraints. Efficiency of symbolic evaluation is highly improved by aggressive simplification techniques. A variety of examples, including program verification, dependence analysis, array privatization, communication vectorization, and elimination of redundant communication, are used to illustrate the effectiveness of our approach. We present results from a preliminary implementation of our framework, which is used as part of a parallelizing compiler that demonstrates the potential performance gains achievable by employing symbolic evaluation to support program parallelization.