Optimizing Sparse Representations for Data

Sparse program representations allow inter-statement dependences to be represented explicitly, enabling dataaow analyzers to restrict the propagation of information to paths where it could potentially aaect the dataaow solution. This paper describes the use of a single sparse program representation , the value dependence graph, in both general and analysis-specic contexts, and demonstrates its utility in reducing the cost of dataaow analysis. We nd that several semantics-preserving transformations are beneecial in both contexts. 1 Introduction The goal of dataaow analysis is to compute assertions about certain program quantities at particular points in a program, such as \after this statement is executed, variable x always has the value 2" or \this procedure call will leave variable z unchanged." A typical dataaow analyzer will associate a set of assertions with each program point, treat each program statement as a mapping function over such assertion sets, and solve the resulting system of equations by iterative or structured means. The memory cost of such an analysis is thus proportional to the number of possible assertion sets and the number of points at which these sets must be stored, while the time cost is proportional to the number of assertion sets and the number of statements through which they must be propagated. Sparse program representations attempt to minimize both of these costs by more directly connecting producers of values with their consumers, so that fewer assertions are kept at each point, and fewer need be propagated through each statement. General sparse representations such as static single assignment (SSA) form CFR + 89] completely describe a program's behavior, while analysis-speciic representations such as sparse evaluation graphs (SEGs) CCF91] represent only those program statements needed to solve a particular dataaow problem. This paper describes the use of a single sparse program