Array-data flow analysis and its use in array privatization

Data-flow analysis of scalar variables and data dependence analysis on array elements are two important program analyses used in optimizing and parallelizing compilers. Traditional data-flow analysis models accesses of array elements simply as accesses to the entire array, and is inadequate for parallelizing loops in array-based programs. On the other hand, data dependence analysis differentiates between different array elements but is flow-insensitive. This paper studies the combination of these two analyses—data-flow analyses—data-flow analysis of accesses to individual array elements. The problem of finding precise array dataflow information in the domain of loop nests where the loop bounds and array indices are affine functions of loop indices was first formulated by Feautrier. Feautrier's algorithm, based on parametric integer programming techniques, is general but inefficient. This paper presents an efficient algorithm that can find the same precise information for many of the programs found in practice. In this paper, we argue that data-flow analysis of individual array elements is necessary for effective automatic parallelization. In particular, we demonstrate the use of array data-flow analysis in an important optimization known as array privatization. By demonstrating that array data-flow analysis can be computed efficiently and by showing the importance of the optimizations enabled by the analysis, this paper suggests that array data-flow analysis may become just as important in future optimizing and parallelizing compilers as data-flow and data dependence analysis are in today's compilers.