Profiling Dependence Vectors for Loop Parallelization �

A dependence relation between two data references is linear if it generates dependence vectors that are linear functions of the loop indices. A linear dependence relation often induces a large number of dependence vectors. Empirical studies also show that linear dependencies often intermix with uniform dependencies in loops [5, 6]. These factors make it difficult to analyze such loops and extract the inherit parallelism. In this paper, we propose to manipulate such dependencies in the dependence vector space and summarize the large number of dependence vectors with their convex hull. The convex hull, as a profile of the dependence vectors, can be used to deduce many important properties of the vectors. We will show how to find the convex hull and then apply it to loop parallelization. The proposed approach will be compared with other schemes. 1