Abstract
Array subscript, in general, is a linear function of loop indices, called linear subscripts, if array enclosed by loops. For linear subscripts, the dependences among iterations could be complex. In case of complex dependence, it is very difficult to extract parallelism from the loops. In this paper, we propose a new compiler technique, called clustering, to overcome this difficulties in parallelizing nested loops with linear subscripts. By applying the integer programming and linearizing the nested loops, we can partition the iterations of loops into clusters. All iterations in the same cluster can be executed at the same time. We can observe that this compiler technique can greatly enhance the parallelism of a nested loop.