Optimal loop parallelization for maximizing iteration-level parallelism
Duo Liu, Zili Shao, Meng Wang, Minyi Guo, Jingling Xue · 2009
This paper solves the open problem of extracting the maximal number of iterations from a loop that can be executed in parallel on chip multiprocessors. Our algorithm solves it optimally by migrating the weights of parallelism-inhibiting dependences on dependence cycles in two phases. First, we model dependence migration with retiming and formulate this classic loop parallelization into a graph optimization problem, i.e., one of finding retiming values for its nodes so that the minimum non-zero edge weight in the graph is maximized. We present our algorithm in three stages with each being built incrementally on the preceding one. Second, the optimal code for a loop is generated from the retimed graph of the loop found in the first phase. We demonstrate the effectiveness of our optimal algorithm by comparing with a number of representative non-optimal algorithms using a set of benchmarks frequently used in prior work.