Abstract
Reduction operations frequently appear in algorithms. Due to their mathematical invariance properties (assuming that round-off errorscan be tolerated), it is reasonable to ignore ordering constraints on the computation of reductions in order to take advantage of the computing power of parallel machines. One obvious and widely-used compilation approach for reductions is syntactic pattern recognition. Either the source language includes explicit reduction operators, or certain specific loops are recognized as equivalent to known reductions. Once such patterns are recognized, hand optimized code for the reductions are incorporated in the target program. The advantage of this approach is simplicity. However, it imposes restrictions on the reduction loops—no data dependence other than that caused by the reduction operation itself is allowed in the reduction loops. In this paper, we present a parallelizing technique, interleaving transformation, for distributed-memory parallel machines. This optimization exploits parallelism embodied in reduction loops through combination of data dependence analysis and region analysis. Data dependence analysis identifies the loop structures and the conditions that can trigger this optimization. Region analysis divides the iteration domain into a sequential region and an order-insensitive region. Parallelism is achieved by distributing the iterations in the order-insensitive region among multiple processors. We use a triangular solver as an example to illustrate the optimization. Experimental results on various distributed-memory parallel machines, including the Connection Machines CM-5, the nCUBE, the IBM SP-2, and a network of Sun Workstations are reported.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.