Matrix Multiplication on Hypercubes Using Full Bandwith and Constant Storage

Abstract

For matrix multiplicatioln on hypercube multiprocessors with the product matrix accumulated in place a processor must receive albout P2/n elements of each input operand, with opeicands of size P x P distributed evenly over N processors. With concurrent communication on all ports, the number of element transfers in sequence can be reduced to P2/fllog1\J for each input operand. We present a two-level partitioning of the matrices and an algolrithm for the matrix: multiplication with optimal data. motion and constant storage. The algorithm has sequential arithmetic complexity 2P3, and parallel arithmetic complexity 2P3/N. The algorithm has been implemented oin the Connection Machine model CM-2. For the performance on the 8K CM-2, we measured iibout 1.6 Gflops, which would scale up to about 13 Gflops for a 64K full machine.