Matrix Multiplication on the Intel Touchstone Delta

Matrix multiplication is a key primitive in block matrix algorithms such as those found in LAPACK. We present results from our study of matrix multiplication algorithms on the Intel Touchstone Delta, a distributed memory message-passing architecture with a two-dimensional mesh topology. We obtain an implementation that uses communications primitives highly suited to the Delta and exploits the single node assembly-coded matrix multiplication. Our algorithm is completely general, able to deal with arbitrary mesh aspect ratios and matrix dimensions, and has achieved parallel eeciency of 86% with overall peak performance in excess of 8 GGops on 256 nodes for an 8800 8800 matrix. We describe our algorithm design and implementation, and present performance results that demonstrate scalability and robust behavior over varying mesh topologies.