| Abstract: | 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 analyze and compare three algorithms and obtain an implementation, BiMMeR, that uses communication primitives highly suited to the Delta and exploits the single node assembly-coded matrix multiplication. Our algorithm is completely general, i.e. able to deal with various data layouts as well as arbitrary mesh aspect ratios and matrix dimensions, and has achieved parallel efficiency of 86 %, with overall peak performance in excess of 8 Gflops on 256 nodes for an 8800 × 8800 matrix. We describe BiMMeR's design and implementation and present performance results that demonstrate scalability and robust behavior over varying mesh topologies. |
