On Composing Matrix Multiplication from Kernels

Matrix multiplication is often treated as a basic unit of computation in terms of which other operations are implemented, yielding high performance. In this paper initial evidence is provided that there is a benefit gained when lower level kernels, from which matrix multiplication is composed, are exposed. In particular it is shown that matrix multiplication itself can be coded at a high level of abstraction as long as interfaces to such low-level kernels are exposed. Furthermore, it is shown that higher performance implementations of parallel matrix-multiplication can be achieved by exploiting access to these kernels. Experiments on Itanium2 and Pentium 4 servers support these insights.