The impact of memory organization on the performance of matrix multiplication

Matrix multiplication may be considered as a model problem for analyzing the performance of more complex algorithms. On Cray and IBM computer systems, there are library routines which for this task operate at high megaflop rates. Other programs from numerical linear algebra do not always achieve this level of sophistication; e.g., they suffer from performance degradation caused by memory access conflicts. This effect has been studied considering the performance of subroutines for matrix multiplication on Cray X-MP, Cray Y-MP, and IBM 3090. Results are analyzed by means of simulation. It is shown that, on a Cray, a degradation of performance by bank conflicts may be reduced if the stride of references to memory is odd. It is demonstrated that a more elaborate approach is required for the IBM 3090 computer system with a more complex storage hierarchy