Forty-three ways of systolic matrix multiplication

This paper investigates different ways of systolic matrix multiplication. We prove that in total there are 43 arrays for multiplication of rectangular matrices. We also prove that, depending on the mutual relation between the dimensions of rectangular matrices, there is either 1 or 21 arrays with minimal number of processing elements. Explicit mathematical formulae for systolic array synthesis are derived. The methodology applied to obtain 43 systolic designs is based on the modification of the synthesis procedure based on dependency vectors and space-time mapping of the dependency graph.