Automatic synthesis of systolic arrays from uniform recurrent equations

Abstract

We describe a systematic method for the design of systolic arrays. This method may be used for algorithms that can be expressed as a set of uniform recurrent equations over a convex set D of Cartesian coordinates. Most of the algorithms already considered for systolic implementation may be represented in this way. The methods consists of two steps: finding a timing-function for the computations that is compatible with the dependences introduced by the equations, then mapping the domain D onto another finite set of coordinates, each representing a processor of the systolic array, in such a way that concurrent computations are mapped onto different processors. The scheduling and mapping functions meet conditions that allow the full automation of the method. The method is exemplified on the convolution product and the matrix product.