An Implemented Method for Incremmental Systolic Design

We present a mathematically rigorous and, at the same time, convenient method for systolic design and derive alternative systolic designs for one expository matrix computation problem: matrix multiplication. Each design is synthesized from a simple program and a proposed layout of processors. The synthesis derives (1) a systolic parallel execution, (2) channel connections for the proposed processor layout, and (3) an arrangement of data streams such that the systolic execution can begin. Our choices of alternative designs are governed by formal theorems. The synthesis method is implementable and is particularly effective if implemented with graphics capability. Our implementation on the Symbolics 3600 displays the resulting designs and simulated executions graphically on the screen. The method has also been successfully applied to other matrix computation problems.

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