Abstract
We propose a class of functions called quasi-linear functions to be used as allocation functions in systolic array synthesis. We describe the special properties of such functions that make them suitable as allocation functions, and give necessary and sufficient conditions that they must satisfy. The main advantage of quasi-linear allocation functions is that they provide a unified framework for dealing with a technique called clustering which is often used as apost-processing technique to improve the efficiency of systolic arrays. We show that it is always possible to choose quasi-linear allocation functions so that the derived arrays have 100% efficiency. Our method is constructive and the allocation function can be obtained automatically. We also generalize our result to deal witharbitrary systolic arrays (outside the context of synthesis). The technique can also be extended to any (piece-wise) systolic array to derive arrays with 100% efficiency.
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