On the design of algorithms for VLSI systolic arrays

This paper is concerned with the mapping of cyclic loop algorithms into special-purpose VLSI arrays. The mapping procedure is based on the mathematical transformations of index sets and data dependence vectors. Necessary and sufficient conditions for the existence of valid transformations are given for algorithms with constant data dependences. Two examples of different algorithms are given to illustrate the proposed mapping procedure; first is the LU decomposition of a matrix which leads to constant data dependence vectors, and secondly is the dynamic programming which leads to dependences which are functions on the index set and are more difficult to be mapped into VLSI arrays.