We present a technique for synthesizing systolic architectures from Recurrence Equations. A class of such equations (Recurrence Equations with Linear Dependencies) is defined and the problem of mapping such equations onto a two dimensional architecture is studied. We show that such a mapping is provided by means of a linear allocation and timing function. An important result is that under such a mapping the dependencies remain linear. After obtaining a two-dimensional architecture by applying such a mapping, a systolic array can be derived if the communication can be spatially and temporally localized. We show that a simple test consisting of finding the zeroes of a matrix is sufficient to determine whether this localization can be achieved by pipelining and give a construction that generates the array when such a pipelining is possible. The technique is illustrated by automatically deriving a well known systolic array for factoring a band matrix into lower and upper triangular factors.
CITATION STYLE
Rajopadhye, S. V., Purushothaman, S., & Fujimoto, R. M. (1986). On synthesizing systolic arrays from recurrence equations with linear dependencies. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 241 LNCS, pp. 488–503). Springer Verlag. https://doi.org/10.1007/3-540-17179-7_30
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