Abstract
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.
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Rajopadhye, S.V., Purushothaman, S., Fujimoto, R.M. (1986). On synthesizing systolic arrays from Recurrence Equations with Linear Dependencies. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1986. Lecture Notes in Computer Science, vol 241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17179-7_30
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DOI: https://doi.org/10.1007/3-540-17179-7_30
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