Abstract
Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. In this paper, this restriction is relaxed to include systems of affine recurrence equations. A system of uniform recurrence equations typically can be embedded in spacetime so that the distance between a variable and a dependent variable does not depend on the problem size. Systems of affine recurrence equations which are not uniform, do not enjoy this property. A method is presented for converting a system of affine recurrence equations to an equivalent system of recurrence equations that is uniform, except for points near the boundaries of its index sets. A characterization of those systems of affine recurrence equations that can be so converted is given, along with an algorithm that decides if a system is amenable to such a conversion, and a procedure that converts those affine systems which can be converted.
This material is based upon work supported by the Office of Naval Research under contract nos. N00014-84-K-0664 and N00014-85-K-0553.
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© 1988 Springer-Verlag Berlin Heidelberg
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Yaacoby, Y., Cappello, P.R. (1988). Converting affine recurrence equations to quasi-uniform recurrence equations. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040399
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DOI: https://doi.org/10.1007/BFb0040399
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