Converting affine recurrence equations to quasi-uniform recurrence equations

Converting Affine Recurrence Equations to Quasi-Uniform Recurrence Equations

Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. Recently, researchers have begun to relax this restriction 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 depende...

A toolbox for affine recurrence equations parallelization

The naive execution of affine recurrence equations

In recognition of the fundamental relation between regular arrays and systems of affine recurrence equations, the ALPHA language was developed as the basis of a computer aided design methodology for regular array architectures. ALPHA is used to initially specify algorithms at a very high algorithmic level. Regular array architecures can then be derived from the algorithmic specification using a...

Minimal Representation of Uniform Recurrence Equations 1

We consider a system of uniform recurrence equations of dimension one. We show how the computation can be carried using minimal memory size with several synchronous processors. This result has applications in register minimization for digital circuitry and parallel simulation of timed event graphs.

Solutions to the Communication Minimization Problem for Affine Recurrence Equations

This paper deals with communication optimization which is a crucial issue in automatic parallelization. From a system of parameter-ized aane recurrence equations, we propose a heuristic which determines an eecient space-time transformation. It reduces rst the distant communications and then the local communications.