From systolic to periodic array design

Given an application described by a system of uniform recurrence equations, systolic arrays are commonly derived with an affine space-time transformation that determines when and where the computations are to be performed. With quasi-affine mappings, the application is mapped onto a periodic array: the combinational logic is the same in every cell, but the connections change from cell to cell, periodically. Quasi-affine mappings allow a complete exploration of the design space. To illustrate this, the author derives convolvers that use any given number of inner product cells. PRESAGE is a software tool for deriving both systolic and periodic arrays. Its methodology is presented when both affine and quasi-affine mappings are used.Anglai