Abstract
Frequently, affine recurrence equations can be scheduled more efficiently by quadratic scheduling functions than by linear scheduling functions. In this paper, the problem of finding optimal quadratic schedules for affine recurrence equations is formulated as a convex nonsmooth programming problem. In particular, sufficient constraints for causality are used generalizing Lamport's condition. In this way, the presented problem formulation becomes independent of the problem size. The research tool AQUAD is described implementing this problem formulation. Several nontrivial examples demonstrate that AQUAD can be effectively used to calculate quadratic schedules for affine recurrence equations. Finally, it is shown how array processors can be synthesized from affine recurrence equations which are scheduled by quadratic functions with a singular Hessian matrix.
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