Scheduling with soft constraints

In a behavioral synthesis system, a typical approach used to guide the scheduler is to impose hard constraints on the relative timing between operations considering performance, area, power, etc., so that the resulting RTL design is favorable in these aspects. The mechanism is often flawed in practice because many such constraints are actually soft constraints which are not necessary, and the constraint system may become inconsistent when many hard constraints are added for different purposes. This paper describes a scheduler that distinguishes soft constraints from hard constraints when exploring the design space. We propose a special class of soft constraints called integer-difference soft constraints, which lead to a totally unimodular constraint matrix in an integer linear programming formulation. By exploiting the total unimodularity, the problem can be solved optimally and efficiently using a linear programming relaxation without expensive branch and bound procedures. We also show how the proposed method can be used to support a variety of design considerations. As an example application, we apply the method to the problem of low-power synthesis with operation gating. In a set of experiments on real-world designs, our method achieves an average of 33.9% reduction in total power; it outperforms a previous method by 17.1% on average and gives close-to-optimal solutions on several designs.