Continuous retiming: algorithms and applications

This paper introduces a continuous version of retiming (called c-retiming). As retiming, a c-retiming of a circuit is also an assignment of values to the nodes in the circuit. However, values in c-retiming can be real numbers as opposed to integers in retiming. Retiming and c-retiming are strongly related. In fact, a c-retiming can be converted to a retiming by a simple rounding, and the potential degradation in clock period is less than the largest gate delay in a circuit. C-retiming has two very attractive properties. It can be computed much more efficiently than retiming. Consequently, one can compute a retiming by computing a proper c-retiming. Our experimental results indicate this approach can drastically speed up the solution of retiming problems. More importantly, c-retiming can be combined with circuit modifications. Because of this property, c-retiming can be used as a tool to study synthesis and optimization problems in conjunction with retiming. We demonstrate this using the classical tree mapping problem, for which we derive an algorithm that produces a solution with a clock period provably close to optimal while considering retiming.