Pipeline Optimization using a Cost Extension of Timed Petri Nets

A major step in arithmetic operators design is the placement of pipeline stages, with the goal of drastically increase the data throughput. Approaches, such as the as-soon-as-possible greedy algorithm, allow pipelining with a frequency target. They can possibly be combined with a retiming operation to reduce the number of pipeline registers. This retiming step is based on a weighted directed graph model, from which the pipeline placement is reduced to an optimisation problem (for example ILP). However, this approach produces only a unique solution, and makes it difficult to add additional constraints on the resulting pipeline. We propose to use a Timed Petri Net extension with cost, where time captures the propagation delay and cost measures the size of pipeline registers. The state space of the model captures exactly the circuit states and the branching points, so its exploration can be guided by comparing the circuit states regarding any feature (number and size of registers, critical path, throughput, etc). The pipeline exploration can be reduced to a weighted branching-time logic model-checking problem, that we prove to be PSPACE-complete on this model. We have implemented this exploration algorithm in a prototype tool. We apply it on some arithmetic operators provided by FloPoCo showing improvements up to 35% compared to the current implementation.