Efficient State-Diagram Construction Methods for Software Pipelining

State diagram based approach has been proposed as an effective way to model resource constraints in traditional instruction scheduling and software pipelining methods. However, the constructed state diagram for software pipelining method (i) is very large and (ii) contains significant amount of replicated, and hence redundant, information on legal latency sequences. As a result, the construction of state diagrams can take very large computation time. In this paper, we propose two methods for the efficient construction of state diagrams. In the first method, we relate the construction of state diagram to a well-known problem in graph theory, namely the enumeration of maximal independent sets of a graph. This facilitates the use of an existing algorithm as a direct method for constructing distinct latency sequences. The second method is a heuristic approach which exploits the structure of state diagram construction to eliminate redundancy at the earliest opportunity in an aggressive fashion. The heuristic method uses a surprisingly simple check which is formally shown to completely eliminate redundancy in the state diagram. From our experimental results on two real architectures, both of the two methods show a great reduction in state diagram construction time.