Exact and Practical Modulo Scheduling for High-Level Synthesis

Loop pipelining is an essential technique in high-level synthesis to increase the throughput and resource utilisation of field-programmable gate array--based accelerators. It relies on modulo schedulers to compute an operator schedule that allows subsequent loop iterations to overlap partially when executed while still honouring all precedence and resource constraints. Modulo schedulers face a bi-criteria problem: minimise the initiation interval (II; i.e., the number of timesteps after which new iterations are started) and minimise the schedule length. We present Moovac, a novel exact formulation that models all aspects (including the II minimisation) of the modulo scheduling problem as a single integer linear program, and discuss simple measures to prevent excessive runtimes, to challenge the old preconception that exact modulo scheduling is impractical. We substantiate this claim by conducting an experimental study covering 188 loops from two established high-level synthesis benchmark suites, four different time limits, and three bounds for the schedule length, to compare our approach against a highly tuned exact formulation and a state-of-the-art heuristic algorithm. In the fastest configuration, an accumulated runtime of under 16 minutes is spent on scheduling all loops, and proven optimal IIs are found for 179 test instances.