Modulo Scheduling with Rational Initiation Intervals in Custom Hardware Design

In modulo scheduling, the number of clock cycles between successive inputs (the initiation interval, II) is traditionally an integer, but in this paper, we explore the benefits of allowing it to be a rational number. This rational II can be interpreted as the average number of clock cycles between successive inputs. As the minimum rational II can be less than the minimum integer II, this translates to higher throughput. We formulate rational-II modulo scheduling as an integer linear programming (ILP) problem that is able to find latency-optimal schedules for a fixed rational II. We have applied our scheduler to a standard benchmark of hardware designs, and our results demonstrate a significant speedup compared to state-of-the-art integer-II and rational-II formulations.