Speeding Up Optimal Modulo Scheduling with Rational Initiation Intervals

Compared to integer initiation intervals (II), rational IIs improve throughput achieved by loop pipelining in many cases. This comes at the expense of a higher need for data path elements (i.e., multiplexers and registers) and the need for solving more complex scheduling problems. To optimally solve these problems, we improved an existing ILP formulation for latency-optimal modulo scheduling with rational IIs that now finds 6.08x more solutions and 6.10x as many optimal ones within the same time budget. Compared to the best alternative from previous work, our improved algorithm finds 1.15x more solutions and 2.97x as many optimal ones.