A Flow Graph Formulation of Optimal Software Pipelining

We present a new approach to the loop scheduling problem, which excels previous solutions in two important aspects: The resource constraints are formulated using flow graphs, and the initiation interval is treated as a rational variable. The approach supports heterogeneous processor architectures and pipelined functional units, and the Integer Linear Programming implementation produces an optimum loop schedule, whereby a minimum is achieved. Our flow graph model facilitates the cyclic binding of loop operations to functional units. Compared to previous research results, the solution can provide faster loop schedules and a significant reduction of the problem complexity and solution time.