A Polynomial Time Method for Optimal Software Pipelining

Software pipelining is one of the most important loop scheduling methods used by parallelizing compilers. It determines a static parallel schedule — a periodic pattern — to overlap instructions of a loop body from different iterations. The main contributions of this paper are the following: First, we propose to express the fine-grain loop scheduling problem (in particular, software pipelining) on the basis of the mathematical formulation of r-periodic scheduling. This formulation overcomes some of the problems encountered by existing software pipelining methods. Second, we demonstrate the feasibility of the proposed method by presenting a polynomial time algorithm to find an optimal schedule in this r-periodic form that maximizes the computation rate (in fact, we show that this schedule maximizes the computation rate theoretically possible).

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