An experimental study of an ILP-based exact solution method for software pipelining

Abstract

Software pipelining has been widely accepted as an efficient technique for scheduling instructions in a loop body for VLIW and Superscalarprocessors. Several software pipelining methods based on heuristic approachs have been proposed in the literature. Mathematical formulations based on integer linear programming (ILP) to obtain rate-optimal schedules are also becoming popular. We term formulations such as ILP exact to indicate that they solve a precisely stated optimality problem. By contrast, we term what are generally called "heuristic" methods inexact since they do not guarantee optimality. We do not use the term heuristic, because various heuristics can also be used to guide approaches such as ILP--without losing any optimality. In this paper we compare our software pipelining method based on the ILP with three inexact methods. These software pipelining methods are applied to 1008 different loops extracted from a variety of benchmark programs, and their performance, in terms of the computation rate of the loop schedule, the number of registers used, and the execution time of the scheduling method. Compared to the inexact approaches and in terms of computation rate and register requirements, the ILP based scheduling method obtains better schedules in a significant number of test cases. The ILP based method obtained optimal schedules reasonably fast, with a median of less than 3 seconds and a geometric mean of less than 3 seconds. We present a case for the ILP approach and its usefulness in performance critical applications and also as a testbed for evaluating other inexact software pipelining methods.