Scheduling and Mapping: Software Pipelining in the Presence of Structural Hazards

Abstract

Recently, software pipelining methods based on an ILP (Integer Linear Programming) framework have been successfully applied to derive rate-optimal schedules for architectures involving clean pipelines - pipelines without structural hazards. The problem for architectures beyond such clean pipelines remains open. One challenge is how, under a unified ILP framework, to simultaneously represent resource constraints for unclean pipelines, and the assignment or mapping of operations from a loop to those pipelines. In this paper we provide a framework which does exactly this, and in addition constructs rate-optimal software pipelined schedules. The proposed formulation and a solution method have been implemented and tested on a set of 1006 loops taken from various scientific and integer benchmark suites. The formulation found a rate-optimal schedule for 75% of the loops, and required a median time of only 2 seconds per loop on a Sparc 10/30.