Time Optimal Software Pipelining of Loops with Control Flows for VLIW Processors

Software pipelining is widely used as a compiler optimization technique to achieve high performance in machines that exploit instruction-level parallelism such as superscalar or VLIW processors. However, surprisingly, there have been few theoretical results on the optimality of software pipelined loops with control flows. The problem of time optimal software pipelining of loops with control flows is such an under-investigated theoretical problem. In this paper, we give a complete treatment on the time optimal software pipelining problem solving two fundamental open problems. First, we show that there exists a (computable) decision procedure that can decide if a given loop with control flows has a time optimal parallel program or not. Second, we present a software pipelining algorithm that computes a time optimal parallel program, which is the most significant outcome from the practical point of view. As part of the formal treatment of software pipelining, we propose a new formalization of software pipelining, which provides a basis of our proof as well as a new theoretical framework for software pipelining research.