The meeting graph: a new model for loop cyclic register allocation

Register allocation is a compiler phase in which the gains can be essential in achieving performance on new architec-tures exploiting instruction level parallelism. We focus our attention on loops and improve the existing methods by introducing a new kind of graph. We model loop unrolling and register allocation together in a common framework, called the meeting graph. We expect our results to signiicantly improve loop register allocation while keeping the amount of code replication low. As a byproduct, we present an optimal algorithm for allocating loop variables to a rotating register le, as well as a new heuristic for loop variables spilling. 1 Introduction The eeciency of register allocation is a crucial problem in modern microprocessors, where the increasing gap between the internal clock cycle and memory latency exacerbates the need to keep the variables in registers and to avoid spill code. In this paper, we address the important problem of loop register allocation and spilling. The two main facts that have motivated our work are the following. First, the usual interference graphs resulting from loop code are circular interval graphs (CIG) 8], on which usual graph problems are known to be easier than on general graphs 6]. Second, loop software pipelining 10], that is necessary to exploit the instruction level parallelism, generates variable lifetimes that may span more than one iteration, enforcing software (loop unrolling 10, 4]) or hardware (rotating registers le 13]) techniques to be used. These two facts have always been treated separately. Our starting point was the following question : what is the eeect of loop unrolling on the interference graph ? Especially, how does its chromatic number evolve with loop unrolling ? To study this question, we have used a new kind of graph, that we call the meeting graph. Its main property is that, in addition to all information contained in the interference graph, it takes into account the loop structure of the code. On the basis of the meeting graph, this paper presents the following results.