A Register Allocation Framework Based on Hierarchical Cyclic Interval Graphs

In this paper, we propose the use of cyclic interval graphs as an alternative representation for register allocation. The \thickness" of the cyclic interval graph captures the notion of overlap between live ranges of variables relative to each particular point of time in the program execution. We demonstrate that cyclic interval graphs provide a feasible and e ective representation that accurately captures the periodic nature of live ranges found in loops. A new heuristic algorithm for minimum register allocation, the fat cover algorithm, has been developed and implemented to exploit such program structure. In addition, a new spilling algorithm is proposed that makes use of the extra information available in the interval graph representation. These two algorithms work together to provide a two-phase register allocation process that does not require iteration of the spilling or coloring phases. We extend the notion of cyclic interval graphs to hierarchical cyclic interval graphs and we outline a framework for a compiler to use this representation when performing register allocation for programs with hierarchical control structure such as nested conditionals and loops. The e ectiveness of our approach has been demonstrated by experimenting with a collection of challenging loops. i