Copy coalescing by graph recoloring

Abstract

Register allocation is always a trade-off between live-range splitting and coalescing. Live-range splitting generally leads to less spilling at the cost of inserting shuffle code. Coalescing removes shuffle code while potentially raising the register demand and causing spilling. Recent research showed that the live-range splitting of the SSA form's Æ-functions leads to chordal interference graphs. This improves upon two long-standing inconveniences of graph coloring register allocation: First, chordal graphs are optimally colorable in quadratic time. Second, the number of colors needed to color the graph is equal to the maximal register pressure in the program. However, the inserted shuffle code incurred by the Æ-functions can slow down the program severely. Hence, to make such an approach work in practice, a coalescing technique is needed that removes most of the shuffle code without causing further spilling. In this paper, we present a coalescing technique designed for, but not limited to, SSA-form register allocation. We exploit that a valid coloring can be easily obtained by an SSA-based register allocator. This initial coloring is then improved by recoloring the interference graph and assigning shuffle-code related nodes the same color. Thereby, we always keep the coloring of the graph valid. Hence, the coalescing is safe, i. e. no spill code will be caused by coalescing. Comparing to iterated register coalescing, the state of the art in safe coalescing, our method is able to remove 22.5% of the costs and 44.3% of the copies iterated coalescing left over. The best solution possible, found by a colaescer using integer linear programming (ILP), was 35.9% of the costs and 51.9% of the copies iterated coalescing left over. The runtime of programs compiled with our heuristic matches that of the programs compiled with the ILP technique.