Punctual coalescing

Abstract

Compilers use register coalescing to avoid generating code for copy instructions. For architectures with register aliasing such as x86, Smith, Ramsey, and Holloway (2004) presented a polynomial-time approach, while Scholz and Eckstein (2002) presented an optimal, exponential-time approach together with a near-optimal, quadratic-time heuristic. Both methods scale poorly after aggressive live range splitting, especially for programs in elementary form where live ranges are split at every program point. In contrast, we mentioned in a previous paper (2008), without giving details, that we have a scalable, linear-time heuristic for programs in elementary form. In an effort to formalize that heuristic, we discovered an even better algorithm, called Punctual Coalescing, which we present here. Punctual Coalescing is scalable, linear time, locally optimal in general, close to globally optimal for straight-line code, and proven correct with the Twelf theorem prover. We define global optimality with an ILP-formulation and we show via experiments that Punctual Coalescing compares well to this and two other approaches. © 2010 Springer-Verlag.