Section: New Results

Studying Optimal Spilling in the Light of SSA

Participants : Florian Brandner [ENSTA ParisTech] , Quentin Colombet [Apple, Cupertino] , Alain Darte.

Recent developments in register allocation, mostly linked to static single assignment (SSA) form, have shown the benefits of decoupling the problem in two phases: a first spilling phase places load and store instructions so that the register pressure at all program points is small enough, a second assignment and coalescing phase maps the variables to physical registers and reduces the number of move instructions among registers. At the end of Quentin Colombet's PhD thesis, we focused on the first phase, for which many open questions remained: in particular, we studied the notion of optimal spilling (what can be expressed?) and the impact of SSA form (does it help?). To identify the important features for optimal spilling on load-store architectures, we developed a new integer linear programming formulation, more accurate and expressive than previous approaches. Among other features, we can express SSA φ-functions, memory-to-memory copies, and the fact that a value can be stored simultaneously in a register and in memory. Based on this formulation, we presented a thorough analysis of the results obtained for the SPECINT 2000 and EEMBC 1.1 benchmarks, from which we drawed the following conclusions: a) rematerialization is extremely important, b) SSA complicates the formulation of optimal spilling, especially because of memory coalescing when the code is not in conventional SSA (CSSA), c) micro-architectural features are significant and thus have to be accounted for, which is not the case with standard cost functions, d) significant savings can be obtained in terms of static spill costs, cache miss rates, and dynamic instruction counts, e) however, cost models based only on static spill costs are not always relevant, in particular when spilling is “at the limit”: in this situation, bad interactions with register coalescing and post-pass scheduling can be exacerbated and it may be better to spill a bit more. This important observation indicates that more research is needed to explore alternative cost models that reliably guide spilling.

Parts of this work were already published at CASES 2011. The publication at ACM Transactions on Architecture and Code Optimization [1] contains more detailed discussions, more examples illustrating new concepts and existing approaches, and additional experiments covering the observed worst-case behavior, a new post-latency heuristic, and empiric evidence showing why static spill costs are a poor metric. Three configurations were added: Appel and George under SSA, Koes and Goldstein, and the heuristic of Braun and Hack. This work was partly supported by the Mediacom contract with STMicroelectronics (ended in 2013).