Abstract. Data-flow analyses usually associate information with control flow regions. Informally, if these regions are too small, like a point between two consecutive statements, we call the analysis dense. On the other hand, if these regions include many such points, then we call it sparse. This paper presents a systematic method to build program representations that support sparse analyses. To pave the way to this framework we clarify the bibliography about well-known intermediate program representations. We show that our approach, up to parameter choice, subsumes many of these representations, such as the SSA, SSI and e-SSA forms. In particular, our algorithms are faster, simpler and more frugal than the previous techniques used to construct SSI -Static Single Information -form programs. We produce intermediate representations isomorphic to Choi et al.'s Sparse Evaluation Graphs (SEG) for the family of data-flow problems that can be partitioned per variables. However, contrary to SEGs, we can handle -sparsely -problems that are not in this family. We have tested our ideas in the LLVM compiler, comparing different program representations in terms of size and construction time.

Recent results have shown how to do graph-coloring-based register allocation in a way that decouples spilling from register assignment. This decoupled approach has the main advantage of simplifying the implementation of register allocators. However, the decoupled model, as described in previous works, faces many problems when dealing with register aliasing, a phenomenon typical in architectures usually seen in embedded systems, such as ARM. In this paper we introduce the semi-elementary form, a program representation that brings decoupled register allocation to architectures with register aliasing. The semi-elementary form is much smaller than program representations used by previous decoupled solutions; thus, leading to register allocators that perform better in terms of time and space. Furthermore, this representation reduces the number of copies that traditional allocators insert into assembly programs. We have empirically validated our results by showing how our representation improves two well known graph coloring based allocators, namely the Iterated Register Coalescer (IRC), and Bouchez et al.'s brute force (BF) method, both augmented with Smith et al. extensions to handle aliasing. Running our techniques on SPEC CPU 2000, we have reduced the number of nodes in the interference graphs by a factor of 4 to 5; hence, speeding-up allocation time by a factor of 3 to 5. Additionally the semi-elementary form reduces by 8% the number of copies that IRC leaves uncoalesced.