Parameterized Construction of Program Representations for Sparse Dataflow Analyses

Abstract

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.

Validation of memory accesses through symbolic analyses

“…We split the live range of a variable v, at program label l, by inserting a copy v = v at l and renaming every use of v to v in points dominated by l. According to Tavares et al [32], it is enough to split live ranges at places where information originates. These places depend on the type of static analysis that we consider.…”

Pointer disambiguation via strict inequalities

“…Sparsity is good for: (i) time and space, as it reduces from cubic to quadratic (on the number of variables) the amount of information that needs to be stored; and (ii) correctness, as it simplifies all the proofs of theorems. A dataflow analysis is said to be sparse if it runs on a program representation that ensures the Static Single Information (SSI) Property [38]. To keep this paper self-contained, we quote Tavares et al's notion of single information property: Following Tavares et al [38], to ensure the SSI property, we split the live range of every variable x at each program point where new information about x can appear.…”

“…The insight that such techniques are effective and useful to such purpose is the key contribution of this paper. However, we go beyond: we rely on recent advances on the construction of sparse dataflow analyses [38] to design an efficient way to solve less-than inequalities. The sparse implementation lets us view this problem as an instance of the abstract interpretation framework; hence, we get correctness for free.…”

Symbolic range analysis of pointers

“…Sparsity is possible because the e-SSA form renames variables at each program point where new abstract information, e.g., ranges of integers and pointers, arises. According to Tavares et al [Tavares et al, 2014], this property single information is sucient to enable sparse implementation of non-relational static analyses [Tavares et al, 2014].…”