Making numerical program analysis fast

Abstract

Numerical abstract domains are a fundamental component in modern static program analysis and are used in a wide range of scenarios (e.g. computing array bounds, disjointness, etc). However, analysis with these domains can be very expensive, deeply affecting the scalability and practical applicability of the static analysis. Hence, it is critical to ensure that these domains are made highly efficient.In this work, we present a complete approach for optimizing the performance of the Octagon numerical abstract domain, a domain shown to be particularly effective in practice. Our optimization approach is based on two key insights: i) the ability to perform online decomposition of the octagons leading to a massive reduction in operation counts, and ii) leveraging classic performance optimizations from linear algebra such as vectorization, locality of reference, scalar replacement and others, for improving the key bottlenecks of the domain. Applying these ideas, we designed new algorithms for the core Octagon operators with better asymptotic runtime than prior work and combined them with the optimization techniques to achieve high actual performance. We implemented our approach in the Octagon operators exported by the popular APRON C library, thus enabling existing static analyzers using APRON to immediately benefit from our work.To demonstrate the performance benefits of our approach, we evaluated our framework on four published static analyzers showing massive speedups for the time spent in Octagon analysis (e.g., up to 146x) as well as significant end-to-end program analysis speedups (up to 18.7x). Based on these results, we believe that our framework can serve as a new basis for static analysis with the Octagon numerical domain.

Fast Numerical Program Analysis with Reinforcement Learning

“…As we will see later, we accomplish this by leveraging recent advances in online decomposition for numerical domains [20][21][22]. We show how to do that for the notoriously expensive Polyhedra analysis; however, the approach is easily extendable to other popular numerical domains, which all benefit from decomposition.…”

“…Ideally, one would always determine and maintain this finest partition for each output Z of a transformer but it may be too expensive to compute. Thus, the online decomposition in [20,21] often computes a (cheaply computable) permissible partition π Z π Z . Note that making the output partition coarser (while keeping the same constraints) does not change the precision of the abstract transformer.…”

“…The work of [20,21] improve the performance of Octagon and Polyhedra domain analysis respectively based on online decomposition without losing precision. We compared against [21] in this paper.…”

“…Recent approaches to attacking this problem have focused on two complementary methods. On one hand is work that designs clever algorithms that exploits the special structure of particular abstract domains to speed up analysis [5,10,15,16,20,21]. These works tackle specific types of analyses but the gains in performance can be substantial.…”

Scalable Minimizing-Operators on Polyhedra via Parametric Linear Programming

“…It motivated studying restricted classes of polyhedra, with simpler and faster algorithms, such as octagons [26]; and even these were found to be too slow, motivating recent algorithmic improvements [32]. We instead sought to conserve the domain of polyhedra as originally described [6,12], but with very different algorithms.…”