An Abstract Domain to Infer Linear Absolute Value Equalities

Abstract

The classic linear (technically, affine) equality abstract domain, which can infer linear equality relations among variables of a program automatically, is one of the earliest and fundamental abstract domains. As a lightweight relational abstract domain, it has been widely used in program analysis. However, it cannot express non-convex properties that appear naturally due to the inherent disjunctive behaviors in a program. In this paper, we introduce a new abstract domain, namely the abstract domain of linear absolute value equalities, which generalizes the linear equality abstract domain with absolute value terms of variables. More clearly, we leverage the absolute value function to design the new abstract domain for discovering linear equality relations among values and absolute values of program variables. The new abstract domain can be used to infer piecewise linear behaviors (e.g., due to conditional branches, absolute value function calls, max/min function calls, etc.) in a program. Experimental results of our prototype are encouraging: In practice, the new abstract domain can find interesting piece-wise linear invariants that are non-convex and out of the expressiveness of the linear equality domain.