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This article presents a new numerical abstract domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent invariants of the form (±x ± y ≤ c), where x and y are program variables and c is a real constant. We focus on giving an efficient representation based on Difference-Bound Matrices—O(n2) memory cost, where n is the number of variables—and graph-based algorithms for all common abstract operators—O(n3) time cost. This includes a normal form algorithm to test equivalence of representation and a widening operator to compute least fixpoint approximations.

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