Automating the Verification of Floating-Point Programs

Fumex, Clément; Marché, Claude; Moy, Yannick

doi:10.1007/978-3-319-72308-2_7

Cited by 9 publications

(12 citation statements)

References 31 publications

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“…Previous work [32] reported that SMT support for floating-point arithmetic is rather limited. However, with recent advances [18], we evaluate the situation again.…”

Section: Evaluation Of Smt Floating-point Supportmentioning

confidence: 99%

Deductive Verification of Floating-Point Java Programs in KeY

Abbasi

Schiffl

Darulová

et al. 2021

Tools and Algorithms for the Construction and Analysis of Systems

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Deductive verification has been successful in verifying interesting properties of real-world programs. One notable gap is the limited support for floating-point reasoning. This is unfortunate, as floating-point arithmetic is particularly unintuitive to reason about due to rounding as well as the presence of the special values infinity and ‘Not a Number’ (NaN). In this paper, we present the first floating-point support in a deductive verification tool for the Java programming language. Our support in the KeY verifier handles arithmetic via floating-point decision procedures inside SMT solvers and transcendental functions via axiomatization. We evaluate this integration on new benchmarks, and show that this approach is powerful enough to prove the absence of floating-point special values—often a prerequisite for further reasoning about numerical computations—as well as certain functional properties for realistic benchmarks.

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“…Previous work [32] reported that SMT support for floating-point arithmetic is rather limited. However, with recent advances [18], we evaluate the situation again.…”

Section: Evaluation Of Smt Floating-point Supportmentioning

confidence: 99%

Deductive Verification of Floating-Point Java Programs in KeY

Abbasi

Schiffl

Darulová

et al. 2021

Tools and Algorithms for the Construction and Analysis of Systems

View full text Add to dashboard Cite

show abstract

“…It was reported in previous work [30] that SMT support for floating-point arithmetic is rather limited. However, with recent advances [16], we evaluate the situation again.…”

Section: Evaluation Of Smt Floating-point Supportmentioning

confidence: 99%

“…While deductive verifiers fully implement many sophisticated data representations (including heap data structures, objects, and ownership), support for floating-point numbers remains rather limited -solely Frama-C and SPARK offer automated support for floating-point arithmetic in C and Ada [30]. This state of affairs is at least partially a result of previous limitations in floating-point support in SMT solvers.…”

Section: Introductionmentioning

confidence: 99%

“…This state of affairs is at least partially a result of previous limitations in floating-point support in SMT solvers. Consequently, deductive verification has been used for floating-point programs only by experts with considerable manual effort [13,30]. This is unfortunate as it makes deductive verification unavailable for a large number of programs across many domains including embedded systems, machine learning, and scientific computing.…”

Section: Introductionmentioning

confidence: 99%

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Deductive Verification of Floating-Point Java Programs in KeY

Abbasi

Schiffl

Darulová

et al. 2021

Preprint

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Deductive verification has been successful in verifying interesting properties of real-world programs. One notable gap is the limited support for floating-point reasoning. This is unfortunate, as floating-point arithmetic is particularly unintuitive to reason about due to rounding as well as the presence of the special values infinity and 'Not a Number' (NaN). In this paper, we present the first floating-point support in a deductive verification tool for the Java programming language. Our support in the KeY verifier handles arithmetic via floating-point decision procedures inside SMT solvers and transcendental functions via axiomatization. We evaluate this integration on new benchmarks, and show that this approach is powerful enough to prove the absence of floating-point special values-often a prerequisite for further reasoning about numerical computations-as well as certain functional properties for realistic benchmarks.

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“…This gives a high level of confidence in the correctness of our formalization. A more detailed presentation of Layer 1 is given in this technical report [11].…”

Section: Function Round Mode Real : Realmentioning

confidence: 99%

A Three-Tier Strategy for Reasoning About Floating-Point Numbers in SMT

Conchon

Iguernelala

et al. 2017

Computer Aided Verification

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The SMT-LIB standard defines a formal semantics for a theory of floating-point (FP) arithmetic (FPA). This formalization reduces FP operations to reals by means of a rounding operator, as done in the IEEE-754 standard. Closely following this description, we propose a three-tier strategy to reason about FPA in SMT solvers. The first layer is a purely axiomatic implementation of the automatable semantics of the SMT-LIB standard. It reasons with exceptional cases (e.g. overflows, division by zero, undefined operations) and reduces finite representable FP expressions to reals using the rounding operator. At the core of our strategy, a second layer handles a set of lemmas about the properties of rounding. For these lemmas to be used effectively, we extend the instantiation mechanism of SMT solvers to tightly cooperate with the third layer, the NRA engine of SMT solvers, which provides interval information. We implemented our strategy in the Alt-Ergo SMT solver and validated it on a set of benchmarks coming from the SMT-LIB competition, but also from the deductive verification of C and SPARK programs. The results show that our approach is promising and compete with existing techniques implemented in state-of-the-art SMT solvers.

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Automating the Verification of Floating-Point Programs

Cited by 9 publications

References 31 publications

Deductive Verification of Floating-Point Java Programs in KeY

Deductive Verification of Floating-Point Java Programs in KeY

Deductive Verification of Floating-Point Java Programs in KeY

A Three-Tier Strategy for Reasoning About Floating-Point Numbers in SMT

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