Verifying floating-point programs with constraint programming and abstract interpretation techniques

Ponsini, Olivier; Michel, Claude; Rueher, Michel

doi:10.1007/s10515-014-0154-2

Cited by 11 publications

(6 citation statements)

References 25 publications

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“…Based on this work, a tool called RangeLab is implemented (Martel 2011) and a technique for improving accuracy of floating-point computations is presented (Martel 2009). Ponsini et al (2014) propose constraint solving techniques for improving the precision of floating-point abstractions. Our results show that interval abstractions and affine arithmetic can yield pessimistic error bounds for nonlinear computations.…”

Section: Related Workmentioning

confidence: 99%

Rigorous Estimation of Floating-Point Round-Off Errors with Symbolic Taylor Expansions

Solovyev

Baranowski

Briggs

et al. 2018

ACM Trans. Program. Lang. Syst.

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Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide very pessimistic overestimates, causing unnecessary verification failure. We have developed a new approach called Symbolic Taylor Expansions that avoids these problems, and implemented a new tool called FPTaylor embodying this approach. Key to our approach is the use of rigorous global optimization, instead of the more familiar interval arithmetic, affine arithmetic, and/or SMT solvers. FPTaylor emits per-instance analysis certificates in the form of HOL Light proofs that can be machine checked. In this article, we present the basic ideas behind Symbolic Taylor Expansions in detail. We also survey as well as thoroughly evaluate six tool families, namely, Gappa (two tool options studied), Fluctuat, PRECiSA, Real2Float, Rosa, and FPTaylor (two tool options studied) on 24 examples, running on the same machine, and taking care to find the best options for running each of these tools. This study demonstrates that FPTaylor estimates round-off errors within much tighter bounds compared to other tools on a significant number of case studies. We also release FPTaylor along with our benchmarks, thus contributing to future studies and tool development in this area.

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Section: Related Workmentioning

confidence: 99%

Rigorous Estimation of Floating-Point Round-Off Errors with Symbolic Taylor Expansions

Solovyev

Baranowski

Briggs

et al. 2018

ACM Trans. Program. Lang. Syst.

View full text Add to dashboard Cite

Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide very pessimistic overestimates, causing unnecessary verification failure. We have developed a new approach called Symbolic Taylor Expansions that avoids these problems, and implemented a new tool called FPTaylor embodying this approach. Key to our approach is the use of rigorous global optimization, instead of the more familiar interval arithmetic, affine arithmetic, and/or SMT solvers. FPTaylor emits per-instance analysis certificates in the form of HOL Light proofs that can be machine checked. In this article, we present the basic ideas behind Symbolic Taylor Expansions in detail. We also survey as well as thoroughly evaluate six tool families, namely, Gappa (two tool options studied), Fluctuat, PRECiSA, Real2Float, Rosa, and FPTaylor (two tool options studied) on 24 examples, running on the same machine, and taking care to find the best options for running each of these tools. This study demonstrates that FPTaylor estimates round-off errors within much tighter bounds compared to other tools on a significant number of case studies. We also release FPTaylor along with our benchmarks, thus contributing to future studies and tool development in this area.

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“…Based on this work, a tool called RangeLab is implemented [36] and a technique for improving accuracy of floating-point computations is presented [35]. Ponsini et al [49] propose constraint solving techniques for improving the precision of floating-point abstractions. Our results show that interval abstractions and affine arithmetic can yield pessimistic error bounds for nonlinear computations.…”

Section: Related Workmentioning

confidence: 99%

Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

Solovyev

Jacobsen

Rakamarić

et al. 2015

FM 2015: Formal Methods

123

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Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide overestimates. Also, there are no available rigorous approaches that handle transcendental functions. We have developed a new approach called Symbolic Taylor Expansions that avoids this difficulty, and implemented a new tool called FPTaylor embodying this approach. Key to our approach is the use of rigorous global optimization, instead of the more familiar interval arithmetic, affine arithmetic, and/or SMT solvers. In addition to providing far tighter upper bounds of round-off error in a vast majority of cases, FPTaylor also emits analysis certificates in the form of HOL Light proofs. We release FPTaylor along with our benchmarks for evaluation. Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor ExpansionsAlexey Solovyev, Charles Jacobsen, Zvonimir Rakamarić, and Ganesh Gopalakrishnan School of Computing, University of Utah, Salt Lake City, UT 84112, USA {monad,charlesj,zvonimir,ganesh}@cs.utah.edu Abstract. Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide overestimates. Also, there are no available rigorous approaches that handle transcendental functions. We have developed a new approach called Symbolic Taylor Expansions that avoids this difficulty, and implemented a new tool called FPTaylor embodying this approach. Key to our approach is the use of rigorous global optimization, instead of the more familiar interval arithmetic, affine arithmetic, and/or SMT solvers. In addition to providing far tighter upper bounds of round-off error in a vast majority of cases, FPTaylor also emits analysis certificates in the form of HOL Light proofs. We release FPTaylor along with our benchmarks for evaluation.

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“…[4], [8], [22], [23], [39]), and various methods have been proposed for verifying floating-point properties through abstract interpretation [35], [36], [65], decision procedures [16], [40], [50], [81], [82], theorem proving [9], [10], and combinations of techniques [13], [14], [62], [63]. Recent work has also focused on estimating bounds on round-off error in floating-point computation [26], [55], [73].…”

Section: Related Workmentioning

confidence: 99%

Floating-point symbolic execution: A case study in N-version programming

Liew

Schemmel

Cadar

et al. 2017

2017 32nd IEEE/ACM International Conference on Automated Software Engineering (ASE)

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Abstract-Symbolic execution is a well-known program analysis technique for testing software, which makes intensive use of constraint solvers. Recent support for floating-point constraint solving has made it feasible to support floating-point reasoning in symbolic execution tools. In this paper, we present the experience of two research teams that independently added floating-point support to KLEE, a popular symbolic execution engine. Since the two teams independently developed their extensions, this created the rare opportunity to conduct a rigorous comparison between the two implementations, essentially a modern case study on Nversion programming. As part of our comparison, we report on the different design and implementation decisions taken by each team, and show their impact on a rigorously assembled and tested set of benchmarks, itself a contribution of the paper.

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Verifying floating-point programs with constraint programming and abstract interpretation techniques

Cited by 11 publications

References 25 publications

Rigorous Estimation of Floating-Point Round-Off Errors with Symbolic Taylor Expansions

Rigorous Estimation of Floating-Point Round-Off Errors with Symbolic Taylor Expansions

Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

Floating-point symbolic execution: A case study in N-version programming

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