Make it real: Effective floating-point reasoning via exact arithmetic

Leeser, Miriam; Mukherjee, Saoni; Ramachandran, Jaideep; Wahl, Thomas

doi:10.7873/date2014.130

Cited by 10 publications

(12 citation statements)

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“…FPhile uses Z3 as its backend SMT solver. Leeser et al [32] translate a given floating-point formula into a corresponding formula for real numbers with appropriately defined rounding operators. Ariadne [2] relies on SMT solving for detecting floating-point exceptions.…”

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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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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“…[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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“…without approximations) over the theory of real and integer arithmetic [7]. In conformance with the Standard, it does so by replacing floating-point expressions with "infinitely precise" real-arithmetic expressions, followed by rounding the result.…”

Section: Realizermentioning

confidence: 99%

“…The floating-point constraints generated by Spf are passed to Realizer [7], a decision procedure for precise floating-point reasoning. The combination of Spf and Realizer thus enables the accurate analysis of programs manipulating floating point numbers.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Execution for Checking the Accuracy of Floating-Point Programs

Ramachandran

Păsăreanu

Wahl

2015

SIGSOFT Softw. Eng. Notes

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Programs with floating-point calculations tend to give rise to hard-to-predict behavior. Such uncertainty cannot be ignored: floating-point errors can have catastrophic consequences, as it happened with the Patriot missile accident in 1991. The likelihood of such incidents can be decreased by using automated technology to reliably analyze numerical code. We present a symbolic execution approach to checking the accuracy of numerical programs, investigating how much a floating-point computation deviates from the "ideal" computation on real values. Our method is implemented in the Symbolic PathFinder tool and leverages and extends the floating-point decision procedure Realizer to check symbolic path constraints and to perform the accuracy checks. We further illustrate the possibility of using our tools to enhance abstract interpretation-based analyses to obtain tighter bounds on the numerical error introduced by floating-point computations. Initial experiments show the promise of our approach.

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Make it real: Effective floating-point reasoning via exact arithmetic

Cited by 10 publications

References 0 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

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

Symbolic Execution for Checking the Accuracy of Floating-Point Programs

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