A unified Coq framework for verifying C programs with floating-point computations

Ramananandro, Tahina; Mountcastle, Paul; Meister, Benoit; Lethin, Richard

doi:10.1145/2854065.2854066

Cited by 23 publications

(16 citation statements)

References 27 publications

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“…VIII. RELATED WORK a) Sound Accuracy Analysis: The tools FPTaylor [37], Gappa [13], PRECiSa [31], real2float [29] and VCFloat [34] are most closely related to our work as they formally verify floating-point roundoff errors. Each tool handles mixedprecision floating-point arithmetic, but other features differ slightly between tools.…”

Section: Discussionmentioning

confidence: 99%

“…PRECiSa and Gappa generate a proof certificate by instantiating library theorems, explicitly encoding verification steps. Any tool that explicitly encodes verification steps, or is to be used interactively [14,34] requires expert knowledge in IEEE754 floating-point semantics [20] or formal verification; in contrast our goal is to make our tool usable by non-experts. Finally, in-logic verification of certificates can often become unreasonably slow.…”

Section: Introductionmentioning

confidence: 99%

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A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

Becker

Zyuzin

Monat

et al. 2018

2018 Formal Methods in Computer Aided Design (FMCAD)

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Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing. Due to the discrepancy between continuous reals and discrete finite-precision values, automated static analysis tools are highly valuable to estimate roundoff errors. The results, however, are only as correct as the implementations of the static analysis tools. This paper presents a formally verified and modular tool which fully automatically checks the correctness of finite-precision roundoff error bounds encoded in a certificate. We present implementations of certificate generation and checking for both Coq and HOL4 and evaluate it on a number of examples from the literature. The experiments use both in-logic evaluation of Coq and HOL4, and execution of extracted code outside of the logics: we benchmark Coq extracted unverified OCaml code and a CakeML-generated verified binary.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

Becker

Zyuzin

Monat

et al. 2018

2018 Formal Methods in Computer Aided Design (FMCAD)

View full text Add to dashboard Cite

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“…Whole program accuracy can be formally verified w.r.t. to a real-valued implementation with substantial user interaction and expertise [34]. Verification of elementary function implementations has also recently been automated, but requires substantial compute resources [23].…”

Section: Related Workmentioning

confidence: 99%

Icing: Supporting Fast-Math Style Optimizations in a Verified Compiler

Becker

Darulová

Myreen

et al. 2019

Computer Aided Verification

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Verified compilers like CompCert and CakeML offer increasingly sophisticated optimizations. However, their deterministic source semantics and strict IEEE 754 compliance prevent the verification of "fast-math" style floating-point optimizations. Developers often selectively use these optimizations in mainstream compilers like GCC and LLVM to improve the performance of computations over noisy inputs or for heuristics by allowing the compiler to perform intuitive but IEEE 754-unsound rewrites. We designed, formalized, implemented, and verified a compiler for Icing, a new language which supports selectively applying fast-math style optimizations in a verified compiler. Icing's semantics provides the first formalization of fast-math in a verified compiler. We show how the Icing compiler can be connected to the existing verified CakeML compiler and verify the end-to-end translation by a sequence of refinement proofs from Icing to the translated CakeML. We evaluated Icing by incorporating several of GCC's fast-math rewrites. While Icing targets CakeML's source language, the techniques we developed are general and could also be incorporated in lower-level intermediate representations.

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“…These techniques can prove the absence of runtime errors, such as division-by-zero, but cannot quantify roundoff errors. Floating-point arithmetic has also been formalized in theorem provers and entire numerical programs have been proven correct and accurate within these [7,39]. Most of these formal verification efforts are, however, to a large part manual.…”

Section: Related Workmentioning

confidence: 99%

Daisy - Framework for Analysis and Optimization of Numerical Programs (Tool Paper)

Darulová

Izycheva

Nasir

et al. 2018

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Automated techniques for analysis and optimization of finite-precision computations have recently garnered significant interest. Most of these were, however, developed independently. As a consequence, reuse and combination of the techniques is challenging and much of the underlying building blocks have been re-implemented several times, including in our own tools. This paper presents a new framework, called Daisy, which provides in a single tool the main building blocks for accuracy analysis of floating-point and fixed-point computations which have emerged from recent related work. Together with its modular structure and optimization methods, Daisy allows developers to easily recombine, explore and develop new techniques. Daisy's input language, a subset of Scala, and its limited dependencies make it furthermore user-friendly and portable.

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A unified Coq framework for verifying C programs with floating-point computations

Cited by 23 publications

References 27 publications

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

Icing: Supporting Fast-Math Style Optimizations in a Verified Compiler

Daisy - Framework for Analysis and Optimization of Numerical Programs (Tool Paper)

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