Formal Verification of a Floating-Point Expansion Renormalization Algorithm

Boldo, Sylvie; Joldeş, Mioara; Muller, Jean-Michel; Popescu, Valentina

doi:10.1007/978-3-319-66107-0_7

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…The Algorithms on TW presented in this paper use as basic blocks the 2Sum, Fast2Sum and 2Prod algorithms presented in the previous section, as well as the following, less classical, VecSum and VecSumErrBranch algorithms. Many properties of these algorithms have been proven elsewhere [26], [24], [2], but in this paper, we will need specific properties, presented below.…”

Section: Other Basic Blocksmentioning

confidence: 99%

Algorithms for Triple-Word Arithmetic

Fabiano¹,

Muller

Picot

2019

IEEE Trans. Comput.

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Triple-word arithmetic consists in representing high-precision numbers as the unevaluated sum of three floating-point numbers (with "nonoverlapping" constraints that are explicited in the paper). We introduce and analyze various algorithms for manipulating triple-word numbers: rounding a triple-word number to a floating-point number, adding, multiplying, dividing, and computing square-roots of triple-word numbers, etc. We compare our algorithms, implemented in the Campary library, with other solutions of comparable accuracy. It turns out that our new algorithms are significantly faster than what one would obtain by just using the usual floating-point expansion algorithms in the special case of expansions of length 3.

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Section: Other Basic Blocksmentioning

confidence: 99%

Algorithms for Triple-Word Arithmetic

Fabiano¹,

Muller

Picot

2019

IEEE Trans. Comput.

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“…Following are two examples of verifying other kinds of algorithms. Boldo et al gave [44] a formal correctness proof in Coq of a new renormalization algorithm, which is used in floating-point expansion (FPE). Hasan and Tahar present [45] the formal verification of Markov's and Chebyshev's inequalities for discrete random variables in HOL.…”

Section: Proofs Of Differential Privacymentioning

confidence: 99%

Formal methods for statistical software

Black¹

2019

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Statistical software" encompasses several distinct classes of software. This report explains what formal methods, tools, and approaches may be able to increase assurance of results of using statistical software and implementing differential privacy. To provide context, we present an exemplary process for assured results. The parts are data assurance, algorithm design, software production, correctness proofs, postproduction assurance of software, and result checking. We note a workshop we organized to support this paper and finish with recommended formal methods, tools, and researchers doing particularly pertinent work.

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“…Recent work in this direction includes Hölzl's comprehensive formalization [51] of Markov chains, an abstract model of probabilistic systems that has numerous applications. Such work has generally been done using versions of HOL and Isabelle/HOL, but floating-point algorithms have also been verified using Coq [52].…”

Section: Formalizing Mathematicsmentioning

confidence: 99%

Computational logic: its origins and applications

Paulson¹

2018

Proc. R. Soc. A.

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Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the ‘logic for computable functions (LCF) approach’ pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users’ code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.

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Formal Verification of a Floating-Point Expansion Renormalization Algorithm

Cited by 6 publications

References 17 publications

Algorithms for Triple-Word Arithmetic

Algorithms for Triple-Word Arithmetic

Formal methods for statistical software

Computational logic: its origins and applications

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