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Multi angle Programming with numerical uncertainties

Auteurs : Darulova, Eva (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. Finite-precision arithmetic, such as fixed-point or floating-point, is a common and efficient choice, but introduces an uncertainty on the computed result that is often very hard to quantify. We need adequate tools to estimate the errors introduced in order to choose suitable approximations which satisfy the accuracy requirements.
    I will present a new programming model where the scientist writes his or her numerical program in a real-valued specification language with explicit error annotations. It is then the task of our verifying compiler to select a suitable floating-point or fixed-point data type which guarantees the needed accuracy. I will show how a combination of SMT theorem proving, interval and affine arithmetic and function derivatives yields an accurate, sound and automated error estimation which can handle nonlinearity, discontinuities and certain classes of loops.
    Additionally, finite-precision arithmetic is not associative so that different, but mathematically equivalent, orders of computation often result in different magnitudes of errors. We have used this fact to not only verify but actively improve the accuracy by combining genetic programming with our error computation with encouraging results.

    Codes MSC :
    65G50 - Roundoff error
    68Q60 - Specification and verification (program logics, model checking, etc.)
    68T20 - Problem solving (heuristics, search strategies, etc.)
    68N30 - Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)

    Informations sur la rencontre

    Nom du congrès : Effective analysis: foundations, implementations, certification / Analyse effective: fondations, programmation, certification
    Organisteurs Congrès : Mahboubi, Assia ; Schuster, Peter ; Spitters, Bas
    Dates : 11/01/06 - 15/01/16
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1508.html

    Citation Data

    DOI : 10.24350/CIRM.V.18915503
    Cite this video as: Darulova, Eva (2016). Programming with numerical uncertainties.CIRM .Audiovisual resource. doi:10.24350/CIRM.V.18915503
    URI : http://dx.doi.org/10.24350/CIRM.V.18915503


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