PICOT Romain
رئاسـة البـحث : Fabienne JÉZÉQUEL
Improved numerical reliability of industrial software
Many studies are devoted to performance of numerical simulations. However it is also important to take into account the impact of rounding errors on the results produced. These rounding errors can be estimated with Discrete Stochastic Arithmetic (DSA), implemented in the CADNA library.
Compensated algorithms improve the accuracy of results, without changing the numerical types used. They have been designed to be generally executed with rounding to nearest. We have established error bounds for these algorithms with directed rounding and shown that they can be used successfully with the random rounding mode of DSA.
We have also studied the impact of a target precision of the results on the numerical types of the different variables. We have developed the PROMISE tool which automatically performs these type changes while validating the results thanks to DSA. The PROMISE tool has thus provided new configurations of types combining single and double precision in various programs and in particular in the MICADO code developed at EDF.
We have shown how to estimate with DSA rounding errors generated in quadruple precision. We have proposed a version of CADNA that integrates quadruple precision and that allowed us in particular to validate the computation of multiple roots of polynomials. Finally we have used this new version of CADNA in the PROMISE tool so that it can provide configurations with three types (single, double and quadruple precision).
مناقـشـة مـذكـرة : 27/03/2018
أعـضاء لجنة المناقـشة :
Sylvie BOLDO, Directrice de recherches, Inria Saclay, Rapporteur
Philippe LANGLOIS, Professeur, Université de Perpignan Via Domitia, Rapporteur
François FÉVOTTE, Ingénieur-Chercheur, Docteur, EDF R&D
Stef GRAILLAT, Professeur, Sorbonne Université
Fabienne JÉZÉQUEL, Maître de conférences, HDR, Université Paris 2 et LIP6
Lionel LACASSAGNE, Professeur, Sorbonne Université
Bruno LATHUILIÈRE, Ingénieur-Chercheur, Docteur, EDF R&D
Nathalie REVOL, Chargée de recherches, Inria Rhône-Alpes
إصدارات 2015-2019
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2019
- S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic”, Journal of computational science, vol. 36, pp. 101017, (Elsevier) (2019)
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2018
- R. Picot : “Amélioration de la fiabilité numérique de codes de calcul industriels”, أطروحة, مناقـشـة مـذكـرة 27/03/2018, رئاسـة البـحث Jézéquel, Fabienne (2018)
- S. Graillat, F. Jézéquel, R. Picot : “Numerical Validation of Compensated Algorithms with Stochastic Arithmetic”, Applied Mathematics and Computation, vol. 329, pp. 339-363, (Elsevier) (2018)
- S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “Numerical validation in quadruple precision using stochastic arithmetic”, TNC'18. Trusted Numerical Computations, vol. 8, Kalpa Publications in Computing, Krakow, Poland, pp. 38-53, (EasyChair) (2018)
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2016
- S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “PROMISE: floating-point precision tuning with stochastic arithmetic”, 17th international symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN 2016), UPPSALA, Sweden, pp. 98-99 (2016)
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2015
- S. Graillat, F. Jézéquel, R. Picot : “Numerical Validation of Compensated Summation Algorithms with Stochastic Arithmetic”, 8th International Workshop on Numerical Software Verification, NSV 2015, vol. 317, Electronic Notes in Theoretical Computer Science, Seattle, United States, pp. 55-69, (Elsevier) (2015)