On CADNA for high performance simulations:

F. Jézéquel, S. sadat Hoseininasab, T. Hilaire. Numerical validation of half precision simulations. 1st Workshop on Code Quality and Security (CQS 2021) , in conjunction with WorldCIST'21 (9th World Conference on Information Systems and Technologies), Terceira Island, Azores, Portugal, March-April 2021. https://hal.archives-ouvertes.fr/hal-03138494

F. Jézéquel. Benefits of stochastic arithmetic in high performance simulations and arbitrary precision codes. plenary presentation, 19th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2020), virtual conference, September 2021.

F. Jézéquel, S. Graillat, D. Mukunoki, T. Imamura, R. Iakymchuk. Can we avoid rounding-error estimation in HPC codes and still get trustworthy results?, NSV'20, 13th International Workshop on Numerical Software Verification, Los Angeles, CA, USA, July 2020. movie of the 30-min talk.

P. Eberhart, B. Landreau, J. Brajard, P. Fortin, and F. Jézéquel. Improving CADNA performance on GPUs. 19th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing (PDSEC) in conjunction with the 32nd International Parallel and Distributed Processing Symposium (IPDPS), Vancouver, Canada, pages 1016-1025, May 2018.

P. Eberhart, J. Brajard, P. Fortin, and F. Jézéquel. Estimation of round-off errors in OpenMP codes. 12th International Workshop on OpenMP (IWOMP), Nara, Japan, October 2016. LNCS 9903, pages 3-16.

P. Eberhart, J. Brajard, P. Fortin, and F. Jézéquel. High performance numerical validation using stochastic arithmetic. Reliable Computing, 21:35-52, 2015. [ bib | pdf ]

F. Jézéquel, J.-L. Lamotte and I. Said. Estimation of numerical reproducibility on CPU and GPU. In 8th Workshop on Computer Aspects of Numerical Algorithms (CANA), Federated Conference on Computer Science and Information Systems (FedCSIS), pages 687-692, Lodz, Poland, September 2015. [ bib ]

On precision autotuning based on CADNA:

Q. Ferro, S. Graillat, T. Hilaire, F. Jézéquel, and B. Lewandowski. Neural Network Precision Tuning Using Stochastic Arithmetic. NSV'22, 15th International Workshop on Numerical Software Verification, Haifa, Israel, August 2022. https://hal.archives-ouvertes.fr/hal-03682645

S. Graillat, F. Jézéquel, R. Picot, F. Févotte, and B. Lathuilière. Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic. Journal of Computational Science, 36, pages 101017, 2019. https://hal.archives-ouvertes.fr/hal-01331917

On CADNA for quadruple precision (128 bits) computation:

S. Graillat, F. Jézéquel, R. Picot, F. Févotte, and B. Lathuilière. Numerical validation in quadruple precision using stochastic arithmetic. TNC'18. Trusted Numerical Computations , M. Martel, N. Damouche, J. Alexandre Dit Sandretto (editors), Kalpa Publications in Computing, vol. 8, pages 38-53, 2018.

On the combination of CADNA and compensated methods :

S. Graillat, F. Jézéquel, and R. Picot. Numerical validation of compensated algorithms with stochastic arithmetic. Applied Mathematics and Computation, 329, pages 339-363, 2018. https://hal.archives-ouvertes.fr/hal-01367769

On the parallelization of CADNA:

F. Jézéquel, J.-L. Lamotte, and O. Chubach. Parallelization of discrete stochastic arithmetic on multicore architectures. In Tenth International Conference on Information Technology: New Generations (ITNG 2013), pages 160-166, April 2013. [ bib ]

On some scientific applications validated using CADNA:

D. Chamont, R. Molina, V. Lafage, F. Jézéquel, Investigating mixed-precision for AGATA pulse-shape analysis. 26th International Conference on Computing in High Energy and Nuclear Physics, (CHEP 2023), Norfolk (USA), May 2023.

P. Fortin, R. Habel, F. Jézéquel, J.-L. Lamotte, and N.S. Scott. Numerical validation and performance optimization on GPUs of an application in atomic physics. In Designing Scientific Applications on GPUs, R. Couturier Ed., Chapman & Hall/CRC, October 2013.

J. Brajard, P. Li, F. Jézéquel, H.-S. Benavides, S. Thiria. Numerical Validation of Data Assimilation Codes Generated by the YAO Software. SIAM Annual Meeting, San Diego, California (USA), July 8-12 2013.

F. Jézéquel and J.-L. Lamotte. Numerical validation of Slater integrals computation on GPU. In The 14th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN'10), pages 78-79, Lyon, France, September 2010. [ bib ]

On Stochastic Arithmetic in Multiprecision:

S. Graillat, F. Jézéquel, E. Queiros Martins, and M. Spyropoulos. Computing multiple roots of polynomials in stochastic arithmetic with Newton method and approximate GCD International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2021), Timisoara, Romania, December 2021. https://hal.inria.fr/hal-03274453

S. Graillat, F. Jézéquel, and M. S. Ibrahim. Dynamical Control of Newton's Method for Multiple Roots of Polynomials. Reliable Computing, 21, pages 117-139, 2016. pdf

S. Graillat, F. Jézéquel, S. Wang, and Y. Zhu. Stochastic Arithmetic in Multiprecision. Mathematics in Computer Science, 5(4):359-375, 2011. [ bib | DOI | http ]

On Discrete Stochastic Arithmetic and the CESTAC method:

J. Vignes. Discrete Stochastic Arithmetic for validating results of numerical software. Numerical Algorithms, 37(1-4):377-390, December 2004. [ bib ]

J. Vignes. A stochastic arithmetic for reliable scientific computation. Mathematics and Computers in Simulation, 35:233-261, 1993. [ bib ]

More information can be requested to the CADNA team
Thanks to Baptiste Mary for the CADNA logo