On the CADNA software:

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 and J.-M. Chesneaux. CADNA: a library for estimating round-off error propagation. Computer Physics Communications, 178(12):933-955, 2008. [ bib ]

F. Jézéquel, J.-M. Chesneaux, and J.-L. Lamotte. A new version of the CADNA library for estimating round-off error propagation in Fortran programs. Computer Physics Communications, 181(11):1927-1928, 2010. [ bib ]

J.-L. Lamotte, J.-M. Chesneaux, and F. Jézéquel. CADNA_C: A version of CADNA for use with C or C++ programs. Computer Physics Communications, 181(11):1925-1926, 2010. [ bib ]

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 ]

On Stochastic Arithmetic in Multiprecision:

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 CADNA for CPU-GPU simulations:

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 ]

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 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 ]

More information can be requested to the CADNA team