J. Chesneaux, HabilitationàHabilitation`Habilitationà diriger des recherches, 1995.

T. J. Dekker, A floating-point technique for extending the available precision, Numerische Mathematik, vol.5, issue.3, pp.224-242, 1971.
DOI : 10.1007/BF01397083

P. Eberhart, J. Brajard, P. Fortin, and F. Jézéquel, High performance numerical validation using stochastic arithmetic, Reliable Computing, vol.21, pp.35-52, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01254446

P. Eberhart, J. Brajard, P. Fortin, and F. Jézéquel, Estimation of Round-off Errors in OpenMP Codes, IWOMP 2016 -12th International Workshop on OpenMP, pp.3-16, 2016.
DOI : 10.1007/978-94-015-8354-1

URL : https://hal.archives-ouvertes.fr/hal-01380131

L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, MPFR, ACM Transactions on Mathematical Software, vol.33, issue.2, pp.1-13, 2007.
DOI : 10.1145/1236463.1236468

URL : https://hal.archives-ouvertes.fr/inria-00103655

S. Graillat, F. Jézéquel, and M. S. Ibrahim, Dynamical control of Newton's method for multiple roots of polynomials, Reliable Computing, vol.21, 2016.

S. Graillat, F. Jézéquel, S. Wang, and Y. Zhu, Stochastic Arithmetic in Multiprecision, Mathematics in Computer Science, vol.15, issue.1, pp.359-375, 2011.
DOI : 10.1016/S0764-4442(99)80439-X

URL : https://hal.archives-ouvertes.fr/hal-01288865

S. Graillat, F. Jézéquel, R. Picot, F. Févotte, and B. Lathuilì-ere, Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01331917

S. Graillat, F. Jézéquel, R. Picot, F. Févotte, and B. Lathuilì-ere, PROMISE: floating-point precision tuning with stochastic arithmetic, 17th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01355005

Y. Hida, X. S. Li, and D. H. Bailey, Library for double-double and quad-double arithmetic, 2008.

M. Hénon, A two-dimensional mapping with a strange attractor, Communications in Mathematical Physics, vol.20, issue.1, pp.69-77, 1976.
DOI : 10.1007/BF01608556

F. Jézéquel and J. Chesneaux, CADNA: a library for estimating round-off error propagation, Computer Physics Communications, vol.178, issue.12, pp.933-955, 2008.
DOI : 10.1016/j.cpc.2008.02.003

M. Joldes, J. Muller, and V. Popescu, Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic, ACM Transactions on Mathematical Software, vol.44, issue.2, pp.15-16, 2017.
DOI : 10.1137/050645671

V. Lefèvre and P. Zimmermann, Optimized Binary64 and Binary128 Arithmetic with GNU MPFR, 2017 IEEE 24th Symposium on Computer Arithmetic (ARITH), 2017.
DOI : 10.1109/ARITH.2017.28

S. Montan, J. Chesneaux, C. Denis, and J. Lamotte, Towards an efficient implementation of CADNA in the BLAS: example of DgemmCADNA routine, 15th GAMM -IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN), 2012.
URL : https://hal.archives-ouvertes.fr/hal-00765529

S. International and . Inc, The SPARC Architecture Manual, 1992.

S. International and . Inc, The SPARC Architecture Manual, Version 9, 1994.

J. Vignes, Discrete Stochastic Arithmetic for Validating Results of Numerical Software, Numerical Algorithms, vol.37, issue.1-4, pp.377-390, 2004.
DOI : 10.1023/B:NUMA.0000049483.75679.ce

URL : https://hal.archives-ouvertes.fr/hal-01146498

A. Zeller, Why Programs Fail: A Guide to Systematic Debugging, 2009.