M. Goldstein, Significance arithmetic on a digital computer, Communications of the ACM, vol.6, issue.3, pp.111-117, 1963.
DOI : 10.1145/366274.366339

J. Gustafson, The end of numerical error, 2015 IEEE 22nd Symposium on Computer Arithmetic, p.74, 2015.
DOI : 10.1109/ARITH.2015.34

S. Collange, D. Defour, S. Graillat, and R. Iakymchuk, Numerical reproducibility for the parallel reduction on multi- and many-core architectures, Parallel Computing, vol.49, pp.83-97, 2015.
DOI : 10.1016/j.parco.2015.09.001
URL : https://hal.archives-ouvertes.fr/lirmm-01206348

W. M. Kahan, July) A critique of John L. Gustafson's. the end of error ? Unum computation and his a radical approach to computation with real numbers, 2016.

C. Denis, P. De-oliveira-castro, and E. Petit, Verificarlo: Checking Floating Point Accuracy through Monte Carlo Arithmetic, 2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH), pp.55-62, 2016.
DOI : 10.1109/ARITH.2016.31
URL : https://hal.archives-ouvertes.fr/hal-01417293

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

J. Denker, 04) Uncertainty as applied to measurements and calculations, 2018.

D. Funaro, Polynomial approximation of differential equations, 2008.

O. Møller, Quasi double-precision in floating point addition, BIT, vol.7, issue.6, pp.37-50, 1965.
DOI : 10.1007/BF01975722

D. E. Knuth, The Art of Computer Programming): Seminumerical Algorithms, 1997.

H. L. Gray and C. J. Harrison, Normalized floating-point arithmetic with an index of significance, Papers presented at the December 1-3, 1959, eastern joint IRE-AIEE-ACM computer conference on, IRE-AIEE-ACM '59 (Eastern), p.244, 1959.
DOI : 10.1145/1460299.1460329

E. A. Bond, Significant digits in computation with approximate numbers, The Mathematics Teacher, vol.24, issue.4, pp.208-212, 1931.

J. M. Hyman, Forsig: an extension of fortran with significance arithmetic, Los Alamos National Lab., NM (USA), 1982.

F. Johansson, 06) Basic implementation of significance arithmetic, 2008.

R. L. Ashenhurst and N. Metropolis, Unnormalized Floating Point Arithmetic, Journal of the ACM, vol.6, issue.3, pp.415-428, 1959.
DOI : 10.1145/320986.320996

G. Langdon, Method and means for tracking digit significance in arithmetic operations executed on decimal computers, p.831, 1978.

V. Lefèvre, J. Muller, A. Tisserand, ´. E. Martin-dorel, G. Melquiond et al., Towards correctly rounded transcendentals Some issues related to double rounding, Proceedings of the 13th IEEE Symposium on Computer Arithmetic, pp.897-924, 1997.

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

D. S. Parker, Monte Carlo arithmetic: exploiting randomness in floating-point arithmetic, 1997.