, IEEE Standard for Floating-Point Arithmetic. IEEE Standard, vol.754, 2008.

D. H. Bailey, Y. Hida, X. S. Li, and B. Thompson, Arprec: An arbitrary precision computation package, Tech. Rep, 2002.
DOI : 10.2172/817634
URL : https://digital.library.unt.edu/ark:/67531/metadc733638/m2/1/high_res_d/817634.pdf

L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, Mpfr: A multiple-precision binary floating-point library with correct rounding, ACM Trans. Math. Softw, vol.33, issue.2, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00070266

Y. Hida, X. Li, and D. Bailey, Library for double-double and quaddouble arithmetic, NERSC Division, 2008.

D. M. Priest, Algorithms for arbitrary precision floating point arithmetic, Proceedings of the 10th IEEE Symposium on Computer Arithmetic (Arith-10, pp.132-144, 1991.
DOI : 10.1109/arith.1991.145549

J. R. Shewchuk, Adaptive precision floating-point arithmetic and fast robust geometric predicates, Discrete & Computational Geometry, vol.18, pp.305-368, 1997.

M. Joldes, J. Muller, V. Popescu, and W. Tucker, CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications, 5th International Congress on Mathematical Software (ICMS), 2016.
DOI : 10.1007/978-3-319-42432-3_29
URL : https://hal.archives-ouvertes.fr/hal-01312858

D. Priest, On properties of floating point arithmetics: Numerical stability and the cost of accurate computations, 1992.

T. Ogita, S. M. Rump, and S. Oishi, Accurate sum and dot product, SIAM Journal on Scientific Computing, vol.26, issue.6, pp.1955-1988, 2005.
DOI : 10.1137/030601818

S. Graillat, P. Langlois, and N. Louvet, Algorithms for accurate, validated and fast polynomial evaluation, Japan J. Indust. Appl. Math, vol.2, issue.3, pp.191-214, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00285603

G. Alefeld and J. Herzberger, Introduction to interval analysis, 1983.

U. Kulisch, Advanced Arithmetic for the Digital Computer, 2002.

S. Graillat, F. Jézéquel, and R. Picot, Numerical validation of compensated summation algorithms with stochastic arithmetic, Electronic Notes in Theoretical Computer Science, vol.317, pp.55-69, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01230860

S. Boldo, S. Graillat, and J. Muller, On the robustness of the 2Sum and Fast2Sum algorithms, ACM Trans. Math. Softw, vol.44, issue.1, pp.1-4, 2017.
URL : https://hal.archives-ouvertes.fr/ensl-01310023

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

S. Rump, INTLAB-INTerval LABoratory, Developments in Reliable Computing, T. Csendes, pp.77-104, 1999.

N. Higham, Accuracy and stability of numerical algorithms, 2002.

C. Jeannerod and S. M. Rump, Improved error bounds for inner products in floating-point arithmetic, SIAM Journal on Matrix Analysis and Applications, vol.34, issue.2, pp.338-344, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00840926

S. M. Rump, Error estimation of floating-point summation and dot product, BIT. Numerical Mathematics, vol.52, issue.1, pp.201-220, 2012.

S. M. Rump, F. B-¨-unger, and C. Jeannerod, Improved error bounds for floating-point products and Horner's scheme, BIT. Numerical Mathematics, vol.56, issue.1, pp.293-307, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01137652

,

T. Dekker, A floating-point technique for extending the available precision, Numerische Mathematik, vol.18, issue.3, pp.224-242, 1971.

D. Knuth, The Art of Computer Programming, Seminumerical Algorithms, vol.2, 1997.

J. Muller, N. Brisebarre, F. De-dinechin, C. Jeannerod, V. Lefèvre et al., , 2010.

J. Hauser, Handling floating-point exceptions in numeric programs, ACM Trans. Program. Lang. Syst, vol.18, issue.2, pp.139-174, 1996.

J. Demmel and H. D. Nguyen, Fast reproducible floating-point summation, 21st IEEE Symposium on Computer Arithmetic, pp.163-172, 2013.
DOI : 10.1109/arith.2013.9
URL : http://www.eecs.berkeley.edu/~hdnguyen/public/papers/ARITH21_Fast_Sum.pdf

P. Sterbenz, Floating-point computation, ser. Prentice-Hall series in automatic computation, 1973.

S. M. Rump, T. Ogita, and S. Oishi, Accurate floating-point summation. I. Faithful rounding, SIAM J. Sci. Comput, vol.31, issue.1, pp.189-224, 2008.

S. M. Rump, Verification methods: rigorous results using floatingpoint arithmetic, Acta Numer, vol.19, pp.287-449, 2010.

A. Neumaier, Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen, ZAMM (Zeitschrift f ¨ ur Angewandte Mathematik und Mechanik), vol.54, pp.39-51, 1974.

M. Pichat, Correction d'une somme en arithmétiquè a virgule flottante, Numerische Mathematik, vol.19, pp.400-406, 1972.

S. Graillat, N. Louvet, and P. Langlois, Compensated Horner scheme, p.66860
URL : https://hal.archives-ouvertes.fr/hal-01539819

F. Perpignan-cedex, , 2005.

S. Graillat, Accurate floating point product and exponentiation, IEEE Transactions on Computers, vol.58, issue.7, pp.994-1000, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00164607

, Accurate simple zeros of polynomials in floating point arithmetic, Computers & Mathematics with Applications, vol.56, issue.4, pp.1114-1120, 2008.

H. Jiang, S. Graillat, C. Hu, S. Lia, X. Liao et al., Accurate evaluation of the k-th derivative of a polynomial, Journal of Computational and Applied Mathematics, vol.191, pp.28-47, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01146529

H. Jiang, S. Graillat, and R. Barrio, Accurate and fast evaluation of elementary symmetric functions, Proceedings of the 21st IEEE Symposium on Computer Arithmetic, pp.183-190, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01216600

N. Louvet, Algorithmes compensés en arithmétique flottante : précision, validation, performances, 2007.