G. Alefeld and D. Claudio, The basic properties of interval arithmetic, its software realizations and some applications, Computers & Structures, vol.67, issue.1-3, pp.3-8, 1998.
DOI : 10.1016/S0045-7949(97)00150-8

A. Ieee, Standard 754-1985 for binary floating-point arithmetic, 1985.

R. P. Brent, Algorithms for minimization without derivatives, N.J, 1973.

M. Daumas, G. Melquiond, and C. Muñoz, Guaranteed Proofs Using Interval Arithmetic, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), pp.188-195, 2005.
DOI : 10.1109/ARITH.2005.25

URL : https://hal.archives-ouvertes.fr/hal-00164621

F. De-dinechin, A. Ershov, and N. Gast, Towards the Post-Ultimate libm, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), 2005.
DOI : 10.1109/ARITH.2005.46

URL : https://hal.archives-ouvertes.fr/inria-00070636

F. De-dinechin, C. Q. Lauter, and G. Melquiond, Assisted verification of elementary functions using Gappa, Proceedings of the 2006 ACM symposium on Applied computing , SAC '06, pp.1318-1322, 2006.
DOI : 10.1145/1141277.1141584

A. Griewank, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2000.
DOI : 10.1137/1.9780898717761

J. Harrison, Floating point verification in HOL light: The exponential function, 1997.
DOI : 10.1007/BFb0000475

N. J. Higham, Accuracy and Stability of Numerical Algorithms, Society for Industrial and Applied Mathematics, 2002.
DOI : 10.1137/1.9780898718027

W. Hofschuster and W. Krämer, FI LIB, eine schnelle und portable Funktionsbibliothek für reelle Argumente und reelle Intervalle im IEEE-double-Format, 1998.

W. Krämer, Sichere und genaue Abschätzung des Approximationsfehlers bei rationalen Approximationen, 1996.

P. Markstein, IA-64 and Elementary Functions : Speed and Precision. Hewlett-Packard Professional Books, 2000.

J. Muller, Elementary Functions, Algorithms and Implementation, 1997.
URL : https://hal.archives-ouvertes.fr/ensl-00000008

M. Neher, ACETAF: A software package for computing validated bounds for Taylor coefficients of analytic functions, ACM Transactions on Mathematical Software, 2003.

A. Neumaier, Interval Methods for Systems of Equations, 1990.
DOI : 10.1017/CBO9780511526473