B. Akbarpour, S. Tahar, and A. Dekdouk, Formalization of fixed-point arithmetic in HOL. Formal Methods in System Design, pp.173-200, 2005.

G. Barrett, Formal methods applied to a floating-point number system, IEEE Transactions on Software Engineering, vol.15, issue.5, pp.611-621, 1989.
DOI : 10.1109/32.24710

Y. Bertot and P. Castéran, Interactive Theorem Proving and Program Development. Coq'Art: the Calculus of Inductive Constructions . Texts in Theoretical Computer Science, p.5, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00344237

[. Burnikel, S. Funke, and M. Seel, EXACT GEOMETRIC COMPUTATION USING CASCADING, International Journal of Computational Geometry & Applications, vol.11, issue.03, pp.245-266, 2001.
DOI : 10.1142/S0218195901000493

S. Boldo and G. Melquiond, When double rounding is odd, Proceedings of the 17th IMACS World Congress on Computational and Applied Mathematics, p.40, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070603

H. Brönnimann, G. Melquiond, and S. Pion, The Boost interval arithmetic library, Proceedings of the 5th Conference on Real Numbers and Computers, pp.65-80, 2003.

[. Brönnimann, G. Melquiond, and S. Pion, Bool_set: multi-valued logic, C++ standardization committee, p.105, 2006.

H. Brönnimann, G. Melquiond, and S. Pion, The design of the Boost interval arithmetic library, Theoretical Computer Science, vol.351, issue.1, pp.111-118, 2006.
DOI : 10.1016/j.tcs.2005.09.062

H. Brönnimann, G. Melquiond, and S. Pion, A proposal to add interval arithmetic to the C++ standard library, C++ standardization committee, p.104, 2006.

Y. Bertot, N. Magaud, and P. Zimmermann, A proof of GMP square root, Journal of Automated Reasoning, vol.29, pp.3-4225, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00101044

S. Boldo, Preuves formelles en arithmétiques à virgule flottante, Ref. pp, vol.6, p.68, 2004.

S. Boutin, Using reflection to build efficient and certified decision procedures, Theoretical Aspects of Computer Software, pp.515-529, 1997.
DOI : 10.1007/BFb0014565
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7587

. Jean-marie-chesneaux, Habilitation à diriger des recherches, Proceedings of the 3rd International Joint Conference on Automated Reasoning Carreño and Paul S. Miner. Specification of the IEEE-854 floating-point standard in HOL and PVS Proceedings of the International Workshop on Higher Order Logic Theorem Proving and its Applications, pp.528-540, 1995.

J. Detrey and . Florent-de-dinechin, A parameterizable floatingpoint logarithm operator for FPGAs, Proceedings of the 39th Asilomar Conference on Signals, Systems and Computers, pp.1186-1190, 2005.

D. Defour, J. Florent-de-dinechin, and . Muller, Correctly rounded exponential function in double precision arithmetic, Advanced Signal Processing Algorithms, pp.156-167, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072387

C. Florent-de-dinechin, G. Lauter, and . Melquiond, Assisted verification of elementary functions using Gappa [Dek71] Theodorus J. Dekker. A floating-point technique for extending the available precision, Proceedings of the 2006 ACM Symposium on Applied Computing, pp.1318-1322, 1971.

J. Demmel, Underflow and the Reliability of Numerical Software, SIAM Journal on Scientific and Statistical Computing, vol.5, issue.4, pp.887-919, 1984.
DOI : 10.1137/0905062

M. Daumas and G. Melquiond, Generating formally certified bounds on values and round-off errors, Proceedings of the 6th Conference on Real Numbers and Computers, pp.55-70, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00070739

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

O. Devillers and F. Preparata, A Probabilistic Analysis of the Power of Arithmetic Filters, DP03] Olivier Devillers and Sylvain Pion Proceedings of the 5th Workshop on Algorithm Engineering and Expereriments, pp.523-547, 1998.
DOI : 10.1007/PL00009400
URL : https://hal.archives-ouvertes.fr/inria-00073727

M. Daumas, L. Rideau, and L. Théry, A Generic Library for Floating-Point Numbers and Its Application to Exact Computing, Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics, pp.169-184, 2001.
DOI : 10.1007/3-540-44755-5_13
URL : https://hal.archives-ouvertes.fr/hal-00157285

D. Milo?, T. Ercegovac, and . Lang, Digital Arithmetic, p.39, 2004.

G. Laurent-fousse, V. Hanrot, P. Lefèvre, P. Pélissier, and . Zimmermann, MPFR: A multiple-precision binary floatingpoint library with correct rounding, p.53, 2005.

A. Samuel and . Figueroa, When is double rounding innocuous? SIGNUM Newsletter, pp.21-26, 1995.

J. Filliâtre, Why: a multi-language multi-prover verification tool, 2003.

[. Filliâtre and C. Marché, Multi-prover Verification of C Programs, Proceedings of the 6th International Conference on Formal Engineering Methods 101 [GM05] Benjamin Grégoire and Assia Mahboubi Proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, pp.15-29, 2004.
DOI : 10.1007/978-3-540-30482-1_10

J. Harrison and . Hol, A tutorial introduction, Proceedings of the First International Conference on Formal Methods in Computer-Aided Design, volume 1166 of Lecture notes on Computer Sciences, pp.265-269

J. Harrison, Floating point verification in HOL light: The exponential function, Algebraic Methodology and Software Technology, pp.246-260, 1997.
DOI : 10.1007/BFb0000475

J. Harrison, A Machine-Checked Theory of Floating Point Arithmetic, Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics, pp.113-130, 1999.
DOI : 10.1007/3-540-48256-3_9

J. Harrison and L. Théry, A skeptic's approach to combining HOL and Maple Standard for Binary Floating- Point Arithmetic Information Management and Technology Division. Patriot missile defense: software problem led to system failure at Dhahran, Saudi Arabia, Journal of Automated Reasoning, vol.21, issue.3, pp.279-294, 1985.
DOI : 10.1023/A:1006023127567

[. Iso, Common Criteria for Information Technology Security Evaluation, p.1, 2005.

C. Jacobi and C. Berg, Formal verification of the VAMP floating point unit. Formal Methods and System Design, pp.227-266, 2005.

L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics Derandomizing polynomial identity tests means proving circuit lower bounds, Ref. pp. 1 Journal of Computational Complexity, vol.13, pp.191-237, 2001.

R. Kaivola and K. R. Kohatsu, Proof engineering in the large: formal verification of Pentium???4 floating-point divider, International Journal on Software Tools for Technology Transfer (STTT), vol.4, issue.3, pp.323-334, 2003.
DOI : 10.1007/s10009-002-0081-6

E. Donald and . Knuth, The Art of Computer Programming: Seminumerical Algorithms, p.83, 1969.

P. Langlois, Applications of the CENA method to automatic accuracy enhancement, Proceedings of the SCAN 2000 International Conference on Scientific Computing, Computer Arithmetic and Validated Numerics, p.7, 2000.

Q. Christoph and . Lauter, Basic building blocks for a triple-double intermediate format, p.85, 2005.

R. Li, S. Boldo, M. D. Makino, and M. Berz, Theorems on efficient argument reductions Taylor models and other validated functional inclusion methods Real number calculations and theorem proving, Proceedings of the 16th Symposium on Computer Arithmetic Proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, pp.129-136, 2003.

J. Strother-moore, T. W. Lynch, and M. Kaufmann, A mechanically checked proof of the AMD5/sub K/86/sup TM/ floating-point division program, IEEE Transactions on Computers, vol.47, issue.9, pp.913-926, 1998.
DOI : 10.1109/12.713311

R. E. Moore, Methods and Applications of Interval Analysis. SIAM, 1979. Ref, p.60

G. Melquiond and S. Pion, Formal certification of arithmetic filters for geometric predicates, Proceedings of the 17th IMACS World Congress on Computational and Applied Mathematics, p.89, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00344518

G. Melquiond and S. Pion, Formally certified floatingpoint filters for homogeneous geometric predicates, Theoretical Informatics and Applications, p.99, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00071232

R. Michard, A. Tisserand, and N. Veyrat-charvillon, Optimisation d'op??rateurs arithm??tiques mat??riels ?? base d'approximations polynomiales, SympA Symposium en Architecture de Machines, p.99, 2006.
DOI : 10.3166/tsi.27.699-718

D. Bruce, H. D. Mccullough, and . Vinod, The numerical reliability of econometric software, p.1, 1999.

S. Owre, J. M. Rushby, and N. Shankar, PVS: A prototype verification system, Proceedings of the 11th International Conference on Automated Deduction, pp.748-752, 1992.
DOI : 10.1007/3-540-55602-8_217

R. C. Jason and . Patterson, Accurate static branch prediction by value range propagation, SIGPLAN Conference on Programming Language Design and Implementation, pp.67-78, 1995.

S. Putot, É. Goubault, M. Douglas, and M. Priest, Static Analysis-Based Validation of Floating-Point Computations, Proceedings of the 10th Symposium on Computer Arithmetic, pp.306-313, 1991.
DOI : 10.1007/978-3-540-24738-8_18

W. Pugh, The Omega test: a fast and practical integer programming algorithm for dependence analysis, Proceedings of the 1991 ACM/IEEE conference on Supercomputing , Supercomputing '91, pp.4-13, 1991.
DOI : 10.1145/125826.125848

G. Revy, Analyse et implantation d'algorithmes rapides pour l'évaluation polynomiale sur les nombres flottants, p.99, 2006.

M. David and . Russinoff, A case study in formal verification of registertransfer logic with ACL2: The floating point adder of the AMD Athlon processor, Lecture Notes in Computer Science, pp.3-36, 1954.

J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities, Journal of the ACM, vol.27, issue.4, pp.701-717, 1980.
DOI : 10.1145/322217.322225

J. Sawada and R. Gamboa, Mechanical Verification of a Square Root Algorithm Using Taylor???s Theorem, Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design, pp.274-291, 2002.
DOI : 10.1007/3-540-36126-X_17

J. R. Shewchuk, Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, Discrete & Computational Geometry, vol.18, issue.3, pp.305-363, 1997.
DOI : 10.1007/PL00009321

H. Pat and . Sterbenz, Floating Point Computation Prentice-Hall Series in Automatic Computation [Tan90] Ping-Tak Peter Tang. Table-driven implementation of the logarithm function in IEEE floating-point arithmetic, ACM Transactions on Mathematical Software, vol.16, issue.4, pp.47378-400, 1974.

J. Van-den, B. Berg, and . Jacobs, The loop Compiler for Java and JML, Lecture Notes in Computer Science, vol.2031, issue.2, pp.299-313, 2001.
DOI : 10.1007/3-540-45319-9_21

C. Yap and T. Dubé, THE EXACT COMPUTATION PARADIGM, Computing in Euclidean Geometry of Lecture Notes Series on Computing, pp.452-492, 1995.
DOI : 10.1142/9789812831699_0011

R. Zumkeller, Formal Global Optimisation with Taylor Models, Proceedings of the 3rd International Joint Conference on Automated Reasoning, pp.408-422, 2006.
DOI : 10.1007/11814771_35