Handbook of mathematical functions with formulas, graphs, and mathematical tables For sale by the Superintendent of Documents, National Bureau of Standards Applied Mathematics Series U.S. Government Printing Office, vol.55, 1964. ,
Extending Coq with Imperative Features and Its Application to SAT Verification, ITP. LNCS, pp.83-98, 2010. ,
DOI : 10.1007/978-3-642-14052-5_8
URL : https://hal.archives-ouvertes.fr/inria-00502496
The Dynamic Dictionary of Mathematical Functions (DDMF), Mathematical Software -ICMS 2010, pp.35-41, 2010. ,
DOI : 10.1007/978-3-642-15582-6_7
URL : https://hal.archives-ouvertes.fr/hal-00783048
Interactive Theorem Proving and Program Development. Coq'Art: The Calculus of Inductive Constructions, Texts in Theoretical Computer Science, 2004. ,
DOI : 10.1007/978-3-662-07964-5
URL : https://hal.archives-ouvertes.fr/hal-00344237
Rigorous global search using taylor models, Proceedings of the 2009 conference on Symbolic numeric computation, SNC '09, pp.11-20 ,
DOI : 10.1145/1577190.1577198
Long-term stability of the tevatron by verified global optimization. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, proceedings of the 8th International Computational Accelerator Physics Conference -ICAP, pp.1-10, 2004. ,
Full Reduction at Full Throttle, CPP. LNCS, pp.362-377, 2011. ,
DOI : 10.1007/3-540-44464-5_13
URL : https://hal.archives-ouvertes.fr/hal-00650940
Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq, 2011 IEEE 20th Symposium on Computer Arithmetic, pp.243-252, 2011. ,
DOI : 10.1109/ARITH.2011.40
URL : https://hal.archives-ouvertes.fr/inria-00534854
Efficient polynomial L-approximations, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), pp.169-176, 2007. ,
DOI : 10.1109/ARITH.2007.17
URL : https://hal.archives-ouvertes.fr/inria-00119513
Computing machine-efficient polynomial approximations, ACM Transactions on Mathematical Software, vol.32, issue.2, pp.236-256, 2006. ,
DOI : 10.1145/1141885.1141890
URL : https://hal.archives-ouvertes.fr/ensl-00086826
Utilisation et certification de l'arithmétique d'intervalles dans un assistant de preuves, 2007. ,
Évaluation efficace de fonctions numériques Outils et exemples, 2009. ,
Sollya: An Environment for the Development of Numerical Codes, Mathematical Software -ICMS 2010, pp.28-31, 2010. ,
DOI : 10.1007/978-3-642-15582-6_5
URL : https://hal.archives-ouvertes.fr/hal-00761644
Efficient and accurate computation of upper bounds of approximation errors, Theoretical Computer Science, vol.412, issue.16, pp.1523-1543, 2011. ,
DOI : 10.1016/j.tcs.2010.11.052
URL : https://hal.archives-ouvertes.fr/ensl-00445343
A Taylor Function Calculus for Hybrid System Analysis: Validation in Coq, NSV-3: Third International Workshop on Numerical Software Verification, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00473270
Assisted verification of elementary functions using Gappa Modern computer algebra, Proceedings of the 2006 ACM Symposium on Applied Computing, pp.1318-1322, 2003. ,
Constructive Reals in Coq: Axioms and Categoricity, Proceedings of TYPES 2000, pp.79-95, 2002. ,
DOI : 10.1007/3-540-45842-5_6
A Small Scale Reflection Extension for the Coq system, 2008. ,
URL : https://hal.archives-ouvertes.fr/inria-00258384
A Purely Functional Library for Modular Arithmetic and Its Application to Certifying Large Prime Numbers, IJCAR. LNCS, pp.423-437, 2006. ,
DOI : 10.1007/11814771_36
Evaluating Derivatives -Principles and Techniques of Algorithmic Differentiation, SIAM, 2000. ,
Rigourous Polynomial Approximations and Applications. Ph.D. dissertation , École Normale Supérieure de Lyon, 2011. ,
Computer Certified Efficient Exact Reals in Coq, pp.90-106, 2011. ,
DOI : 10.1007/978-3-642-04027-6_12
Worst cases for correct rounding of the elementary functions in double precision, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001, 2001. ,
DOI : 10.1109/ARITH.2001.930110
Robust Space Trajectory and Space System Design using Differential Algebra, 2008. ,
Rigorous Analysis of Nonlinear Motion in Particle Accelerators, 1998. ,
Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics, vol.4, issue.4, pp.379-456, 2003. ,
Formalisation et automatisation de preuves en analyses réelle et numérique, 2001. ,
Proving Bounds on Real-Valued Functions with Computations, Proceedings of the 4th International Joint Conference on Automated Reasoning, pp.2-17, 2008. ,
DOI : 10.1007/978-3-540-71070-7_2
URL : https://hal.archives-ouvertes.fr/hal-00180138
Methods and Applications of Interval Analysis, Society for Industrial and Applied Mathematics, 1979. ,
DOI : 10.1137/1.9781611970906
Projet ANR TaMaDi ? Dilemme du fabricant de tables ? Table Maker's Dilemma (ref. ANR, 2010. ,
Elementary Functions, Algorithms and Implementation, 2006. ,
URL : https://hal.archives-ouvertes.fr/ensl-00000008
On Taylor Model Based Integration of ODEs, SIAM Journal on Numerical Analysis, vol.45, issue.1, pp.236-262, 2007. ,
DOI : 10.1137/050638448
Taylor forms ? use and limits, Reliable Computing, vol.9, issue.1, pp.43-79, 2003. ,
DOI : 10.1023/A:1023061927787
Certified exact transcendental real number computation in coq, Theorem Proving in Higher Order Logics, pp.246-261, 2008. ,
CRlibm, Correctly Rounded mathematical library, 2006. ,
Sur un procédé convergent d'approximations successives pour déterminer les polynômes d'approximation (in French), C.R. Académie des Sciences, pp.2063-2065, 1934. ,
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable, ACM Transactions on Mathematical Software, vol.20, issue.2, pp.163-177, 1994. ,
DOI : 10.1145/178365.178368
URL : https://hal.archives-ouvertes.fr/hal-00917741
Differentiably Finite Power Series, European Journal of Combinatorics, vol.1, issue.2, pp.175-188, 1980. ,
DOI : 10.1016/S0195-6698(80)80051-5
URL : http://doi.org/10.1016/s0195-6698(80)80051-5
Fast evaluation of elementary mathematical functions with correctly rounded last bit, ACM Transactions on Mathematical Software, vol.17, issue.3, pp.410-423, 1991. ,
DOI : 10.1145/114697.116813
Formal Global Optimization with Taylor Models, Proc. of the 4th International Joint Conference on Automated Reasoning, pp.408-422, 2008. ,
DOI : 10.1007/11814771_35
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.680.8497