A. Ayad and C. Marché, Multi-Prover Verification of Floating-Point Programs, Fifth International Joint Conference on Automated Reasoning, pp.127-141, 2010.
DOI : 10.1007/978-3-642-14203-1_11
URL : https://hal.archives-ouvertes.fr/inria-00534333

M. Barnett and K. R. Leino, Weakest-precondition of unstructured programs, Proceedings of the 6th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering, PASTE '05, pp.82-87, 2005.

M. Barnett, K. R. Leino, K. Rustan, M. Leino, and W. Schulte, The Spec# Programming System: An Overview, pp.49-69, 2004.
DOI : 10.1007/978-3-540-30569-9_3

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

P. Baudin, P. Cuoq, J. Filliâtre, C. Marché, B. Monate et al., ACSL: ANSI/ISO C Specification Language, version 1, 2011.

F. Bobot, J. Filliâtre, C. Marché, and A. Paskevich, Why3: Shepherd your herd of provers, Boogie 2011: First International Workshop on Intermediate Verification Languages, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00790310

S. Boldo and J. Filliâtre, Formal Verification of Floating-Point Programs, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), pp.187-194, 2007.
DOI : 10.1109/ARITH.2007.20
URL : https://hal.archives-ouvertes.fr/hal-01174892

S. Boldo, J. Filliâtre, and G. Melquiond, Combining Coq and Gappa for Certifying Floating-Point Programs, 16th Symposium on the Integration of Symbolic Computation and Mechanised Reasoning, pp.59-74, 2009.
DOI : 10.1109/TC.2008.200
URL : https://hal.archives-ouvertes.fr/inria-00432726

S. Boldo and C. Marché, Formal Verification of Numerical Programs: From C Annotated Programs to Mechanical Proofs, Mathematics in Computer Science, vol.1, issue.2, 2011.
DOI : 10.1007/s11786-011-0099-9
URL : https://hal.archives-ouvertes.fr/hal-00777605

R. S. Boyer and Y. Yu, Automated proofs of object code for a widely used microprocessor, Journal of the ACM, vol.43, issue.1, pp.166-192, 1996.
DOI : 10.1145/227595.227603

L. Burdy, Y. Cheon, D. R. Cok, M. D. Ernst, J. R. Kiniry et al., An overview of JML tools and applications, International Journal on Software Tools for Technology Transfer, vol.box, issue.3, pp.212-232, 2005.
DOI : 10.1007/s10009-004-0167-4

L. Burdy and M. Pavlova, Java bytecode specification and verification, Proceedings of the 2006 ACM symposium on Applied computing , SAC '06, pp.1835-1839, 2006.
DOI : 10.1145/1141277.1141708

V. A. Carreño and P. S. Miner, Specification of the IEEE-854 floating-point standard in HOL and PVS, HOL95: 8th International Workshop on Higher-Order Logic Theorem Proving and Its Applications, 1995.

D. Clutterbuck and B. Carre, The verification of low-level code, Software Engineering Journal, vol.3, issue.3, pp.97-111, 1988.
DOI : 10.1049/sej.1988.0012

S. Conchon, E. Contejean, and J. Kanig, CC(X): Efficiently combining equality and solvable theories without canonizers, SMT 2007: 5th International Workshop on Satisfiability Modulo, 2007.

M. Cosnard, J. Muller, Y. Robert, and D. Trystram, Computation costs versus communication costs in parallel Gaussian elimination, Parallel Algorithms and architectures, pp.19-29, 1986.
URL : https://hal.archives-ouvertes.fr/hal-00857132

P. Cousot, R. Cousot, J. Feret, L. Mauborgne, A. Miné et al., The ASTRE?? Analyzer, ESOP, number 3444 in Lecture Notes in Computer Science, pp.21-30, 2005.
DOI : 10.1007/978-3-540-31987-0_3

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, TPHOLs '01, pp.169-184, 2001.
DOI : 10.1007/3-540-44755-5_13
URL : https://hal.archives-ouvertes.fr/hal-00157285

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

D. Delmas, E. Goubault, S. Putot, J. Souyris, K. Tekkal et al., Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software, FMICS, pp.53-69, 2009.
DOI : 10.1007/978-3-642-04570-7_6

G. Dowek and C. .. Muñoz, Conflict detection and resolution for 1, Proceedings of the 7th AIAA Aviation, Technology, Integration, and Operations Conference, pp.2007-7737, 2007.

G. Dowek, C. Muñoz, and V. Carreño, Provably Safe Coordinated Strategy for Distributed Conflict Resolution, AIAA Guidance, Navigation, and Control Conference and Exhibit, pp.2005-6047, 2005.
DOI : 10.2514/6.2005-6047

D. Elsner and J. , Fenlason, and friends. Using as, 2009.

J. Filliâtre, Preuve de programmes impératifs en théorie des types, 1999.

J. Filliâtre, Verification of non-functional programs using interpretations in type theory, Journal of functional Programming, vol.13, issue.4, pp.709-745, 2003.
DOI : 10.1017/S095679680200446X

J. Filliâtre, Formal Verification of MIX Programs, 2007.

J. Filliâtre, T. Hubert, and C. Marché, The Caduceus tool for the verification of C programs

J. Filliâtre and C. Marché, Multi-prover Verification of C Programs, 6th International Conference on Formal Engineering Methods, pp.15-29, 2004.
DOI : 10.1007/978-3-540-30482-1_10

J. Filliâtre and C. Marché, The Why/Krakatoa/Caduceus Platform for Deductive Program Verification, Damm and Hermanns, pp.173-177
DOI : 10.1007/978-3-540-73368-3_21

D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, vol.23, issue.1, pp.5-47, 1991.
DOI : 10.1145/103162.103163

H. H. Goldstine and J. Von-neumann, Planning and coding of problems for an electronic computing instrument, pp.34-235, 1961.

H. P. Sharangpani and M. L. Barton, Statistical analysis of floating point flaw in the Pentium processor, 1994.

J. Harrison, Formal Verification of Floating Point Trigonometric Functions, Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design, pp.217-233, 1954.
DOI : 10.1007/3-540-40922-X_14

P. Herms, C. Marché, and B. Monate, A Certified Multi-prover Verification Condition Generator, VSTTE, Lecture Notes in Computer Science, 2012.
DOI : 10.1007/3-540-48118-4_45
URL : https://hal.archives-ouvertes.fr/hal-00639977

T. Hickey, Q. Ju, and M. H. Van-emden, Interval arithmetic: From principles to implementation, Journal of the ACM, vol.48, issue.5, pp.1038-1068, 2001.
DOI : 10.1145/502102.502106

N. J. Higham, Accuracy and stability of numerical algorithms, SIAM, 2002.
DOI : 10.1137/1.9780898718027

M. Kaufmann, J. S. Moore, and P. Manolios, Computer-Aided Reasoning: An Approach, 2000.

G. T. Leavens, Not a Number of Floating Point Problems., The Journal of Object Technology, vol.5, issue.2, pp.75-83, 2006.
DOI : 10.5381/jot.2006.5.2.c8

X. Leroy, Formal certification of a compiler back-end or: programming a compiler with a proof assistant, Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages, POPL '06, pp.42-54, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00000963

X. Leroy, A Formally Verified Compiler Back-end, Journal of Automated Reasoning, vol.27, issue.1, pp.363-446, 2009.
DOI : 10.1007/s10817-009-9155-4
URL : https://hal.archives-ouvertes.fr/inria-00360768

G. Li, S. Owens, and K. Slind, Structure of a Proof-Producing Compiler for a Subset of Higher Order Logic, Proceedings of the 16th European conference on Programming, ESOP'07, pp.205-219, 2007.
DOI : 10.1007/978-3-540-71316-6_15

J. Matthews, J. S. Moore, I. Ray, and D. Vroon, Verification Condition Generation Via Theorem Proving, Proceedings of the 13th International Conference on Logic for Programming , Artificial Intelligence, and Reasoning, pp.362-376, 2006.
DOI : 10.1007/11916277_25

W. D. Maurer, Proving the correctness of a flight-director program for an airborne minicomputer, Proceedings of the ACM SIGMINI/SIGPLAN interface meeting on Programming systems in the small processor environment, SIGMINI '76, pp.103-108, 1976.

G. Melquiond, De l'arithmétique d'intervalles à la certification de programmes, 2006.

G. Melquiond, 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

A. Miné, Relational Abstract Domains for the Detection of Floating-Point Run-Time Errors, Proc. of the European Symposium on Programming, pp.3-17, 2004.
DOI : 10.1007/978-3-540-24725-8_2

D. Monniaux, The pitfalls of verifying floating-point computations, ACM Transactions on Programming Languages and Systems, vol.30, issue.3, p.12, 2008.
DOI : 10.1145/1353445.1353446
URL : https://hal.archives-ouvertes.fr/hal-00128124

D. Monniaux, Analyse statique : de la théorie à la pratique. Habilitation to direct research, 2009.

R. Moore, Interval Analysis, 1966.

M. O. Myreen, Formal verification of machine-code programs, 2008.

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

M. Pavlova, Vérification de bytecode et ses application, 2007.

D. M. Russinoff, Abstract, LMS Journal of Computation and Mathematics, vol.11, pp.148-200, 1998.
DOI : 10.1112/S1461157000000176

A. Stump, C. W. Barrett, D. L. Dill, and J. Levitt, A decision procedure for an extensional theory of arrays, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science, p.29, 2001.
DOI : 10.1109/LICS.2001.932480

. Program and G. Loop, 116 9.7 CFG for assembly code generated by gcc -S from example in Figure 9, p.116

.. An, 129 10.2 Assembly code in SSE2 mode of Figure 10 130 10.3 Memory model 131 10.4 C code of a program with arrays defined as local variables, p.133

.. Maximum, 142 10.9 Assembly code in SSE2 mode of Figure 10, p.145