Round off error analysis for Gram-Schmidt method and solution of linear least squares problems, BIT, vol.20, issue.4, pp.345-368, 1971. ,
DOI : 10.1007/BF01939404
Finding effective compilation sequences, ACM SIGPLAN/SIGBED Conference on Languages, Compilers, and Tools for Embedded Systems (LCTES'04), pp.231-239, 2004. ,
DOI : 10.1145/997163.997196
IEEE Standard for Binary Floating-Point Arithmetic, SIAM, 2008. ,
Modern Compiler Implementation in ML, 1998. ,
DOI : 10.1017/CBO9780511811449
Towards intelligent PID control, Automatica, vol.28, issue.1, pp.1-9, 1992. ,
DOI : 10.1016/0005-1098(92)90002-W
Automatic detection of floating-point exceptions, Symposium on Principles of Programming Languages, POPL'13, pp.549-560, 2013. ,
A dynamic program analysis to find floating-point accuracy problems, Programming Language Design and Implementation, PLDI '12, pp.453-462, 2012. ,
Static analysis by abstract interpretation of embedded critical software, ACM SIGSOFT Software Engineering Notes, vol.36, issue.1, pp.1-8, 2011. ,
DOI : 10.1145/1921532.1921553
URL : https://hal.archives-ouvertes.fr/inria-00528632
Lattice Theory, 1967. ,
DOI : 10.1090/coll/025
A static analyzer for large safety-critical software, Proceedings of the ACM SIGPLAN 2003 Conference on Programming Language Design and Implementation 2003, pp.196-207, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00128135
Lustre : A declarative language for programming synchronous systems, Conference Record of the Fourteenth Annual ACM Symposium on Principles of Programming Languages, pp.178-188, 1987. ,
DOI : 10.1145/41625.41641
Interval Slopes as a Numerical Abstract Domain for Floating-Point Variables, Static Analysis -17th International Symposium, SAS 2010 Proceedings, pp.184-200, 2010. ,
DOI : 10.1007/978-3-642-15769-1_12
Numerical reproducibility for the parallel reduction on multi- and many-core architectures, Parallel Computing, vol.49, 2014. ,
DOI : 10.1016/j.parco.2015.09.001
URL : https://hal.archives-ouvertes.fr/lirmm-01206348
Adaptive optimizing compilers for the 21st century, The Journal of Supercomputing, vol.23, issue.1, pp.7-22, 2002. ,
DOI : 10.1023/A:1015729001611
Abstract interpretation, Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '77, pp.238-252, 1977. ,
DOI : 10.1145/512950.512973
URL : https://hal.archives-ouvertes.fr/hal-01108790
Abstract Interpretation Frameworks, Journal of Logic and Computation, vol.2, issue.4, pp.511-547, 1992. ,
DOI : 10.1093/logcom/2.4.511
The ASTRE?? Analyzer, Programming Languages and Systems, 14th European Symposium on Programming,ESOP 2005, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2005, Proceedings, pp.21-30, 2005. ,
DOI : 10.1007/978-3-540-31987-0_3
Systematic design of program transformation frameworks by abstract interpretation, Principles of Programming Languages, pp.178-190, 2002. ,
Efficient accomodation of may-alias information in SSA form, Programming Language Design and Implementation (PLDI), pp.36-45, 1993. ,
Impact of Accuracy Optimization on the Convergence of Numerical Iterative??Methods, Lecture Notes in Computer Science, vol.9527, pp.143-160, 2015. ,
DOI : 10.1007/978-3-319-27436-2_9
URL : https://hal.archives-ouvertes.fr/hal-01272514
Intra-procedural Optimization of the Numerical Accuracy of Programs, FMICS'15, pp.31-46, 2015. ,
DOI : 10.1007/978-3-319-19458-5_3
URL : https://hal.archives-ouvertes.fr/hal-01164340
Optimizing the accuracy of a rocket trajectory simulation by program transformation, Proceedings of the 12th ACM International Conference on Computing Frontiers, CF '15, pp.1-40, 2015. ,
DOI : 10.1145/2742854.2742894
URL : https://hal.archives-ouvertes.fr/hal-01133695
Transformation of a PID Controller for Numerical Accuracy, Electronic Notes in Theoretical Computer Science, vol.317, pp.47-54, 2015. ,
DOI : 10.1016/j.entcs.2015.10.006
URL : https://hal.archives-ouvertes.fr/hal-01255942
Amélioration à la compilation de la précision de programmes numériques, 8th Journées nationales du Groupement De Recherche CNRS du Génie de la Programmation et du Logiciel, GDR- GPL'2016, pp.27-34, 2016. ,
Data-types optimization for floating-point formats by program transformation, 2016 International Conference on Control, Decision and Information Technologies (CoDIT), 2016. ,
DOI : 10.1109/CoDIT.2016.7593626
URL : https://hal.archives-ouvertes.fr/hal-01290292
Improving the numerical accuracy of programs by automatic transformation, International Journal on Software Tools for Technology Transfer, vol.19, issue.6, 2016. ,
DOI : 10.1007/s10009-016-0435-0
URL : https://hal.archives-ouvertes.fr/hal-01373666
Numerically accurate code generation, IEEE/ACM International Symposium on Code Generation and Optimization, CGO'16, p.page xxiii, 2016. ,
Toward a Standard Benchmark Format and Suite for Floating-Point Analysis, Lecture Notes in Computer Science, vol.57, issue.2, 2016. ,
DOI : 10.1007/978-3-642-38856-9_2
Sound compilation of reals, Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL '14, pp.235-248, 2014. ,
DOI : 10.1145/2535838.2535874
Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software, Formal Methods for Industrial Critical Systems, 14th International Workshop, pp.53-69, 2009. ,
DOI : 10.1007/978-3-642-04570-7_6
Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software, Formal Methods for Industrial Critical Systems, pp.53-69, 2009. ,
DOI : 10.1007/978-3-642-04570-7_6
Fast Reproducible Floating-Point Summation, 2013 IEEE 21st Symposium on Computer Arithmetic, pp.163-172, 2013. ,
DOI : 10.1109/ARITH.2013.9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.6586
Parallel Reproducible Summation, IEEE Transactions on Computers, vol.64, issue.7, pp.2060-2070, 2015. ,
DOI : 10.1109/TC.2014.2345391
Static analysis of digital filters Held as Part of the Joint European Conferences on Theory and Practice of Software, Programming Languages and Systems, 13th European Symposium on Programming Proceedings, volume 2986 of Lecture Notes in Computer Science, pp.33-48, 2004. ,
From Control Systems to Control Software, IEEE Control Systems Magazine, vol.30, issue.6, pp.50-71, 2010. ,
DOI : 10.1109/MCS.2010.938196
SOAP: Structural optimization of arithmetic expressions for high-level synthesis, 2013 International Conference on Field-Programmable Technology (FPT), pp.112-119, 2013. ,
DOI : 10.1109/FPT.2013.6718340
Testing-Based Compiler Validation for Synchronous Languages, NASA Formal Methods -6th International Symposium, NFM 2014, Proceedings, pp.246-251, 2014. ,
DOI : 10.1007/978-3-319-06200-6_19
URL : http://hdl.handle.net/2060/20140013438
What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, vol.23, issue.1, pp.5-48, 1991. ,
DOI : 10.1145/103162.103163
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.7712
Matrix computations (3, 1996. ,
Static Analysis by Abstract Interpretation of Numerical Programs and Systems, and FLUCTUAT, Static Analysis Symposium, SAS, pp.1-3, 2013. ,
DOI : 10.1007/978-3-642-38856-9_1
Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter, Programming Languages and Systems, 11th European Symposium on Programming, ESOP 2002, held as Part of the Joint European Conference on Theory and Practice of Software, ETAPS 2002, Proceedings, volume 2305 of Lecture Notes in Computer Science, pp.209-212, 2002. ,
DOI : 10.1007/3-540-45927-8_15
Some future challenges in the validation of control systems, European Congress on Embedded Real Time Software, ERTS 2006, Proceedings, 2006. ,
Static Analysis of Finite Precision Computations, Verification, Model Checking, and Abstract Interpretation, 2011. ,
DOI : 10.1007/978-3-540-24738-8_18
Synchronous Programming of Reactive Systems, 2010. ,
Lambda Calculi A Guide For Computer Scientists, 1994. ,
Orthogonalization routine in SLEPc Technical Report STR-1, 2007. ,
Paulin-Mohring. The Coq Proof Assistant -A tutorial -Version 8, 2004. ,
A New Abstract Domain for the Representation of Mathematically Equivalent Expressions, SAS'12, pp.75-93, 2012. ,
DOI : 10.1007/978-3-642-33125-1_8
URL : https://hal.archives-ouvertes.fr/hal-00698618
An introduction to partial evaluation, ACM Computing Surveys, vol.28, issue.3, pp.480-503, 1996. ,
DOI : 10.1145/243439.243447
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.2016
An Introduction to Numerical Analysis, J. Wiley & Sons, 1989. ,
Optimal code motion: theory and practice, ACM Transactions on Programming Languages and Systems, vol.16, issue.4, pp.1117-1155, 1994. ,
DOI : 10.1145/183432.183443
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.5417
How to ensure a faithful polynomial evaluation with the compensated horner algorithm, ARITH-18, pp.141-149, 2007. ,
Composing dataflow analyses and transformations, 29th SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp.270-282, 2002. ,
DOI : 10.1145/565816.503298
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.6534
Practical Verification for the Working Programmer with CodeContracts and Abstract Interpretation, Verification, Model Checking, and Abstract Interpretation -12th International Conference, VMCAI, pp.19-22, 2011. ,
DOI : 10.1007/978-3-540-78791-4_14
Propagation of Roundoff Errors in Finite Precision Computations: A Semantics Approach, Programming Languages and Systems, 11th European Symposium on Programming, ESOP 2002, held as Part of the Joint European Conference on Theory and Practice of Software Proceedings, volume 2305 of Lecture Notes in Computer Science, pp.194-208, 2002. ,
DOI : 10.1007/3-540-45927-8_14
An Overview of Semantics for the Validation of Numerical Programs, Model Checking, and Abstract Interpretation, 6th International Conference, VMCAI 2005, pp.59-77, 2005. ,
DOI : 10.1007/978-3-540-30579-8_4
Semantics of roundoff error propagation in finite precision calculations. Higher- Order and Symbolic Computation, pp.7-30, 2006. ,
Semantics-Based Transformation of Arithmetic Expressions, Static Analysis, 14th International Symposium, SAS 2007, Proceedings, pp.298-314, 2007. ,
DOI : 10.1007/978-3-540-74061-2_19
Accurate evaluation of arithmetic expressions (invited talk) Electronic Notes in Theoretical Computer Science, pp.3-16, 2012. ,
The octagon abstract domain, Proceedings of the Eighth Working Conference on Reverse Engineering, WCRE'01, p.310, 2001. ,
Relational Abstract Domains for the Detection of Floating-Point Run-Time Errors, Programming Languages and Systems, 13th European Symposium on Programming, ESOP 2004, Held as Part of the Joint European Conferences on Theory and Practice of Software, pp.3-17, 2004. ,
DOI : 10.1007/978-3-540-24725-8_2
Domaines numérique abstraits faiblement relationnels, 2005. ,
The pitfalls of verifying floating-point computations, ACM Transactions on Programming Languages and Systems, vol.30, issue.3, 2008. ,
DOI : 10.1145/1353445.1353446
URL : https://hal.archives-ouvertes.fr/hal-00128124
Interval arithmetic and automatic error analysis in digital computing, p.25, 1962. ,
Interval analysis, 1966. ,
On the definition of ulp(x), 2005. ,
URL : https://hal.archives-ouvertes.fr/inria-00070503
Handbook of Floating-Point Arithmetic, 2010. ,
DOI : 10.1007/978-0-8176-4705-6
URL : https://hal.archives-ouvertes.fr/ensl-00379167
USS Yorktown Dead in Water After Divide by Zero, pp.45-0700, 1998. ,
Automatically improving accuracy for floating point expressions, PLDI'15, pp.1-11, 2015. ,
Precise interprocedural dataflow analysis with applications to constant propagation, Theoretical Computer Science, vol.167, issue.1-2, pp.131-170, 1996. ,
DOI : 10.1016/0304-3975(96)00072-2
URL : http://doi.org/10.1016/0304-3975(96)00072-2
Efficient Strongly Relational Polyhedral Analysis, Verification, Model Checking, and Abstract Interpretation, 7th International Conference, pp.111-125, 2006. ,
DOI : 10.1007/11609773_8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.8322
Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions, FM'15, pp.532-550, 2015. ,
DOI : 10.1007/978-3-319-19249-9_33
The value flow graph: A program representation for optimal program transformations, ESOP'90, 3rd European Symposium on Programming, pp.389-405, 1990. ,
DOI : 10.1007/3-540-52592-0_76
A lattice-theoretical fixpoint theorem and its applications, Pacific journal of mathematics, pp.285-309, 1955. ,
DOI : 10.2140/pjm.1955.5.285
Equality saturation : a new approach to optimization, ACM SIGPLAN-SIGACT POPL'09, pp.264-276, 2009. ,
Equality saturation : A new approach to optimization, Logical Methods in Computer Science, vol.7, issue.1, 2011. ,
Fine-tuning the accuracy of numerical computations in avionics automatic code generators, European Congress Embedded Real Time Software and Systems, ERTS 2016, pp.180-187, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01292294
An approach for exploring code improving transformations, ACM Transactions on Programming Languages and Systems, vol.19, issue.6, pp.1053-1084, 1997. ,
DOI : 10.1145/267959.267960