What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Formal Verification of Floating Point Trigonometric Functions
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
An overview of JML tools and applications
International Journal on Software Tools for Technology Transfer (STTT) - Special section on formal methods for industrial critical systems
SIAM Journal on Scientific Computing
Guaranteed Proofs Using Interval Arithmetic
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
Formal Verification of Floating-Point Programs
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
The pitfalls of verifying floating-point computations
ACM Transactions on Programming Languages and Systems (TOPLAS)
Combining Coq and Gappa for Certifying Floating-Point Programs
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Certification of bounds on expressions involving rounded operators
ACM Transactions on Mathematical Software (TOMS)
Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software
FMICS '09 Proceedings of the 14th International Workshop on Formal Methods for Industrial Critical Systems
The Why/Krakatoa/Caduceus platform for deductive program verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
The spec# programming system: an overview
CASSIS'04 Proceedings of the 2004 international conference on Construction and Analysis of Safe, Secure, and Interoperable Smart Devices
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Multi-Prover verification of floating-point programs
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Hardware-dependent proofs of numerical programs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
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On certain recently developed architectures, a numerical program may give different answers depending on the execution hardware and the compilation. Our goal is to formally prove properties about numerical programs that are true for multiple architectures and compilers. We propose an approach that states the rounding error of each floating-point computation whatever the environment and the compiler choices. This approach is implemented in the Frama-C platform for static analysis of C code. Small case studies using this approach are entirely and automatically proved.