Understanding Z: a specification language and its formal semantics
Understanding Z: a specification language and its formal semantics
Formal Methods Applied to a Floating-Point Number System
IEEE Transactions on Software Engineering
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
On properties of floating point arithmetics: numerical stability and the cost of accurate computations
Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Algorithms to reveal properties of floating-point arithmetic
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
A Mechanically Checked Proof of Correctness of the AMD K5 Floating Point Square Root Microcode
Formal Methods in System Design
Additive symmetries: the non-negative case
Theoretical Computer Science - Real numbers and computers
Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Isar - A Generic Interpretative Approach to Readable Formal Proof Documents
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
A Machine-Checked Theory of Floating Point Arithmetic
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Proof of Imperative Programs in Type Theory
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Multiplications of Floating Point Expansions
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Defining the IEEE-854 Floating-Point Standard in PVS
Defining the IEEE-854 Floating-Point Standard in PVS
Static and Dynamic Numerical Characteristics of Floating-Point Arithmetic
IEEE Transactions on Computers
Formalization of Cadence SPW Fixed-Point Arithmetic in HOL
IFM '02 Proceedings of the Third International Conference on Integrated Formal Methods
Dependent Types, Theorem Proving, and Applications for a Verifying Compiler
Verified Software: Theories, Tools, Experiments
Proving Bounds on Real-Valued Functions with Computations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Floats and Ropes: A Case Study for Formal Numerical Program Verification
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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
An overview of semantics for the validation of numerical programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Multi-Prover verification of floating-point programs
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Floating-point arithmetic in the Coq system
Information and Computation
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
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In this paper we present a general library to reason about floating-point numbers within the Coq system. Most of the results of the library are proved for an arbitrary floating-point format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors.