Table-driven implementation of the logarithm function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Fast evaluation of elementary mathematical functions with correctly rounded last bit
ACM Transactions on Mathematical Software (TOMS)
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
A Machine-Checked Theory of Floating Point Arithmetic
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Guaranteed Proofs Using Interval Arithmetic
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
MPFR: A multiple-precision binary floating-point library with correct rounding
ACM Transactions on Mathematical Software (TOMS)
Proving Bounds on Real-Valued Functions with Computations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Real number calculations and theorem proving
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
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The process of proving some mathematical theorems can be greatly reduced by relying on numerically-intensive computations with a certified arithmetic. This article presents a formalization of floating-point arithmetic that makes it possible to efficiently compute inside the proofs of the Coq system. This certified library is a multi-radix and multi-precision implementation free from underflow and overflow. It provides the basic arithmetic operators and a few elementary functions.