Exact Real Computer Arithmetic with Continued Fractions
IEEE Transactions on Computers
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
Codifying Guarded Definitions with Recursive Schemes
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
A monadic, functional implementation of real numbers
Mathematical Structures in Computer Science
Coinductive correctness of homographic and quadratic algorithms for exact real numbers
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
IJCAR'06 Proceedings of the Third 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 '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Certified Exact Transcendental Real Number Computation in Coq
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Formal Verification of Exact Computations Using Newton's Method
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Computer certified efficient exact reals in Coq
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Designing and proving correct a convex hull algorithm with hypermaps in Coq
Computational Geometry: Theory and Applications
Hi-index | 0.00 |
In this paper we describe some certified algorithms for exact real arithmetic based on co-recursion. Our work is based on previous experiences using redundant digits of base 2 but generalizes them using arbitrary integer bases. The goal is to take benefit of fast native integer computation. We extend a technique to compute converging series. We use this technique to compute the product and the inverse. We describe how we implement and certify our algorithms in the proof system Coq and evaluate the efficiency of the library inside the prover.