On the rapid computation of various polylogarithmic constants
Mathematics of Computation
The functional approach to programming
The functional approach to programming
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Verifying the Accuracy of Polynomial Approximations in HOL
TPHOLs '97 Proceedings of the 10th 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
New Algorithms for Improved Transcendental Functions on IA-64
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
Formal Verification of Square Root Algorithms
Formal Methods in System Design
Mechanical Verification of a Square Root Algorithm Using Taylor's Theorem
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
Formal Verification Methods for Industrial Hardware Design
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
Digitisation, Representation, and Formalisation
MKM '03 Proceedings of the Second International Conference on Mathematical Knowledge Management
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Provably faithful evaluation of polynomials
Proceedings of the 2006 ACM symposium on Applied computing
Formalization of fixed-point arithmetic in HOL
Formal Methods in System Design
Theorem Proving for Verification (Invited Tutorial)
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Real Number Calculations and Theorem Proving
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Cooperating Theorem Provers: A Case Study Combining HOL-Light and CVC Lite
Electronic Notes in Theoretical Computer Science (ENTCS)
Challenges for formal verification in industrial setting
FMICS'06/PDMC'06 Proceedings of the 11th international workshop, FMICS 2006 and 5th international workshop, PDMC conference on Formal methods: Applications and technology
Verifying nonlinear real formulas via sums of squares
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Improved bound for stochastic formal correctness of numerical algorithms
Innovations in Systems and Software Engineering
Efficient and accurate computation of upper bounds of approximation errors
Theoretical Computer Science
A Biologically Inspired Measure for Coexpression Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Proofs of numerical programs when the compiler optimizes
Innovations in Systems and Software Engineering
FM'05 Proceedings of the 2005 international conference on Formal Methods
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Floating-Point verification using theorem proving
SFM'06 Proceedings of the 6th international conference on Formal Methods for the Design of Computer, Communication, and Software Systems
Hardware-dependent proofs of numerical programs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
| Hi-index | 0.00 |
We have formal verified a number of algorithms for evaluating transcendental functions in double-extended precision floating point arithmetic in the Intel庐 IA-64 architecture. These algorithms are used in the Itanium驴 processor to provide compatibility with IA-32 (x86) hard-ware transcendentals, and similar ones are used in mathematical software libraries. In this paper we describe in some depth the formal verification of the sin and cos functions, including the initial range reduction step. This illustrates the different facets of verification in this field, covering both pure mathematics and the detailed analysis of floating point rounding.