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Computer Arithmetic and Formal Proofs - 1st Edition - ISBN: 9781785481123, 9780081011706

Computer Arithmetic and Formal Proofs

1st Edition

Verifying Floating-point Algorithms with the Coq System

Authors: Sylvie Boldo Guillaume Melquiond
Hardcover ISBN: 9781785481123
eBook ISBN: 9780081011706
Imprint: ISTE Press - Elsevier
Published Date: 16th November 2017
Page Count: 326
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Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs.

This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation.

Key Features

  • Describes the notions of specification and weakest precondition computation and their practical use
  • Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic
  • Includes real analysis and a case study about numerical analysis


Graduate students in computer science; Researchers in either computer arithmetic or formal verification

Table of Contents

1. Floating-Point Arithmetic
2. The Coq System
3. Formalization of Formats and Basic Operators
4. Automated Methods
5. Error-Free Computations and Applications
6. Example Proofs of Advanced Operators
7. Compilation of FP Programs
8. Deductive Program Verification
9. Real and Numerical Analysis


No. of pages:
© ISTE Press - Elsevier 2017
16th November 2017
ISTE Press - Elsevier
Hardcover ISBN:
eBook ISBN:

About the Authors

Sylvie Boldo

Sylvie Boldo is a Research Director at INRIA in Orsay, France.

Affiliations and Expertise

INRIA, France

Guillaume Melquiond

Guillaume Melquiond is a Researcher at INRIA in Orsay, France.

Affiliations and Expertise

INRIA, France

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