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Computer arithmetic and formal proofs : verifying floating-point algorithms with the Coq system

Author: Sylvie Boldo; Guillaume Melquiond
Publisher: London : ISTE Press ; Oxford, UK : Elsevier, 2017.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Boldo, Sylvie.
Computer arithmetic and formal proofs : verifying floating-point algorithms with the Coq system.
London, England ; ISTE Press : Elsevier, ©2017
xx, 306 pages
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sylvie Boldo; Guillaume Melquiond
ISBN: 9780081011706 0081011709
OCLC Number: 1012400060
Description: 1 online resource
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
Responsibility: Sylvie Boldo, Guillaume Melquiond.

Abstract:

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. Describes the notions of specification and weakest precondition computation and their practical useShows how to tackle algorithms that extend beyond the realm of simple floating-point arithmeticIncludes real analysis and a case study about numerical analysis.

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