Computer Arithmetic and Formal Proofs

Verifying Floating-point Algorithms with the Coq System

Nonfiction, Science & Nature, Mathematics, Discrete Mathematics, Computers, Advanced Computing, Computer Science
Cover of the book Computer Arithmetic and Formal Proofs by Guillaume Melquiond, Sylvie Boldo, Elsevier Science
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Author: Guillaume Melquiond, Sylvie Boldo ISBN: 9780081011706
Publisher: Elsevier Science Publication: November 17, 2017
Imprint: ISTE Press - Elsevier Language: English
Author: Guillaume Melquiond, Sylvie Boldo
ISBN: 9780081011706
Publisher: Elsevier Science
Publication: November 17, 2017
Imprint: ISTE Press - Elsevier
Language: English

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 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
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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.  

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