Computer Arithmetic and Formal Proofs

Verifying Floating-Point Algorithms with the Coq System
Erscheinungsjahr 2017
ISBN: 978-1-78548-112-3
Verlag: Elsevier Science

Buch, Englisch, 326 Seiten, Format (B × H): 155 mm x 231 mm, Gewicht: 726 g

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.

Zielgruppe

Graduates students in computer science; Researchers in either computer arithmetic or formal verification.

Autoren/Hrsg.

Boldo, Sylvie

Melquiond, Guillaume

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten

Inhaltsverzeichnis

1. Floating-Point Arithmetic2. The Coq System3. Formalization of Formats and Basic Operators4. Automated Methods5. Error-Free Computations and Applications6. Example Proofs of Advanced Operators7. Compilation of FP Programs8. Deductive Program Verification9. Real and Numerical Analysis

Über Autor(innen)

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

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