Computer Arithmetic and Formal Proofs : Verifying Floating-Point Algorithms with the Coq System

Sylvie Boldo

ISBN 10: 1785481126 / ISBN 13: 9781785481123

Published by Elsevier Science, 2017

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Seller Inventory # 9781785481123

Bibliographic Details

• Title: Computer Arithmetic and Formal Proofs : Verifying Floating-Point Algorithms with the Coq System
• Publisher: Elsevier Science
• Publication Date: 2017
• Language: English
• ISBN 10: 1785481126
• ISBN 13: 9781785481123
• Binding: Buch
• Condition: Neu
• Dimensions: 231W x 155H x 23D millimeters 231 millimeters width by 155 millimeters height by 23 millimeters depth
• Weight: 726 grams

About this title

Synopsis

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

About the Authors

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

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