TY  - BOOK
AU  - Boldo,Sylvie
AU  - Melquiond,Guillaume
TI  - Computer arithmetic and formal proofs: verifying floating-point algorithms with the Coq system 
SN  - 9780081011706
AV  - QA76.9.C62 
U1  - 004.01/51 23
PY  - 2017///
CY  - London, Oxford, UK
PB  - ISTE Press, Elsevier
KW  - Coq (Electronic resource)
KW  - Computer arithmetic
KW  - Floating-point arithmetic
KW  - Computer algorithms
N1  - Includes bibliographical references and index
N2  - 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
UR  - https://www.sciencedirect.com/science/book/9781785481123
ER  -