Computer Arithmetic and Formal Proofs

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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  • Author : Sylvie Boldo
  • Publisher : Elsevier
  • Pages : 326 pages
  • ISBN : 0081011709
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKComputer Arithmetic and Formal Proofs

Computer Arithmetic and Formal Proofs

Computer Arithmetic and Formal Proofs
  • Author : Sylvie Boldo,Guillaume Melquiond
  • Publisher : Elsevier
  • Release : 17 November 2017
GET THIS BOOKComputer Arithmetic and Formal Proofs

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

Handbook of Floating-Point Arithmetic

Handbook of Floating-Point Arithmetic
  • Author : Jean-Michel Muller,Nicolas Brunie,Florent de Dinechin,Claude-Pierre Jeannerod,Mioara Joldes,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Serge Torres
  • Publisher : Birkhäuser
  • Release : 02 May 2018
GET THIS BOOKHandbook of Floating-Point Arithmetic

Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding

Static Analysis

Static Analysis
  • Author : Cezara Drăgoi,Suvam Mukherjee,Kedar Namjoshi
  • Publisher : Springer Nature
  • Release : 13 October 2021
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This book constitutes the refereed proceedings of the 28th International Symposium on Static Analysis, SAS 2021, held in Chicago, IL, USA, in October 2021. The 18 regular and 4 short papers, carefully reviewed and selected from 48 submissions, are presented in this book together with 1-page summaries of the three invited talks. The papers cover topics such as static program analysis, abstract domain, abstract interpretation, automated deduction, debugging techniques, deductive methods, model checking, data science, program optimizations and transformations, program synthesis, program verification, and security

Intelligent Computer Mathematics

Intelligent Computer Mathematics
  • Author : Florian Rabe,William M. Farmer,Grant O. Passmore,Abdou Youssef
  • Publisher : Springer
  • Release : 02 August 2018
GET THIS BOOKIntelligent Computer Mathematics

​This book constitutes the refereed proceedings of the 11th International Conference on Intelligent Computer Mathematics, CICM 2018, held in Hagenberg, Austria, in August 2018. The 23 full papers presented were carefully reviewed and selected from a total of 36 submissions. The papers focos on the Calculemus, Digital Mathematics Libraries, and Mathematical Knowledge Management tracks which also correspond to the subject areas of the predecessor meetings. Orthogonally, the Systems and Projects track called for descriptions of digital resources, such as data and systems, and of

Essential Logic for Computer Science

Essential Logic for Computer Science
  • Author : Rex Page,Ruben Gamboa
  • Publisher : MIT Press
  • Release : 08 January 2019
GET THIS BOOKEssential Logic for Computer Science

An introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory. Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses

Formal Methods: Applications and Technology

Formal Methods: Applications and Technology
  • Author : Lubos Brim,Boudewijn Haverkort,Martin Leucker,Jaco van de Pol
  • Publisher : Springer
  • Release : 27 June 2007
GET THIS BOOKFormal Methods: Applications and Technology

This book constitutes the thoroughly refereed joint post-proceedings of the two International Workshops on Formal Methods for Industrial Critical Systems, FMICS 2006, and on Parallel and Distributed Methods in Verification, PDMC 2006, held in Bonn, Germany in August 2006 in the course of the 17th International Conference on Concurrency Theory, CONCUR 2006.

Modern Computer Arithmetic

Modern Computer Arithmetic
  • Author : Richard P. Brent,Paul Zimmermann
  • Publisher : Cambridge University Press
  • Release : 25 November 2010
GET THIS BOOKModern Computer Arithmetic

Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and

Proofs and Computations

Proofs and Computations
  • Author : Helmut Schwichtenberg,Stanley S. Wainer
  • Publisher : Cambridge University Press
  • Release : 15 December 2011
GET THIS BOOKProofs and Computations

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a

Proof and Disproof in Formal Logic

Proof and Disproof in Formal Logic
  • Author : Richard Bornat
  • Publisher : OUP Oxford
  • Release : 21 July 2005
GET THIS BOOKProof and Disproof in Formal Logic

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system—a collection of rules and axioms which define a universe of logical proofs—is what gives us programming languages and modern-day

Intelligent Computer Mathematics

Intelligent Computer Mathematics
  • Author : James H. Davenport,William M. Farmer,Florian Rabe,Josef Urban
  • Publisher : Springer
  • Release : 18 July 2011
GET THIS BOOKIntelligent Computer Mathematics

This book constitutes the joint refereed proceedings of three international events, namely the 18th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2011, the 10th International Conference on Mathematical Knowledge Management, MKM 2011, and a new track on Systems and Projects descriptions that span both the Calculemus and MKM topics, all held in Bertinoro, Italy, in July 2011. All 51 submissions passed through a rigorous review process. A total of 15 papers were submitted to Calculemus, of which 9 were accepted. Systems and

Computer Arithmetic and Enclosure Methods

Computer Arithmetic and Enclosure Methods
  • Author : Lidiya Atanassova,Jurgen Herzberger,Jürgen Herzberger
  • Publisher : North Holland
  • Release : 24 May 1992
GET THIS BOOKComputer Arithmetic and Enclosure Methods

Scientists concerned with the interaction between computer arithmetic, programming languages and scientific computing will be particularly interested in this book. It focuses on papers presented at the conference and highlights the increasing impact of SCAN-91 in this area. The volume contains original research and expository articles on the field of interaction between computer arithmetic and its realization in programming languages and the construction and investigation of numerical algorithms for computing guaranteed error-bounds for the solution of various problems in applied

Knowing Machines

Knowing Machines
  • Author : Donald A. MacKenzie
  • Publisher : MIT Press
  • Release : 24 May 1998
GET THIS BOOKKnowing Machines

The essays are tied together by their explorations of connections (primarily among technology, society, and knowledge) and by their general focus on modern "high" technology. They also share an emphasis on the complexity of technological formation and fixation and on the role of belief (especially self-validating belief) in technological change.