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Computer Arithmetic And Formal Proofs

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Computer Arithmetic and Formal Proofs

Computer Arithmetic and Formal Proofs Book
Author : Sylvie Boldo,Guillaume Melquiond
Publisher : Elsevier
Release : 2017-11-17
ISBN : 0081011709
Language : En, Es, Fr & De

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Book Description :

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

Computer Arithmetic and Enclosure Methods

Computer Arithmetic and Enclosure Methods Book
Author : Lidiya Atanassova,Jurgen Herzberger,Jürgen Herzberger
Publisher : North Holland
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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 mathematics and engineering. Main subjects are: software tools for enclosure algorithms and inclusion methods with the help of interval arithmetic, in particular for the numerical solution of differential equations.

Handbook of Floating Point Arithmetic

Handbook of Floating Point Arithmetic Book
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 : 2018-05-02
ISBN : 3319765264
Language : En, Es, Fr & De

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Book Description :

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 program. The handbook is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.

Computer Arithmetic

Computer Arithmetic Book
Author : Earl E Swartzlander,Carl E Lemonds
Publisher : World Scientific
Release : 2015-02-12
ISBN : 981465115X
Language : En, Es, Fr & De

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Book Description :

Computer Arithmetic Volume III is a compilation of key papers in computer arithmetic on floating-point arithmetic and design. The intent is to show progress, evolution, and novelty in the area of floating-point arithmetic. This field has made extraordinary progress since the initial software routines on mainframe computers have evolved into hardware implementations in processors spanning a wide range of performance. Nevertheless, these papers pave the way to the understanding of modern day processors design where computer arithmetic are supported by floating-point units. The goal of Volume III is to collect the defining document for floating-point arithmetic and many of the key papers on the implementation of both binary and decimal floating-point arithmetic into a single volume. Although fewer than forty papers are included, their reference lists will direct the interested reader to other excellent work that could not be included here. Volume III is specifically oriented to the needs of designers and users of both general-purpose computers and special-purpose digital processors. The book should also be useful to systems engineers, computer architects, and logic designers. It is also intended to serve as a primary text for a course on floating-point arithmetic, as well as a supplementary text for courses in digital arithmetic and high-speed signal processing. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:OverviewFloating-Point AdditionFloating-Point MultiplicationRoundingFused Multiply AddFloating-Point DivisionElementary FunctionsDecimal Floating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:The papers that are included cover the key concepts needed to develop efficient (fast, small and low-power) floating-point processing unitsThe papers include presentations by the initial developers in their own words to better explain the basic techniquesIncludes five papers on decimal floating-point arithmetic, which has been added to the IEEE standardKeywords:Floating-Point Addition;Floating-Point Multiplication;Floating-Point Division;Decimal Floating-Point Arithmetic

Ideas That Created the Future

Ideas That Created the Future Book
Author : Harry R. Lewis
Publisher : Unknown
Release : 2021
ISBN : 0262045303
Language : En, Es, Fr & De

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Book Description :

"An anthology of classic papers in computer science with introductions by the editor"--

Knowing Machines

Knowing Machines Book
Author : Donald A. MacKenzie
Publisher : MIT Press
Release : 1998
ISBN : 9780262631884
Language : En, Es, Fr & De

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Book Description :

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.

Computer Arithmetic Scientific Computation and Mathematical Modelling

Computer Arithmetic  Scientific Computation and Mathematical Modelling Book
Author : Edgar W. Kaucher
Publisher : Unknown
Release : 1991
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Computer Arithmetic Scientific Computation and Mathematical Modelling book written by Edgar W. Kaucher, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Conference Proceedings

Conference Proceedings Book
Author : European Microwave Conference
Publisher : Unknown
Release : 1991
ISBN : 9780946821426
Language : En, Es, Fr & De

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Book Description :

Download Conference Proceedings book written by European Microwave Conference, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

14th IEEE Symposium on Computer Arithmetic

14th IEEE Symposium on Computer Arithmetic Book
Author : Israel Koren,Peter Kornerup
Publisher : IEEE
Release : 1999
ISBN : 9780769501161
Language : En, Es, Fr & De

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Book Description :

The proceedings of the April 1999 symposium consists of 31 papers that report scientific work being done on computer arithmetic, number systems, and the implementation of arithmetic processing components. The papers are divided into the general areas of processor enhancements, addition, division, cryptography and graphics, divide and square root, alternative number systems, residue number systems, CORDIC algorithms, multiplication and rounding, and floating point. No subject index. Annotation copyrighted by Book News, Inc., Portland, OR.

A Computer System for Checking Proofs

A Computer System for Checking Proofs Book
Author : Scott D. Johnson
Publisher : Unknown
Release : 1982
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download A Computer System for Checking Proofs book written by Scott D. Johnson, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Formal Methods in Computer aided Design

Formal Methods in Computer aided Design Book
Author : Anonim
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Formal Methods in Computer aided Design book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Tutorial Programming Language Design

Tutorial  Programming Language Design Book
Author : Anthony I. Wasserman
Publisher : Unknown
Release : 1980
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Tutorial Programming Language Design book written by Anthony I. Wasserman, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Formal Proofs and Refutations

Formal Proofs and Refutations Book
Author : Jesse Alama
Publisher : Unknown
Release : 2009
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Formal Proofs and Refutations book written by Jesse Alama, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

AFIPS Conference Proceedings

AFIPS Conference Proceedings Book
Author : Anonim
Publisher : Unknown
Release : 1972
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download AFIPS Conference Proceedings book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Conference Record of the Thirty Fifth Asilomar Conference on Signals Systems Computers

Conference Record of the Thirty Fifth Asilomar Conference on Signals  Systems   Computers Book
Author : Asilomar Conference on Signals, Systems & Computers
Publisher : Unknown
Release : 2001
ISBN : 9780780371477
Language : En, Es, Fr & De

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Book Description :

Download Conference Record of the Thirty Fifth Asilomar Conference on Signals Systems Computers book written by Asilomar Conference on Signals, Systems & Computers, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Computer Arithmetic

Computer Arithmetic Book
Author : Behrooz Parhami
Publisher : Oxford University Press, USA
Release : 2010
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Ideal for graduate and senior undergraduate courses in computer arithmetic and advanced digital design, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, provides a balanced, comprehensive treatment of computer arithmetic. It covers topics in arithmetic unit design and circuit implementation that complement the architectural and algorithmic speedup techniques used in high-performance computer architecture and parallel processing. Using a unified and consistent framework, the text begins with number representation and proceeds through basic arithmetic operations, floating-point arithmetic, and function evaluation methods. Later chapters cover broad design and implementation topics-including techniques for high-throughput, low-power, fault-tolerant, and reconfigurable arithmetic. An appendix provides a historical view of the field and speculates on its future. An indispensable resource for instruction, professional development, and research, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, combines broad coverage of the underlying theories of computer arithmetic with numerous examples of practical designs, worked-out examples, and a large collection of meaningful problems. This second edition includes a new chapter on reconfigurable arithmetic, in order to address the fact that arithmetic functions are increasingly being implemented on field-programmable gate arrays (FPGAs) and FPGA-like configurable devices. Updated and thoroughly revised, the book offers new and expanded coverage of saturating adders and multipliers, truncated multipliers, fused multiply-add units, overlapped quotient digit selection, bipartite and multipartite tables, reversible logic, dot notation, modular arithmetic, Montgomery modular reduction, division by constants, IEEE floating-point standard formats, and interval arithmetic. Features: * Divided into 28 lecture-size chapters * Emphasizes both the underlying theories of computer arithmetic and actual hardware designs * Carefully links computer arithmetic to other subfields of computer engineering * Includes 717 end-of-chapter problems ranging in complexity from simple exercises to mini-projects * Incorporates many examples of practical designs * Uses consistent standardized notation throughout * Instructor's manual includes solutions to text problems * An author-maintained website http://www.ece.ucsb.edu/~parhami/text_comp_arit.htm contains instructor resources, including complete lecture slides

International Conference on Computer Design

International Conference on Computer Design Book
Author : Anonim
Publisher : Unknown
Release : 1995
ISBN : 9780818671654
Language : En, Es, Fr & De

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Book Description :

Download International Conference on Computer Design book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Computer Performance Evaluation

Computer Performance Evaluation Book
Author : Anonim
Publisher : Unknown
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Computer Performance Evaluation book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.