Modern Computer Arithmetic
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Modern Computer Arithmetic
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Author : Richard P. Brent
language : en
Publisher: Cambridge University Press
Release Date : 2010-11-25
Modern Computer Arithmetic written by Richard P. Brent and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Computers categories.
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 implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors.
Modern Computer Arithmetic
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Author : Richard P. Brent
language : en
Publisher: Cambridge University Press
Release Date : 2010-11-25
Modern Computer Arithmetic written by Richard P. Brent and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Computers categories.
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 favorite 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 implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors.
Modern Computer Arithmetic
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 2014-05-14
Modern Computer Arithmetic written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Computer arithmetic categories.
Contains all state-of-the-art algorithms dealing with multiple-precision integers or floating-point numbers in a ready-to-implement format.
Computer Arithmetic And Formal Proofs
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Author : Sylvie Boldo
language : en
Publisher: Elsevier
Release Date : 2017-11-17
Computer Arithmetic And Formal Proofs written by Sylvie Boldo and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Computers categories.
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
Advanced Computer Arithmetic Design
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Author : Michael J. Flynn
language : en
Publisher: Wiley-Interscience
Release Date : 2001
Advanced Computer Arithmetic Design written by Michael J. Flynn and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
Innovative techniques and cutting-edge research in computer arithmetic design Computer arithmetic is a fundamental discipline that drives many modern digital technologies. High-performance VLSI implementations of 3-D graphics, encryption, streaming digital audio and video, and signal processing all require fast and efficient computer arithmetic algorithms. The demand for these fast implementations has led to a wealth of new research in innovative techniques and designs. Advanced Computer Arithmetic Design is the result of ten years of effort at Stanford University under the Sub-Nanosecond Arithmetic Processor (SNAP) project, which author Michael Flynn directs. Written with computer designers and researchers in mind, this volume focuses on design, rather than on other aspects of computer arithmetic such as number systems, representation, or precision. Each chapter begins with a review of conventional design approaches, analyzes the possibilities for improvement, and presents new research that advances the state of the art. The authors present new data in these vital areas: ? Addition and the Ling adder ? Improvements to floating-point addition ? Encoding to reduce execution times for multiplication ? The effects of technology scaling on multiplication ? Techniques for floating-point division ? Approximation techniques for high-level functions such as square root, logarithms, and trigonometric functions ? Assessing cost performance of arithmetic units ? Clocking to increase computer operation frequency ? New implementation of continued fractions to the approximation of functions This volume presents the results of a decade's research in innovative and progressive design techniques. Covering all the most important research topics in the field, Advanced Computer Arithmetic Design is the most up-to-date and comprehensive treatment of new research currently available.
Digital Arithmetic
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Author : Milos D. Ercegovac
language : en
Publisher: Elsevier
Release Date : 2004
Digital Arithmetic written by Milos D. Ercegovac and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
The authoritative reference on the theory and design practice of computer arithmetic.
The Elements Of Computing Systems
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Author : Noam Nisan
language : en
Publisher:
Release Date : 2008
The Elements Of Computing Systems written by Noam Nisan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.
This title gives students an integrated and rigorous picture of applied computer science, as it comes to play in the construction of a simple yet powerful computer system.
Handbook Of Floating Point Arithmetic
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Author : Jean-Michel Muller
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-11
Handbook Of Floating Point Arithmetic written by Jean-Michel Muller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-11 with Mathematics categories.
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.
Bignum Math Implementing Cryptographic Multiple Precision Arithmetic
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Author : Tom St Denis
language : en
Publisher: Elsevier
Release Date : 2006-08-18
Bignum Math Implementing Cryptographic Multiple Precision Arithmetic written by Tom St Denis and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-18 with Computers categories.
Implementing cryptography requires integers of significant magnitude to resist cryptanalytic attacks. Modern programming languages only provide support for integers which are relatively small and single precision. The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms. Bignum math is the backbone of modern computer security algorithms. It is the ability to work with hundred-digit numbers efficiently using techniques that are both elegant and occasionally bizarre. This book introduces the reader to the concept of bignum algorithms and proceeds to build an entire library of functionality from the ground up. Through the use of theory, pseudo-code and actual fielded C source code the book explains each and every algorithm that goes into a modern bignum library. Excellent for the student as a learning tool and practitioner as a reference alike BigNum Math is for anyone with a background in computer science who has taken introductory level mathematic courses. The text is for students learning mathematics and cryptography as well as the practioner who needs a reference for any of the algorithms documented within. * Complete coverage of Karatsuba Multiplication, the Barrett Algorithm, Toom-Cook 3-Way Multiplication, and More * Tom St Denis is the developer of the industry standard cryptographic suite of tools called LibTom. * This book provides step-by-step exercises to enforce concepts
Computer Arithmetic
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Author : Earl E. Swartzlander, Jr.
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-18
Computer Arithmetic written by Earl E. Swartzlander, Jr. and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-18 with Computers categories.
This is the new edition of the classic book Computer Arithmetic in three volumes published originally in 1990 by IEEE Computer Society Press. As in the original, the book contains many classic papers treating advanced concepts in computer arithmetic, which is very suitable as stand-alone textbooks or complementary materials to textbooks on computer arithmetic for graduate students and research professionals interested in the field.Told in the words of the initial developers, this book conveys the excitement of the creators, and the implementations provide insight into the details necessary to realize real chips. This second volume presents topics on error tolerant arithmetic, digit on-line arithmetic, number systems, and now in this new edition, a topic on implementations of arithmetic operations, all wrapped with an updated overview and a new introduction for each chapter.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.