Download or read book Finite Precision Number Systems and Arithmetic written by Peter Kornerup and published by Cambridge University Press. This book was released on 2010-09-30 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.
Download or read book Lectures on Finite Precision Computations written by Francoise Chaitin-Chatelin and published by SIAM. This book was released on 1996-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Fundamentals of Numerical Computation Computer Oriented Numerical Analysis written by G. Alefeld and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computer Arithmetic written by Earl E Swartzlander and published by World Scientific. This book was released on 2015-03-17 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Error Tolerant ArithmeticOn-Line ArithmeticVLSI Adder ImplementationsVLSI Multiplier ImplementationsFloating-Point VLSI ChipsNumber RepresentationImplementations Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers advanced arithmetic operationsIt does this in the words of the original creatorsKeywords:Computer Arithmetic;Fault Tolerant;Arithmetic;On-Line Arithmetic;Adder Implementations;Multiplier Implementations;Floating Point Chips;Number Representation;Implementations
Download or read book Computer Number Systems and Arithmetic written by Norman Ross Scott and published by Prentice Hall. This book was released on 1985 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Floating Point Arithmetic written by Jean-Michel Muller and published by Springer Science & Business Media. This book was released on 2009-11-11 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Accuracy and Stability of Numerical Algorithms written by Nicholas J. Higham and published by SIAM. This book was released on 2002-01-01 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.
Download or read book Dynamics of Number Systems written by Petr Kurka and published by Springer. This book was released on 2016-06-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a source of valuable and useful information on the topics of dynamics of number systems and scientific computation with arbitrary precision. It is addressed to scholars, scientists and engineers, and graduate students. The treatment is elementary and self-contained with relevance both for theory and applications. The basic prerequisite of the book is linear algebra and matrix calculus.
Download or read book Embedded Systems Design with Special Arithmetic and Number Systems written by Amir Sabbagh Molahosseini and published by Springer. This book was released on 2017-03-20 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems.
Download or read book Numerical Computing with IEEE Floating Point Arithmetic written by Michael L. Overton and published by SIAM. This book was released on 2001-01-01 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Elementary Functions written by Jean-Michel Muller and published by Birkhäuser. This book was released on 2016-11-16 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom-Cook family of multiplication algorithms. The techniques presented in this book will be of interest to implementers of elementary function libraries or circuits and programmers of numerical applications. Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find this a useful reference and resource. PRAISE FOR PREVIOUS EDITIONS “[T]his book seems like an essential reference for the experts (which I'm not). More importantly, this is an interesting book for the curious (which I am). In this case, you'll probably learn many interesting things from this book. If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class." — MAA Reviews (Review of Second Edition) "The rich content of ideas sketched or presented in some detail in this book is supplemented by a list of over three hundred references, most of them of 1980 or more recent. The book also contains some relevant typical programs." — Zentralblatt MATH (Review of Second Edition) “I think that the book will be very valuable to students both in numerical analysis and in computer science. I found [it to be] well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find." — Numerical Algorithms (Review of First Edition)
Download or read book Numerical Computing with MATLAB written by Cleve B. Moler and published by SIAM. This book was released on 2010-08-12 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.
Download or read book Implementation and Application of Automata written by Markus Holzer and published by Springer. This book was released on 2014-07-05 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Conference on Implementation and Application of Automata, CIAA 2014, held in Giessen, Germany, in July/August 2014. The 21 revised full papers presented together with 4 invited papers were carefully selected from 36 submissions. The papers cover all aspects of implementation, application, and theory of automata and related structures such as algorithms on automata, automata and logic, bioinformatics, complexity of automata operations, compilers, computer-aided verification, concurrency, data structure design for automata, data and image compression, design and architecture of automata software, digital libraries, DNA/molecular/membrane computing, document engineering, editors, environments, experimental studies and practical experience, implementation of verification methods and model checking, industrial applications, natural language and speech processing, networking, new algorithms for manipulating automata, object-oriented modeling, pattern-matching, pushdown automata and context-free grammars, quantum computing, structured and semi-structured documents, symbolic manipulation environments for automata, transducers and multi-tape automata, techniques for graphical display of automata, VLSI, viruses and related phenomena, and world-wide Web.
Download or read book Verification Model Checking and Abstract Interpretation written by Ranjit Jhala and published by Springer Science & Business Media. This book was released on 2011-01-11 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2011, held in Austin, TX, USA, in January 2011, co-located with the Symposium on Principles of Programming Languages, POPL 2011. The 24 revised full papers presented together with 4 invited talks were carefully reviewed and selected from 71 initial submissions. The papers showcases state-of-the-art research in areas such as verification, model checking, abstract interpretation and address any programming paradigm, including concurrent, constraint, functional, imperative, logic and object-oriented programming. Further topics covered are static analysis, deductive methods, program certification, debugging techniques, abstract domains, type systems, and optimization.
Download or read book Numerical Mathematics written by Matheus Grasselli and published by Jones & Bartlett Learning. This book was released on 2008 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Mathematics presents the innovative approach of using numerical methods as a practical laboratory for all undergraduate mathematics courses in science and engineering streams. The authors bridge the gap between numerical methods and undergraduate mathematics and emphasize the graphical visualization of mathematical properties, numerical verification of formal statements, and illustrations of the mathematical ideas. Students using Numerical Mathematics as a supplementary reference for basic mathematical courses will be encouraged to deveolp their mathematical intuition with an effective component of technology, while students using it as the primary text for numerical courses will have a broader, reinforced understanding of the subject.
Download or read book Equivalents of the Riemann Hypothesis Volume 1 Arithmetic Equivalents written by Kevin Broughan and published by Cambridge University Press. This book was released on 2017-11-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.
Download or read book Numerical Computing with IEEE Floating Point Arithmetic written by Michael L. Overton and published by Soc for Industrial & Applied Math. This book was released on 2001 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
