Computer Arithmetic In Theory And Practice

Author : Ulrich W. Kulisch,Willard L. Miranker
Publisher : Academic Press
Page : 268 pages
File Size : 55,6 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483264738

Get Book

Computer Arithmetic in Theory and Practice by Ulrich W. Kulisch,Willard L. Miranker Pdf

Computer Arithmetic in Theory and Practice deals with computer arithmetic and the various implementations of the entire arithmetic package on diverse processors, including microprocessors. It illustrates the importance of theoretical development in the sound implementation of arithmetic on computers, and argues that such an implementation requires the establishment of various isomorphisms between different definitions of arithmetic operations. Comprised of seven chapters, this volume begins with an introduction to the theory of computer arithmetic by giving an axiomatic characterization of the essential properties of sets and subsets; complete lattices and complete subnets; screens and roundings; and arithmetic operations. The discussion then turns to the concepts of a ringoid and a vectoid as well as those of ordered or weakly ordered ringoids and vectoids; interval arithmetic; and floating-point arithmetic. The operations in interval spaces are defined by means of semimorphisms. The final chapter shows how to embed the five basic data types (integer, real, complex, real interval, and complex interval) together with the arithmetic operations that are defined for all of these types into existing higher programming languages. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.

Author : Ulrich Kulisch
Publisher : Walter de Gruyter
Page : 456 pages
File Size : 42,8 Mb
Release : 2013-04-30
Category : Mathematics
ISBN : 9783110301793

Get Book

Computer Arithmetic and Validity by Ulrich Kulisch Pdf

This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.

Author : Adams
Publisher : Academic Press
Page : 626 pages
File Size : 54,8 Mb
Release : 1992-12-03
Category : Computers
ISBN : 9780080958750

Get Book

Scientific Computing with Automatic Result Verification by Adams Pdf

Scientific Computing with Automatic Result Verification

Author : Sławomir Gryś
Publisher : CRC Press
Page : 213 pages
File Size : 54,8 Mb
Release : 2023-09-26
Category : Computers
ISBN : 9781000934892

Get Book

Computer Arithmetic in Practice by Sławomir Gryś Pdf

Computer Arithmetic in Practice: Exercises and Programming is a simple, brief introductory volume for undergraduate and graduate students at university courses interested in understanding the foundation of computers. It is focused on numeric data formats and capabilities of computers to perform basic arithmetic operations. It discusses mainly such topics as: Basic concepts of computer architecture Assembly language programming skills Data formats used to express integer and real numbers Algorithms of basic arithmetic operations Short overview of nonlinear functions evaluation Discussion on limited number representation and computer arithmetic Exercises and programming tasks This book provides an accessible overview of common data formats used to write numbers in programming languages and how the computer performs four basic arithmetic operations from the point of view of the processor instruction set. The book is primarily didactic in nature, therefore the theoretical information is enriched with many numerical examples and exercises to be solved using a ‘sheet of paper and a pencil’. Answers are provided for most of the tasks. The theoretical discussed issues are illustrated by listings of algorithms presenting the way to implement arithmetic operations in low-level language. It allows development of the skills of optimal programming, taking into consideration the computer architecture and limitations. Creating software using low-level language programming, despite the initial difficulties, gives the ability to control the code and create efficient applications. This allows for effective consolidation of knowledge and acquisition of practical skills required at this stage of education, mainly a specialist in the field of information technology, electronics, telecommunications, other related disciplines, or at the level of general education with introduction to information technology. It may be also useful for engineers interested in their own professional development and teachers as well.

Author : Milos D. Ercegovac,Tomás Lang
Publisher : Elsevier
Page : 736 pages
File Size : 43,5 Mb
Release : 2004
Category : Computers
ISBN : 9781558607989

Get Book

Digital Arithmetic by Milos D. Ercegovac,Tomás Lang Pdf

The authoritative reference on the theory and design practice of computer arithmetic.

Author : Christian Ullrich
Publisher : Academic Press
Page : 316 pages
File Size : 50,6 Mb
Release : 2014-05-10
Category : Computers
ISBN : 9781483267814

Get Book

Computer Arithmetic and Self-Validating Numerical Methods by Christian Ullrich Pdf

Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods, held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.

Author : Earl E Swartzlander
Publisher : World Scientific
Page : 486 pages
File Size : 50,6 Mb
Release : 2015-03-17
Category : Mathematics
ISBN : 9789814641487

Get Book

Computer Arithmetic by Earl E Swartzlander Pdf

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

Author : John Brooksmith
Publisher : Unknown
Page : 424 pages
File Size : 55,8 Mb
Release : 1889
Category : Arithmetic
ISBN : OCLC:32862651

Get Book

Arithmetic in Theory and Practice by John Brooksmith Pdf

Author : Richard P. Brent,Paul Zimmermann
Publisher : Cambridge University Press
Page : 238 pages
File Size : 52,8 Mb
Release : 2010-11-25
Category : Computers
ISBN : 9781139492287

Get Book

Modern Computer Arithmetic by Richard P. Brent,Paul Zimmermann Pdf

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.

Author : Jean-Michel Muller
Publisher : Birkhäuser
Page : 283 pages
File Size : 45,6 Mb
Release : 2016-11-16
Category : Computers
ISBN : 9781489979834

Get Book

Elementary Functions by Jean-Michel Muller Pdf

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)

Author : Urszula Bentkowska
Publisher : Springer
Page : 163 pages
File Size : 52,9 Mb
Release : 2019-02-08
Category : Technology & Engineering
ISBN : 9783030129279

Get Book

Interval-Valued Methods in Classifications and Decisions by Urszula Bentkowska Pdf

This book describes novel algorithms based on interval-valued fuzzy methods that are expected to improve classification and decision-making processes under incomplete or imprecise information. At first, it introduces interval-valued fuzzy sets. It then discusses new methods for aggregation on interval-valued settings, and the most common properties of interval-valued aggregation operators. It then presents applications such as decision making using interval-valued aggregation, and classification in case of missing values. Interesting applications of the developed algorithms to DNA microarray analysis and in medical decision support systems are shown. The book is intended not only as a timely report for the community working on fuzzy sets and their extensions but also for researchers and practitioners dealing with the problems of uncertain or imperfect information.

Author : J. Brook-Smith
Publisher : Unknown
Page : 424 pages
File Size : 47,7 Mb
Release : 1893
Category : Electronic
ISBN : OCLC:963469597

Get Book

Arithmetic in Theory and Practice by J. Brook-Smith Pdf

Author : R. Albrecht,G. Alefeld,H.J. Stetter
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783709169186

Get Book

Validation Numerics by R. Albrecht,G. Alefeld,H.J. Stetter Pdf

The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

Author : Tsau-Young Lin,Churn-Jung Liau,Janusz Kacprzyk
Publisher : Springer Nature
Page : 936 pages
File Size : 46,9 Mb
Release : 2023-03-29
Category : Mathematics
ISBN : 9781071626283

Get Book

Granular, Fuzzy, and Soft Computing by Tsau-Young Lin,Churn-Jung Liau,Janusz Kacprzyk Pdf

The first edition of the Encyclopedia of Complexity and Systems Science (ECSS, 2009) presented a comprehensive overview of granular computing (GrC) broadly divided into several categories: Granular computing from rough set theory, Granular Computing in Database Theory, Granular Computing in Social Networks, Granular Computing and Fuzzy Set Theory, Grid/Cloud Computing, as well as general issues in granular computing. In 2011, the formal theory of GrC was established, providing an adequate infrastructure to support revolutionary new approaches to computer/data science, including the challenges presented by so-called big data. For this volume of ECSS, Second Edition, many entries have been updated to capture these new developments, together with new chapters on such topics as data clustering, outliers in data mining, qualitative fuzzy sets, and information flow analysis for security applications. Granulations can be seen as a natural and ancient methodology deeply rooted in the human mind. Many daily "things" are routinely granulated into sub "things": The topography of earth is granulated into hills, plateaus, etc., space and time are granulated into infinitesimal granules, and a circle is granulated into polygons of infinitesimal sides. Such granules led to the invention of calculus, topology and non-standard analysis. Formalization of general granulation was difficult but, as shown in this volume, great progress has been made in combing discrete and continuous mathematics under one roof for a broad range of applications in data science.

Author : Ramon E. Moore
Publisher : Elsevier
Page : 447 pages
File Size : 46,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483277844

Get Book

Reliability in Computing by Ramon E. Moore Pdf

Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms. The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence. The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions. The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.