Computer Arithmetic in Theory and Practice

Computer Arithmetic in Theory and Practice PDF

Author: Ulrich W. Kulisch

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 268

ISBN-13: 1483264734

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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.

Computer Arithmetic and Validity

Computer Arithmetic and Validity PDF

Author: Ulrich Kulisch

Publisher: Walter de Gruyter

Published: 2013-04-30

Total Pages: 456

ISBN-13: 3110301792

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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.

Computer Science with MATHEMATICA ®

Computer Science with MATHEMATICA ® PDF

Author: Roman Maeder

Publisher: Cambridge University Press

Published: 2000-02-28

Total Pages: 414

ISBN-13: 9780521663953

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This introductory course shows scientists and engineers how Mathematica can be used to do scientific computations.

Computer Arithmetic

Computer Arithmetic PDF

Author: Behrooz Parhami

Publisher: Oxford University Press, USA

Published: 2010

Total Pages: 684

ISBN-13:

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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.

Digital Arithmetic

Digital Arithmetic PDF

Author: Milos D. Ercegovac

Publisher: Elsevier

Published: 2004

Total Pages: 736

ISBN-13: 1558607986

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

Computer Arithmetic in Practice

Computer Arithmetic in Practice PDF

Author: Sławomir Gryś

Publisher: CRC Press

Published: 2023-09-26

Total Pages: 213

ISBN-13: 1000934896

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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.

Modern Computer Arithmetic

Modern Computer Arithmetic PDF

Author: Richard P. Brent

Publisher: Cambridge University Press

Published: 2010-11-25

Total Pages: 238

ISBN-13: 1139492284

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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.

Computer Arithmetic and Self-Validating Numerical Methods

Computer Arithmetic and Self-Validating Numerical Methods PDF

Author: Christian Ullrich

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 316

ISBN-13: 1483267814

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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.

Computer Aided Systems Theory - EUROCAST 2007

Computer Aided Systems Theory - EUROCAST 2007 PDF

Author: Roberto Moreno Díaz

Publisher: Springer

Published: 2007-11-16

Total Pages: 1236

ISBN-13: 3540758674

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This book constitutes the thoroughly refereed post-proceedings of the 11th International Conference on Computer Aided Systems Theory, EUROCAST 2007. Coverage in the 144 revised full papers presented includes formal approaches, computation and simulation in modeling biological systems, intelligent information processing, heuristic problem solving, signal processing architectures, robotics and robotic soccer, cybercars and intelligent vehicles and artificial intelligence components.

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