Computer Arithmetic

Algorithms and Hardware Designs
Author: Behrooz Parhami
Publisher: Oxford University Press, USA
ISBN: 9780195328486
Category: Computers
Page: 641
View: 6836

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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. 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

Computer Arithmetic

Algorithms and Hardware Implementations
Author: Mircea Vlăduţiu
Publisher: Springer Science & Business Media
ISBN: 364218314X
Category: Computers
Page: 270
View: 2205

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The subject of this book is the analysis and design of digital devices that implement computer arithmetic. The book's presentation of high-level detail, descriptions, formalisms and design principles means that it can support many research activities in this field, with an emphasis on bridging the gap between algorithm optimization and hardware implementation. The author provides a unified view linking the domains of digital design and arithmetic algorithms, based on original formalisms and hardware description languages. A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures. The book is suitable for researchers and students engaged with hardware design in computer science and engineering. A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures. The book is suitable for researchers and students engaged with hardware design in computer science and engineering.

Computer Arithmetic and Verilog HDL Fundamentals


Author: Joseph Cavanagh
Publisher: CRC Press
ISBN: 1351834118
Category: Computers
Page: 971
View: 2779

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Verilog Hardware Description Language (HDL) is the state-of-the-art method for designing digital and computer systems. Ideally suited to describe both combinational and clocked sequential arithmetic circuits, Verilog facilitates a clear relationship between the language syntax and the physical hardware. It provides a very easy-to-learn and practical means to model a digital system at many levels of abstraction. Computer Arithmetic and Verilog HDL Fundamentals details the steps needed to master computer arithmetic for fixed-point, decimal, and floating-point number representations for all primary operations. Silvaco International’s SILOS, the Verilog simulator used in these pages, is simple to understand, yet powerful enough for any application. It encourages users to quickly prototype and de-bug any logic function and enables single-stepping through the Verilog source code. It also presents drag-and-drop abilities. Introducing the three main modeling methods—dataflow, behavioral, and structural—this self-contained tutorial— Covers the number systems of different radices, such as octal, decimal, hexadecimal, and binary-coded variations Reviews logic design fundamentals, including Boolean algebra and minimization techniques for switching functions Presents basic methods for fixed-point addition, subtraction, multiplication, and division, including the use of decimals in all four operations Addresses floating-point addition and subtraction with several numerical examples and flowcharts that graphically illustrate steps required for true addition and subtraction for floating-point operands Demonstrates floating-point division, including the generation of a zero-biased exponent Designed for electrical and computer engineers and computer scientists, this book leaves nothing unfinished, carrying design examples through to completion. The goal is practical proficiency. To this end, each chapter includes problems of varying complexity to be designed by the reader.

Digital Arithmetic


Author: Miloš D. Ercegovac,Tomás Lang
Publisher: Elsevier
ISBN: 1558607986
Category: Computers
Page: 709
View: 925

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

Computer Arithmetic Algorithms, Second Edition


Author: Israel Koren
Publisher: A K Peters/CRC Press
ISBN: 9781568811604
Category: Computers
Page: 296
View: 3771

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This text explains the fundamental principles of algorithms available for performing arithmetic operations on digital computers. These include basic arithmetic operations like addition, subtraction, multiplication, and division in fixed-point and floating-point number systems as well as more complex operations such as square root extraction and evaluation of exponential, logarithmic, and trigonometric functions. The algorithms described are independent of the particular technology employed for their implementation.

Advanced computer arithmetic design


Author: Michael J. Flynn,Stuart F. Oberman
Publisher: Wiley-Interscience
ISBN: 9780471412090
Category: Computers
Page: 325
View: 9788

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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.

Hardware Implementation of Finite-Field Arithmetic


Author: Jean-Pierre Deschamps
Publisher: McGraw Hill Professional
ISBN: 0071545824
Category: Technology & Engineering
Page: 360
View: 2974

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Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC) Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. This comprehensive resource begins with an overview of mathematics, covering algebra, number theory, finite fields, and cryptography. The book then presents algorithms which can be executed and verified with actual input data. Logic schemes and VHDL models are described in such a way that the corresponding circuits can be easily simulated and synthesized. The book concludes with a real-world example of a finite-field application--elliptic-curve cryptography. This is an essential guide for hardware engineers involved in the development of embedded systems. Get detailed coverage of: Modulo m reduction Modulo m addition, subtraction, multiplication, and exponentiation Operations over GF(p) and GF(pm) Operations over the commutative ring Zp[x]/f(x) Operations over the binary field GF(2m) using normal, polynomial, dual, and triangular

Numerical Methods

Design, Analysis, and Computer Implementation of Algorithms
Author: Anne Greenbaum,Timothy P. Chartier
Publisher: Princeton University Press
ISBN: 1400842670
Category: Mathematics
Page: 464
View: 3174

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Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online

Algorithms and Design Methods for Digital Computer Arithmetic


Author: Behrooz Parhami
Publisher: N.A
ISBN: 9780199766932
Category: Computer algorithms
Page: 623
View: 9011

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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.Readership: Graduate and senior undergraduate courses in computer arithmetic and advanced digital design.

Elementary Functions

Algorithms and Implementation
Author: Jean-Michel Muller
Publisher: Birkhäuser
ISBN: 1489979832
Category: Computers
Page: 283
View: 3159

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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)

Principles of Computer Hardware


Author: Alan Clements
Publisher: Oxford University Press
ISBN: 0199273138
Category: Computers
Page: 656
View: 5121

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The fourth edition of this work provides a readable, tutorial based introduction to the subject of computer hardware for undergraduate computer scientists and engineers and includes a companion website to give lecturers additional notes.

Structure and Interpretation of Computer Programs


Author: Harold Abelson
Publisher: Mit Press
ISBN: 9780262011532
Category: Computers
Page: 657
View: 4911

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Structure and Interpretation of Computer Programs has had a dramatic impact on computer science curricula over the past decade. This long-awaited revision contains changes throughout the text. There are new implementations of most of the major programming systems in the book, including the interpreters and compilers, and the authors have incorporated many small changes that reflect their experience teaching the course at MIT since the first edition was published. A new theme has been introduced that emphasizes the central role played by different approaches to dealing with time in computational models: objects with state, concurrent programming, functional programming and lazy evaluation, and nondeterministic programming. There are new example sections on higher-order procedures in graphics and on applications of stream processing in numerical programming, and many new exercises. In addition, all the programs have been reworked to run in any Scheme implementation that adheres to the IEEE standard.

Introduction to Parallel Processing

Algorithms and Architectures
Author: Behrooz Parhami
Publisher: Springer Science & Business Media
ISBN: 0306469642
Category: Business & Economics
Page: 532
View: 5494

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THE CONTEXT OF PARALLEL PROCESSING The field of digital computer architecture has grown explosively in the past two decades. Through a steady stream of experimental research, tool-building efforts, and theoretical studies, the design of an instruction-set architecture, once considered an art, has been transformed into one of the most quantitative branches of computer technology. At the same time, better understanding of various forms of concurrency, from standard pipelining to massive parallelism, and invention of architectural structures to support a reasonably efficient and user-friendly programming model for such systems, has allowed hardware performance to continue its exponential growth. This trend is expected to continue in the near future. This explosive growth, linked with the expectation that performance will continue its exponential rise with each new generation of hardware and that (in stark contrast to software) computer hardware will function correctly as soon as it comes off the assembly line, has its down side. It has led to unprecedented hardware complexity and almost intolerable dev- opment costs. The challenge facing current and future computer designers is to institute simplicity where we now have complexity; to use fundamental theories being developed in this area to gain performance and ease-of-use benefits from simpler circuits; to understand the interplay between technological capabilities and limitations, on the one hand, and design decisions based on user and application requirements on the other.

Discovering Modern C++

An Intensive Course for Scientists, Engineers, and Programmers
Author: Peter Gottschling
Publisher: Addison-Wesley Professional
ISBN: 0134383664
Category: Computers
Page: 480
View: 7002

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As scientific and engineering projects grow larger and more complex, it is increasingly likely that those projects will be written in C++. With embedded hardware growing more powerful, much of its software is moving to C++, too. Mastering C++ gives you strong skills for programming at nearly every level, from “close to the hardware” to the highest-level abstractions. In short, C++ is a language that scientific and technical practitioners need to know. Peter Gottschling’s Discovering Modern C++ is an intensive introduction that guides you smoothly to sophisticated approaches based on advanced features. Gottschling introduces key concepts using examples from many technical problem domains, drawing on his extensive experience training professionals and teaching C++ to students of physics, math, and engineering. This book is designed to help you get started rapidly and then master increasingly robust features, from lambdas to expression templates. You’ll also learn how to take advantage of the powerful libraries available to C++ programmers: both the Standard Template Library (STL) and scientific libraries for arithmetic, linear algebra, differential equations, and graphs. Throughout, Gottschling demonstrates how to write clear and expressive software using object orientation, generics, metaprogramming, and procedural techniques. By the time you’re finished, you’ll have mastered all the abstractions you need to write C++ programs with exceptional quality and performance.

The Quest for Artificial Intelligence


Author: Nils J. Nilsson
Publisher: Cambridge University Press
ISBN: 1139642820
Category: Computers
Page: N.A
View: 4483

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Artificial intelligence (AI) is a field within computer science that is attempting to build enhanced intelligence into computer systems. This book traces the history of the subject, from the early dreams of eighteenth-century (and earlier) pioneers to the more successful work of today's AI engineers. AI is becoming more and more a part of everyone's life. The technology is already embedded in face-recognizing cameras, speech-recognition software, Internet search engines, and health-care robots, among other applications. The book's many diagrams and easy-to-understand descriptions of AI programs will help the casual reader gain an understanding of how these and other AI systems actually work. Its thorough (but unobtrusive) end-of-chapter notes containing citations to important source materials will be of great use to AI scholars and researchers. This book promises to be the definitive history of a field that has captivated the imaginations of scientists, philosophers, and writers for centuries.

The Algorithm Design Manual


Author: Steven S Skiena
Publisher: Springer Science & Business Media
ISBN: 1848000707
Category: Computers
Page: 730
View: 3032

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This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography. NEW to the second edition: • Doubles the tutorial material and exercises over the first edition • Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video • Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them • Includes several NEW "war stories" relating experiences from real-world applications • Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java