Advanced Arithmetic for the Digital Computer

Advanced Arithmetic for the Digital Computer

Author: Ulrich W. Kulisch

Publisher: Springer Science & Business Media

Published: 2012-09-07

Total Pages: 151

ISBN-13: 3709105250

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The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.


Advanced Computer Arithmetic Design

Advanced Computer Arithmetic Design

Author: Michael J. Flynn

Publisher: Wiley-Interscience

Published: 2001

Total Pages: 352

ISBN-13:

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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.


Computer Arithmetic and Validity

Computer Arithmetic and Validity

Author: Ulrich Kulisch

Publisher: ISSN

Published: 2013

Total Pages: 0

ISBN-13: 9783110301731

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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 capability of the computer can be enhanced. 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.


Digital Arithmetic

Digital Arithmetic

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 Algorithms

Computer Arithmetic Algorithms

Author: Israel Koren

Publisher: CRC Press

Published: 2018-10-08

Total Pages: 298

ISBN-13: 1439863717

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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.


Computer Arithmetic

Computer Arithmetic

Author: Behrooz Parhami

Publisher:

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. 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 and Verilog HDL Fundamentals

Computer Arithmetic and Verilog HDL Fundamentals

Author: Joseph Cavanagh

Publisher: CRC Press

Published: 2017-12-19

Total Pages: 971

ISBN-13: 143981127X

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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.


The Preparation of Programs for an Electronic Digital Computer

The Preparation of Programs for an Electronic Digital Computer

Author: Maurice Vincent Wilkes

Publisher:

Published: 1951

Total Pages: 192

ISBN-13:

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This is often considered the first book on computer programming. It was written for the EDSAC (Electronic Delay Storage Automatic Calculator) computer that began operation in 1949 as the world's first regularly operated stored program computer. The idea of a library of subroutines was developed for the EDSAC, and is described in this book. Maurice Wilkes lead the development of the EDSAC.


Modern Computer Arithmetic

Modern Computer Arithmetic

Author: Richard P. Brent

Publisher: Cambridge University Press

Published: 2010-11-25

Total Pages: 236

ISBN-13: 9780521194693

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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 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.