Modern Computer Arithmetic

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Modern Computer Arithmetic

Author : Richard P. Brent
Publisher : Cambridge University Press
ISBN 13 : 9780521194693
Total Pages : 236 pages
Book Rating : 4.1/5 (946 download)

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Book Synopsis Modern Computer Arithmetic by : Richard P. Brent

Download or read book Modern Computer Arithmetic written by Richard P. Brent and published by Cambridge University Press. This book was released on 2010-11-25 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modern Computer Arithmetic

Author : Richard P. Brent
Publisher : Cambridge University Press
ISBN 13 : 1139492284
Total Pages : 238 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Modern Computer Arithmetic by : Richard P. Brent

Download or read book Modern Computer Arithmetic written by Richard P. Brent and published by Cambridge University Press. This book was released on 2010-11-25 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic

Author : Tom St Denis
Publisher : Elsevier
ISBN 13 : 9780080488387
Total Pages : 291 pages
Book Rating : 4.4/5 (883 download)

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Book Synopsis BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic by : Tom St Denis

Download or read book BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic written by Tom St Denis and published by Elsevier. This book was released on 2006-08-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implementing cryptography requires integers of significant magnitude to resist cryptanalytic attacks. Modern programming languages only provide support for integers which are relatively small and single precision. The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms. Bignum math is the backbone of modern computer security algorithms. It is the ability to work with hundred-digit numbers efficiently using techniques that are both elegant and occasionally bizarre. This book introduces the reader to the concept of bignum algorithms and proceeds to build an entire library of functionality from the ground up. Through the use of theory, pseudo-code and actual fielded C source code the book explains each and every algorithm that goes into a modern bignum library. Excellent for the student as a learning tool and practitioner as a reference alike BigNum Math is for anyone with a background in computer science who has taken introductory level mathematic courses. The text is for students learning mathematics and cryptography as well as the practioner who needs a reference for any of the algorithms documented within. * Complete coverage of Karatsuba Multiplication, the Barrett Algorithm, Toom-Cook 3-Way Multiplication, and More * Tom St Denis is the developer of the industry standard cryptographic suite of tools called LibTom. * This book provides step-by-step exercises to enforce concepts

The Elements of Computing Systems

Author : Noam Nisan
Publisher : MIT Press
ISBN 13 : 0262257920
Total Pages : 354 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis The Elements of Computing Systems by : Noam Nisan

Download or read book The Elements of Computing Systems written by Noam Nisan and published by MIT Press. This book was released on 2008-01-25 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook with a hands-on approach that leads students through the gradual construction of a complete and working computer system including the hardware platform and the software hierarchy. In the early days of computer science, the interactions of hardware, software, compilers, and operating system were simple enough to allow students to see an overall picture of how computers worked. With the increasing complexity of computer technology and the resulting specialization of knowledge, such clarity is often lost. Unlike other texts that cover only one aspect of the field, The Elements of Computing Systems gives students an integrated and rigorous picture of applied computer science, as its comes to play in the construction of a simple yet powerful computer system. Indeed, the best way to understand how computers work is to build one from scratch, and this textbook leads students through twelve chapters and projects that gradually build a basic hardware platform and a modern software hierarchy from the ground up. In the process, the students gain hands-on knowledge of hardware architecture, operating systems, programming languages, compilers, data structures, algorithms, and software engineering. Using this constructive approach, the book exposes a significant body of computer science knowledge and demonstrates how theoretical and applied techniques taught in other courses fit into the overall picture. Designed to support one- or two-semester courses, the book is based on an abstraction-implementation paradigm; each chapter presents a key hardware or software abstraction, a proposed implementation that makes it concrete, and an actual project. The emerging computer system can be built by following the chapters, although this is only one option, since the projects are self-contained and can be done or skipped in any order. All the computer science knowledge necessary for completing the projects is embedded in the book, the only pre-requisite being a programming experience. The book's web site provides all tools and materials necessary to build all the hardware and software systems described in the text, including two hundred test programs for the twelve projects. The projects and systems can be modified to meet various teaching needs, and all the supplied software is open-source.

Advanced Computer Arithmetic Design

Author : Michael J. Flynn
Publisher : Wiley-Interscience
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advanced Computer Arithmetic Design by : Michael J. Flynn

Download or read book Advanced Computer Arithmetic Design written by Michael J. Flynn and published by Wiley-Interscience. This book was released on 2001 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Formal Proofs

Author : Sylvie Boldo
Publisher : Elsevier
ISBN 13 : 0081011709
Total Pages : 326 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Computer Arithmetic and Formal Proofs by : Sylvie Boldo

Download or read book Computer Arithmetic and Formal Proofs written by Sylvie Boldo and published by Elsevier. This book was released on 2017-11-17 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. Describes the notions of specification and weakest precondition computation and their practical use Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic Includes real analysis and a case study about numerical analysis

Numerical Computing with IEEE Floating Point Arithmetic

Author : Michael L. Overton
Publisher : SIAM
ISBN 13 : 0898715717
Total Pages : 105 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Numerical Computing with IEEE Floating Point Arithmetic by : Michael L. Overton

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.

Handbook of Floating-Point Arithmetic

Author : Jean-Michel Muller
Publisher : Springer Science & Business Media
ISBN 13 : 9780817647056
Total Pages : 572 pages
Book Rating : 4.6/5 (47 download)

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Book Synopsis Handbook of Floating-Point Arithmetic by : Jean-Michel Muller

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 572 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.

Modern Computer Arithmetic

Author : Richard P. Brent
Publisher :
ISBN 13 : 9781107214439
Total Pages : 221 pages
Book Rating : 4.2/5 (144 download)

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Book Synopsis Modern Computer Arithmetic by : Richard P. Brent

Download or read book Modern Computer Arithmetic written by Richard P. Brent and published by . This book was released on 2011 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Digital Computer Arithmetic

Author : Joseph Cavanagh
Publisher : McGraw-Hill Companies
ISBN 13 :
Total Pages : 490 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Digital Computer Arithmetic by : Joseph Cavanagh

Download or read book Digital Computer Arithmetic written by Joseph Cavanagh and published by McGraw-Hill Companies. This book was released on 1984 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Cryptography Arithmetic

Author : Amos R. Omondi
Publisher : Springer Nature
ISBN 13 : 3030341429
Total Pages : 338 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Cryptography Arithmetic by : Amos R. Omondi

Download or read book Cryptography Arithmetic written by Amos R. Omondi and published by Springer Nature. This book was released on 2020-01-30 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern cryptosystems, used in numerous applications that require secrecy or privacy - electronic mail, financial transactions, medical-record keeping, government affairs, social media etc. - are based on sophisticated mathematics and algorithms that in implementation involve much computer arithmetic. And for speed it is necessary that the arithmetic be realized at the hardware (chip) level. This book is an introduction to the implementation of cryptosystems at that level. The aforementioned arithmetic is mostly the arithmetic of finite fields, and the book is essentially one on the arithmetic of prime fields and binary fields in the context of cryptography. The book has three main parts. The first part is on generic algorithms and hardware architectures for the basic arithmetic operations: addition, subtraction, multiplication, and division. The second part is on the arithmetic of prime fields. And the third part is on the arithmetic of binary fields. The mathematical fundamentals necessary for the latter two parts are included, as are descriptions of various types of cryptosystems, to provide appropriate context. This book is intended for advanced-level students in Computer Science, Computer Engineering, and Electrical and Electronic Engineering. Practitioners too will find it useful, as will those with a general interest in "hard" applications of mathematics.

Algorithms for Computer Algebra

Author : Keith O. Geddes
Publisher : Springer Science & Business Media
ISBN 13 : 0585332479
Total Pages : 594 pages
Book Rating : 4.5/5 (853 download)

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Book Synopsis Algorithms for Computer Algebra by : Keith O. Geddes

Download or read book Algorithms for Computer Algebra written by Keith O. Geddes and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Modern Computer Algebra

Author : Joachim von zur Gathen
Publisher : Cambridge University Press
ISBN 13 : 1107039037
Total Pages : 811 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Modern Computer Algebra by : Joachim von zur Gathen

Download or read book Modern Computer Algebra written by Joachim von zur Gathen and published by Cambridge University Press. This book was released on 2013-04-25 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.

Multiple-Base Number System

Author : Vassil Dimitrov
Publisher : CRC Press
ISBN 13 : 1439830479
Total Pages : 294 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Multiple-Base Number System by : Vassil Dimitrov

Download or read book Multiple-Base Number System written by Vassil Dimitrov and published by CRC Press. This book was released on 2017-12-19 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer arithmetic has become so fundamentally embedded into digital design that many engineers are unaware of the many research advances in the area. As a result, they are losing out on emerging opportunities to optimize its use in targeted applications and technologies. In many cases, easily available standard arithmetic hardware might not necessarily be the most efficient implementation strategy. Multiple-Base Number System: Theory and Applications stands apart from the usual books on computer arithmetic with its concentration on the uses and the mathematical operations associated with the recently introduced multiple-base number system (MBNS). The book identifies and explores several diverse and never-before-considered MBNS applications (and their implementation issues) to enhance computation efficiency, specifically in digital signal processing (DSP) and public key cryptography. Despite the recent development and increasing popularity of MBNS as a specialized tool for high-performance calculations in electronic hardware and other fields, no single text has compiled all the crucial, cutting-edge information engineers need to optimize its use. The authors’ main goal was to disseminate the results of extensive design research—including much of their own—to help the widest possible audience of engineers, computer scientists, and mathematicians. Dedicated to helping readers apply discoveries in advanced integrated circuit technologies, this single reference is packed with a wealth of vital content previously scattered throughout limited-circulation technical and mathematical journals and papers—resources generally accessible only to researchers and designers working in highly specialized fields. Leveling the informational playing field, this resource guides readers through an in-depth analysis of theory, architectural techniques, and the latest research on the subject, subsequently laying the groundwork users require to begin applying MBNS.

Computer Number Systems and Arithmetic

Author : Norman Ross Scott
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computer Number Systems and Arithmetic by : Norman Ross Scott

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:

Computer Arithmetic

Author : Behrooz Parhami
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 684 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Computer Arithmetic by : Behrooz Parhami

Download or read book Computer Arithmetic written by Behrooz Parhami and published by Oxford University Press, USA. This book was released on 2010 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modern Computer Architecture and Organization

Author : Jim Ledin
Publisher : Packt Publishing Ltd
ISBN 13 : 183898710X
Total Pages : 561 pages
Book Rating : 4.8/5 (389 download)

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Book Synopsis Modern Computer Architecture and Organization by : Jim Ledin

Download or read book Modern Computer Architecture and Organization written by Jim Ledin and published by Packt Publishing Ltd. This book was released on 2020-04-30 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: A no-nonsense, practical guide to current and future processor and computer architectures, enabling you to design computer systems and develop better software applications across a variety of domains Key Features Understand digital circuitry with the help of transistors, logic gates, and sequential logic Examine the architecture and instruction sets of x86, x64, ARM, and RISC-V processors Explore the architecture of modern devices such as the iPhone X and high-performance gaming PCs Book DescriptionAre you a software developer, systems designer, or computer architecture student looking for a methodical introduction to digital device architectures but overwhelmed by their complexity? This book will help you to learn how modern computer systems work, from the lowest level of transistor switching to the macro view of collaborating multiprocessor servers. You'll gain unique insights into the internal behavior of processors that execute the code developed in high-level languages and enable you to design more efficient and scalable software systems. The book will teach you the fundamentals of computer systems including transistors, logic gates, sequential logic, and instruction operations. You will learn details of modern processor architectures and instruction sets including x86, x64, ARM, and RISC-V. You will see how to implement a RISC-V processor in a low-cost FPGA board and how to write a quantum computing program and run it on an actual quantum computer. By the end of this book, you will have a thorough understanding of modern processor and computer architectures and the future directions these architectures are likely to take.What you will learn Get to grips with transistor technology and digital circuit principles Discover the functional elements of computer processors Understand pipelining and superscalar execution Work with floating-point data formats Understand the purpose and operation of the supervisor mode Implement a complete RISC-V processor in a low-cost FPGA Explore the techniques used in virtual machine implementation Write a quantum computing program and run it on a quantum computer Who this book is for This book is for software developers, computer engineering students, system designers, reverse engineers, and anyone looking to understand the architecture and design principles underlying modern computer systems from tiny embedded devices to warehouse-size cloud server farms. A general understanding of computer processors is helpful but not required.