Modern Computer Arithmetic

Author: Richard P. Brent,Paul Zimmermann

Publisher: Cambridge University Press

ISBN: 1139492284

Category: Computers

Page: N.A

View: 7754

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.
Posted in Computers

Modern Computer Arithmetic

Author: Richard P. Brent,Paul Zimmermann

Publisher: Cambridge University Press

ISBN: 9780521194693

Category: Computers

Page: 236

View: 2658

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.
Posted in Computers

Advanced computer arithmetic design

Author: Michael J. Flynn,Stuart F. Oberman

Publisher: Wiley-Interscience

ISBN: 9780471412090

Category: Computers

Page: 325

View: 4129

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.
Posted in Computers

Computer Arithmetic

Algorithms and Hardware Implementations

Author: Mircea Vlăduţiu

Publisher: Springer Science & Business Media

ISBN: 364218314X

Category: Computers

Page: 270

View: 7402

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.
Posted in Computers

Handbook of Floating-Point Arithmetic

Author: Jean-Michel Muller,Nicolas Brisebarre,Florent de Dinechin,Claude-Pierre Jeannerod,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Damien Stehlé,Serge Torres

Publisher: Springer Science & Business Media

ISBN: 9780817647056

Category: Mathematics

Page: 572

View: 4457

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.
Posted in Mathematics

Numerical computing with IEEE floating point arithmetic

Author: Michael L. Overton

Publisher: SIAM

ISBN: 9780898718072

Category: Computer arithmetic

Page: 104

View: 2745

This title provides an easily accessible yet detailed discussion of IEEE Std 754-1985, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and the cutting edge of industry, it is supported by virtually every modern computer. Other topics include the floating point architecture of the Intel microprocessors and a discussion of programming language support for the standard.
Posted in Computer arithmetic

Computer Arithmetic and Formal Proofs

Verifying Floating-point Algorithms with the Coq System

Author: Sylvie Boldo,Guillaume Melquiond

Publisher: Elsevier

ISBN: 0081011709

Category: Computers

Page: 326

View: 2474

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
Posted in Computers

The Elements of Computing Systems

Building a Modern Computer from First Principles

Author: Noam Nisan,Shimon Schocken

Publisher: MIT Press

ISBN: 9780262140874

Category: Computers

Page: 325

View: 3177

This title gives students an integrated and rigorous picture of applied computer science, as it comes to play in the construction of a simple yet powerful computer system.
Posted in Computers

Digital Arithmetic

Author: Miloš D. Ercegovac,Tomás Lang

Publisher: Elsevier

ISBN: 1558607986

Category: Computers

Page: 709

View: 6483

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

Computer Arithmetic

Volume I

Author: Earl E Swartzlander

Publisher: World Scientific

ISBN: 9814651583

Category: Mathematics

Page: 396

View: 5322

The book provides many of the basic papers in computer arithmetic. These papers describe the concepts and basic operations (in the words of the original developers) that would be useful to the designers of computers and embedded systems. Although the main focus is on the basic operations of addition, multiplication and division, advanced concepts such as logarithmic arithmetic and the calculations of elementary functions are also covered. 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:OverviewAdditionParallel Prefix AdditionMulti-Operand AdditionMultiplicationDivisionLogarithmsElementary FunctionsFloating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers the basic arithmetic operationsIt does this in the words of the creatorsKeywords:Computer Arithmetic;Adders;Parallel Prefix Adders;Multi-operand Adders;Multipliers;Dividers;Logarithmic Arithmetic;Elementary Function Evaluation
Posted in Mathematics

Computer Arithmetic Algorithms, Second Edition

Author: Israel Koren

Publisher: CRC Press

ISBN: 1439863717

Category: Computers

Page: 296

View: 8479

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.
Posted in Computers

Computer Arithmetic

Algorithms and Hardware Designs

Author: Behrooz Parhami

Publisher: Oxford University Press, USA

ISBN: 9780195328486

Category: Computers

Page: 641

View: 3996

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
Posted in Computers

Hardware Implementation of Finite-Field Arithmetic

Author: Jean-Pierre Deschamps

Publisher: McGraw Hill Professional

ISBN: 0071545824

Category: Technology & Engineering

Page: 360

View: 1791

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
Posted in Technology & Engineering

BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic

Author: Tom St Denis

Publisher: Elsevier

ISBN: 9780080488387

Category: Computers

Page: 291

View: 2256

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
Posted in Computers

Computer Organization and Design MIPS Edition

The Hardware/Software Interface

Author: David A. Patterson,John L. Hennessy

Publisher: Newnes

ISBN: 0124078869

Category: Computers

Page: 800

View: 4196

Computer Organization and Design, Fifth Edition, is the latest update to the classic introduction to computer organization. The text now contains new examples and material highlighting the emergence of mobile computing and the cloud. It explores this generational change with updated content featuring tablet computers, cloud infrastructure, and the ARM (mobile computing devices) and x86 (cloud computing) architectures. The book uses a MIPS processor core to present the fundamentals of hardware technologies, assembly language, computer arithmetic, pipelining, memory hierarchies and I/O.Because an understanding of modern hardware is essential to achieving good performance and energy efficiency, this edition adds a new concrete example, Going Faster, used throughout the text to demonstrate extremely effective optimization techniques. There is also a new discussion of the Eight Great Ideas of computer architecture. Parallelism is examined in depth with examples and content highlighting parallel hardware and software topics. The book features the Intel Core i7, ARM Cortex-A8 and NVIDIA Fermi GPU as real-world examples, along with a full set of updated and improved exercises. This new edition is an ideal resource for professional digital system designers, programmers, application developers, and system software developers. It will also be of interest to undergraduate students in Computer Science, Computer Engineering and Electrical Engineering courses in Computer Organization, Computer Design, ranging from Sophomore required courses to Senior Electives. Winner of a 2014 Texty Award from the Text and Academic Authors Association Includes new examples, exercises, and material highlighting the emergence of mobile computing and the cloud Covers parallelism in depth with examples and content highlighting parallel hardware and software topics Features the Intel Core i7, ARM Cortex-A8 and NVIDIA Fermi GPU as real-world examples throughout the book Adds a new concrete example, "Going Faster," to demonstrate how understanding hardware can inspire software optimizations that improve performance by 200 times Discusses and highlights the "Eight Great Ideas" of computer architecture: Performance via Parallelism; Performance via Pipelining; Performance via Prediction; Design for Moore's Law; Hierarchy of Memories; Abstraction to Simplify Design; Make the Common Case Fast; and Dependability via Redundancy Includes a full set of updated and improved exercises
Posted in Computers

Computer Arithmetic

Volume I

Author: Earl E Swartzlander

Publisher: World Scientific

ISBN: 9814651583

Category: Mathematics

Page: 396

View: 2286

The book provides many of the basic papers in computer arithmetic. These papers describe the concepts and basic operations (in the words of the original developers) that would be useful to the designers of computers and embedded systems. Although the main focus is on the basic operations of addition, multiplication and division, advanced concepts such as logarithmic arithmetic and the calculations of elementary functions are also covered. 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:OverviewAdditionParallel Prefix AdditionMulti-Operand AdditionMultiplicationDivisionLogarithmsElementary FunctionsFloating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers the basic arithmetic operationsIt does this in the words of the creatorsKeywords:Computer Arithmetic;Adders;Parallel Prefix Adders;Multi-operand Adders;Multipliers;Dividers;Logarithmic Arithmetic;Elementary Function Evaluation
Posted in Mathematics

Introduction to Modern Number Theory

Fundamental Problems, Ideas and Theories

Author: Yu. I. Manin,Alexei A. Panchishkin

Publisher: Springer Science & Business Media

ISBN: 9783540276920

Category: Mathematics

Page: 514

View: 588

This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
Posted in Mathematics

Young Children Reinvent Arithmetic

Implications of Piaget's Theory

Author: Constance Kamii

Publisher: Teachers College Press

ISBN: 0807776246

Category: Education

Page: N.A

View: 1833

In this fully revised second edition of the classic Young Children Reinvent Arithmetic, Constance Kamii describes and develops an innovative program of teaching arithmetic in the early elementary grades. Kamii bases her educational strategies on renowned constructivist Jean Piaget's scientific ideas of how children develop logico-mathematical thinking. Written in collaboration with a classroom teacher, and premised upon the conviction that children are capable of much more than teachers and parents generally realize, the book provides a rich theoretical foundation and a compelling explanation of educational goals and objectives. Kamii calls attention to the ways in which traditional textbook-based teaching can be harmful to children’s development of numerical reasoning, and uses extensive research and classroom-tested studies to illuminate the efficacy of the approach. This book is full of practical suggestions and developmentally appropriate activities that can be used to stimulate numerical thinking among students of varying abilities and learning styles, both within and outside of the classroom. “In this new edition of her important book, Connie Kamii demonstrates scholarship not just in what she has written, but in her willingness to incorporate new ideas and findings. Many people update their books; few assiduously revise them, confronting what they believe to be past errors or gaps in their thinking. Such intellectual honesty, along with consistent connections between theory and practice, make this book a solid contribution to mathematics education of young children.” —Douglas Clements, State University of New York at Buffalo “The development of young children’s logico-mathematical knowledge is at the heart of this text. Similar to the first edition, this revision provides a rich theoretical foundation as well as child-centered activities and principles of teaching that support problem solving, communicating, reasoning, making connections, and representing mathematical ideas. In this great resource for preservice and in-service elementary teachers, Professor Kamii continues to help us understand the implications of Piagetian theory.” —Frances R. Curcio, New York University
Posted in Education

Modern Computer Algebra

Author: Joachim von zur Gathen,Jürgen Gerhard

Publisher: Cambridge University Press

ISBN: 1107245257

Category: Computers

Page: N.A

View: 7507

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.
Posted in Computers

Hacker's Delight

Author: Henry S. Warren

Publisher: Addison-Wesley

ISBN: 0133085015

Category: Computers

Page: 512

View: 7146

In Hacker’s Delight, Second Edition, Hank Warren once again compiles an irresistible collection of programming hacks: timesaving techniques, algorithms, and tricks that help programmers build more elegant and efficient software, while also gaining deeper insights into their craft. Warren’s hacks are eminently practical, but they’re also intrinsically interesting, and sometimes unexpected, much like the solution to a great puzzle. They are, in a word, a delight to any programmer who is excited by the opportunity to improve. Extensive additions in this edition include A new chapter on cyclic redundancy checking (CRC), including routines for the commonly used CRC-32 code A new chapter on error correcting codes (ECC), including routines for the Hamming code More coverage of integer division by constants, including methods using only shifts and adds Computing remainders without computing a quotient More coverage of population count and counting leading zeros Array population count New algorithms for compress and expand An LRU algorithm Floating-point to/from integer conversions Approximate floating-point reciprocal square root routine A gallery of graphs of discrete functions Now with exercises and answers
Posted in Computers