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.
Author: Richard P. Brent,Paul Zimmermann
Publisher: Cambridge University Press
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 of these models are extracted and lead to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic are developed in the book. It illustrates how the extended arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.
Theory, Implementation, and Applications
Author: Ulrich Kulisch
Publisher: Walter de Gruyter
This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.
Programming Using the MathCW Portable Software Library
Author: Nelson H.F. Beebe
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
Author: Earl E Swartzlander
Publisher: World Scientific
Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.
Author: Joachim von zur Gathen,Jürgen Gerhard
Publisher: Cambridge University Press
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.
Author: Michael J. Flynn,Stuart F. Oberman
Offers a comprehensive introduction to the fundamentalstructures and applications of a wide range of contemporary codingoperations This book offers a comprehensive introduction to the fundamentalstructures and applications of a wide range of contemporary codingoperations. This text focuses on the ways to structure informationso that its transmission will be in the safest, quickest, and mostefficient and error-free manner possible. All coding operations arecovered in a single framework, with initial chapters addressingearly mathematical models and algorithmic developments which led tothe structure of code. After discussing the general foundations ofcode, chapters proceed to cover individual topics such as notionsof compression, cryptography, detection, and correction codes. Bothclassical coding theories and the most cutting-edge models areaddressed, along with helpful exercises of varying complexities toenhance comprehension. Explains how to structure coding information so that itstransmission is safe, error-free, efficient, and fast Includes a pseudo-code that readers may implement in theirpreferential programming language Features descriptive diagrams and illustrations, and almost 150exercises, with corrections, of varying complexity to enhancecomprehension Foundations of Coding: Compression, Encryption,Error-Correction is an invaluable resource for understandingthe various ways information is structured for its secure andreliable transmission in the 21st-century world.
Compression, Encryption, Error Correction
Author: Jean-Guillaume Dumas,Jean-Louis Roch,Éric Tannier,Sébastien Varrette
Publisher: John Wiley & Sons
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
Verifying Floating-point Algorithms with the Coq System
Author: Sylvie Boldo,Guillaume Melquiond
The book "Computer Arithmetic of Geometrical Figures. Algorithms and Hardware Design" deals with a full theory, as yet not well known, and with engineering solutions for the computer arithmetic of geometrical figures ' planar and spatial. The book covers the codes structure, algorithms of coding and decoding figures, arithmetical operations with figures. The theory is supplemented by numerous examples. The arrangement of several versions of geometrical processor is considered ' data representation, operating blocks, hardwares realization of coding, decoding and arithmetic operations algorithms. The processor's internal performance is appraised. The book is meant for students, engineers and for a users aiming to apply the computer arithmetic of geometrical figures in his own development of custom designed processors.
Author: Solomon Khmelnik
Publisher: Solomon Khmelnik
Publisher: Tata McGraw-Hill Education
Category: Computer graphics
Computer Organization and Design: The Hardware/Software Interface presents the interaction between hardware and software at a variety of levels, which offers a framework for understanding the fundamentals of computing. This book focuses on the concepts that are the basis for computers. Organized into nine chapters, this book begins with an overview of the computer revolution. This text then explains the concepts and algorithms used in modern computer arithmetic. Other chapters consider the abstractions and concepts in memory hierarchies by starting with the simplest possible cache. This book discusses as well the complete data path and control for a processor. The final chapter deals with the exploitation of parallel machines. This book is a valuable resource for students in computer science and engineering. Readers with backgrounds in assembly language and logic design who want to learn how to design a computer or understand how a system works will also find this book useful.
The Hardware / Software Interface
Author: John L. Hennessy,David A. Patterson
Emphasizes the Basic Principles of Computational Arithmetic and Computational Structure Design Taking an interdisciplinary approach to the nanoscale generation of computer devices and systems, Computer Arithmetics for Nanoelectronics develops a consensus between computational properties provided by data structures and phenomenological properties of nano and molecular technology. Covers All Stages of the Design Cycle, from Task Formulation to Molecular-Based Implementation The book introduces the theoretical base and properties of various data structures, along with techniques for their manipulation, optimization, and implementation. It also assigns the computational properties of logic design data structures to 3D structures, furnishes information-theoretical measures and design aspects, and discusses the testability problem. The last chapter presents a nanoscale prospect for natural computing based on assorted computing paradigms from nature. Balanced Coverage of State-of-the-Art Concepts, Techniques, and Practices Up-to-date, comprehensive, and pragmatic in its approach, this text provides a unified overview of the relationship between the fundamentals of digital system design, computer architectures, and micro- and nanoelectronics.
Author: Vlad P. Shmerko,Svetlana N. Yanushkevich,Sergey Edward Lyshevski
Publisher: CRC Press
Category: Technology & Engineering
Author: Jürg Nievergelt,J. Craig Farrar,Edward M. Reingold
Publisher: Prentice Hall
Mathematics of Computing -- Numerical Analysis.
Author: Christian Ullrich
Announcements for the following year included in some vols.
Author: University of Michigan
Also contains brochures, directories, manuals, and programs from various College of Engineering student organizations such as the Society of Women Engineers and Tau Beta Pi.
Author: University of Michigan. College of Engineering
Category: Catalogs, College
Author: J. Sandford Smith
Category: Electronic data processing