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Computer arithmetic plays a key role in the computer designers' quest for user-friendliness, compactness, simplicity, high performance, low cost, and low power. This text emphasizes the underlying theory and actual hardware designs, and links computer arithmetic to other subfields of computing.
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)
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.
Genetic programming is a method for getting a computer to solve a problem by telling it what needs to be done instead of how to do it. Koza, Bennett, Andre, and Keane present genetically evolved solutions to dozens of problems of design, optimal control, classification, system identification, function learning, and computational molecular biology. Among the solutions are 14 results competitive with human-produced results, including 10 rediscoveries of previously patented inventions. Researchers in artificial intelligence, machine learning, evolutionary computation, and genetic algorithms will find this an essential reference to the most recent and most important results in the rapidly growing field of genetic programming. * Explains how the success of genetic programming arises from seven fundamental differences distinguishing it from conventional approaches to artificial intelligence and machine learning * Describes how genetic programming uses architecture-altering operations to make on-the-fly decisions on whether to use subroutines, loops, recursions, and memory * Demonstrates that genetic programming possesses 16 attributes that can reasonably be expected of a system for automatically creating computer programs * Presents the general-purpose Genetic Programming Problem Solver * Focuses on the previously unsolved problem of analog circuit synthesis, presenting genetically evolved filters, amplifiers, computational circuits, a robot controller circuit, source identification circuits, a temperature-measuring circuit, a voltage reference circuit, and more * Introduces evolvable hardware in the form of field-programmable gate arrays * Includes an introduction to genetic programming for the uninitiated
5th International Workshop, FPL '95, Oxford, United Kingdom, August 29 - September 1, 1995. Proceedings
Author: Will Moore
This volume constitutes the proceedings of the Fifth International Workshop on Field-Programmable Logic and Its Applications, FPL '95, held in Oxford, UK in August/September 1995. The volume presents 46 full revised papers carefully selected by the program committee from a large number and wide range of submissions. The papers document the progress achieved since the predecessor conference (see LNCS 849). They are organized in sections on architectures, platforms, tools, arithmetic and signal processing, embedded systems and other applications, and reconfigurable design and models.
13th International Conference, FPL 2003, Lisbon, Portugal, September 1-3, 2003, Proceedings
Author: Peter Y.K. Cheung
Publisher: Springer Science & Business Media
This book constitutes the refereed proceedings of the 13th International Conference on Field-Programmable Logic and Applications, FPL 2003, held in Lisbon, Portugal in September 2003. The 90 revised full papers and 56 revised poster papers presented were carefully reviewed and selected from 216 submissions. The papers are organized in topical sections on technologies and trends, communications applications, high level design tools, reconfigurable architecture, cryptographic applications, multi-context FPGAs, low-power issues, run-time reconfiguration, compilation tools, asynchronous techniques, bio-related applications, codesign, reconfigurable fabrics, image processing applications, SAT techniques, application-specific architectures, DSP applications, dynamic reconfiguration, SoC architectures, emulation, cache design, arithmetic, bio-inspired design, SoC design, cellular applications, fault analysis, and network applications.