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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.
13th International Conference, FPL 2003 Lisbon, Portugal, September 1–3, 2003 Proceedings
Author: Peter Y.K. Cheung
This book contains the papers presented at the 13th International Workshop on Field Programmable Logic and Applications (FPL) held on September 1–3, 2003. The conference was hosted by the Institute for Systems and Computer Engineering-Research and Development of Lisbon (INESC-ID) and the Depa- ment of Electrical and Computer Engineering of the IST-Technical University of Lisbon, Portugal. The FPL series of conferences was founded in 1991 at Oxford University (UK), and has been held annually since: in Oxford (3 times), Vienna, Prague, Darmstadt,London,Tallinn,Glasgow,Villach,BelfastandMontpellier.Itbrings together academic researchers, industrial experts, users and newcomers in an - formal,welcomingatmospherethatencouragesproductiveexchangeofideasand knowledge between delegates. Exciting advances in ?eld programmable logic show no sign of slowing down. New grounds have been broken in architectures, design techniques, run-time - con?guration, and applications of ?eld programmable devices in several di?erent areas. Many of these innovations are reported in this volume. The size of FPL conferences has grown signi?cantly over the years. FPL in 2002 saw 214 papers submitted, representing an increase of 83% when compared to the year before. The interest and support for FPL in the programmable logic community continued this year with 216 papers submitted. The technical p- gram was assembled from 90 selected regular papers and 56 posters, resulting in this volume of proceedings. The program also included three invited plenary keynote presentations from LSI Logic, Xilinx and Cadence, and three industrial tutorials from Altera, Mentor Graphics and Dafca.