Download or read book Computer Arithmetic in Theory and Practice written by Ulrich Kulisch and published by . This book was released on 1981 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Computer Arithmetic and Validity written by Ulrich Kulisch and published by Walter de Gruyter. This book was released on 2013-04-30 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and mathematical capability of the digital computer can be enhanced in a quite natural way. 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 into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer 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.
Download or read book Computer Arithmetic in Theory and Practice written by Ulrich W. Kulisch and published by Academic Press. This book was released on 2014-05-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Arithmetic in Theory and Practice deals with computer arithmetic and the various implementations of the entire arithmetic package on diverse processors, including microprocessors. It illustrates the importance of theoretical development in the sound implementation of arithmetic on computers, and argues that such an implementation requires the establishment of various isomorphisms between different definitions of arithmetic operations. Comprised of seven chapters, this volume begins with an introduction to the theory of computer arithmetic by giving an axiomatic characterization of the essential properties of sets and subsets; complete lattices and complete subnets; screens and roundings; and arithmetic operations. The discussion then turns to the concepts of a ringoid and a vectoid as well as those of ordered or weakly ordered ringoids and vectoids; interval arithmetic; and floating-point arithmetic. The operations in interval spaces are defined by means of semimorphisms. The final chapter shows how to embed the five basic data types (integer, real, complex, real interval, and complex interval) together with the arithmetic operations that are defined for all of these types into existing higher programming languages. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.
Download or read book Computer Arithmetic and Validity written by Ulrich Kulisch and published by ISSN. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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.
Download or read book Number Theory for Computing written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.
Download or read book Computer Arithmetic Algorithms written by Israel Koren and published by CRC Press. This book was released on 2018-10-08 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Arithmetic and Logic in Computer Systems written by Mi Lu and published by John Wiley & Sons. This book was released on 2005-03-04 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.
Download or read book Computer Arithmetic and Verilog HDL Fundamentals written by Joseph Cavanagh and published by CRC Press. This book was released on 2017-12-19 with total page 971 pages. Available in PDF, EPUB and Kindle. Book excerpt: Verilog Hardware Description Language (HDL) is the state-of-the-art method for designing digital and computer systems. Ideally suited to describe both combinational and clocked sequential arithmetic circuits, Verilog facilitates a clear relationship between the language syntax and the physical hardware. It provides a very easy-to-learn and practical means to model a digital system at many levels of abstraction. Computer Arithmetic and Verilog HDL Fundamentals details the steps needed to master computer arithmetic for fixed-point, decimal, and floating-point number representations for all primary operations. Silvaco International’s SILOS, the Verilog simulator used in these pages, is simple to understand, yet powerful enough for any application. It encourages users to quickly prototype and de-bug any logic function and enables single-stepping through the Verilog source code. It also presents drag-and-drop abilities. Introducing the three main modeling methods—dataflow, behavioral, and structural—this self-contained tutorial— Covers the number systems of different radices, such as octal, decimal, hexadecimal, and binary-coded variations Reviews logic design fundamentals, including Boolean algebra and minimization techniques for switching functions Presents basic methods for fixed-point addition, subtraction, multiplication, and division, including the use of decimals in all four operations Addresses floating-point addition and subtraction with several numerical examples and flowcharts that graphically illustrate steps required for true addition and subtraction for floating-point operands Demonstrates floating-point division, including the generation of a zero-biased exponent Designed for electrical and computer engineers and computer scientists, this book leaves nothing unfinished, carrying design examples through to completion. The goal is practical proficiency. To this end, each chapter includes problems of varying complexity to be designed by the reader.
Download or read book Basic Category Theory for Computer Scientists written by Benjamin C. Pierce and published by MIT Press. This book was released on 1991-08-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
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.
Download or read book Theory of Computer Arithmetic Algorithms and Design of Digital Arithmetic Processes written by Algirdas Avižienis and published by . This book was released on 1968 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Digital Arithmetic written by Milos D. Ercegovac and published by Elsevier. This book was released on 2004 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authoritative reference on the theory and design practice of computer arithmetic.
Download or read book Higher Arithmetic written by Harold M. Edwards and published by American Mathematical Soc.. This book was released on 2008 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the topics featured in this textbook are: congruences; the fundamental theorem of arithmetic; exponentiation and orders; primality testing; the RSA cipher system; polynomials; modules of hypernumbers; signatures of equivalence classes; and the theory of binary quadratic forms. The book contains exercises with answers.
Download or read book Number Theory for Computing written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.
