Theory Of Computer Arithmetic
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Computer Arithmetic In Theory And Practice
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Author : Ulrich W. Kulisch
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Computer Arithmetic In Theory And Practice written by Ulrich W. Kulisch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
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.
Computer Arithmetic And Validity
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Author : Ulrich Kulisch
language : en
Publisher: Walter de Gruyter
Release Date : 2013-04-30
Computer Arithmetic And Validity written by Ulrich Kulisch and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-30 with Mathematics categories.
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.
Theory Of Computer Arithmetic
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Author : Algirdas A. Avizienis
language : en
Publisher:
Release Date : 1968
Theory Of Computer Arithmetic written by Algirdas A. Avizienis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Computer programming categories.
Instructor S Manual For Computer Arithmetic
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Author : Behrooz Parhami
language : en
Publisher:
Release Date : 2000-01-15
Instructor S Manual For Computer Arithmetic written by Behrooz Parhami and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-15 with categories.
This title provides a view of computer arithmetic, covering 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.
Theory Of Computer Arithmetic Algorithms And Design Of Digital Arithmetic Processes
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Author : Algirdas Avižienis
language : en
Publisher:
Release Date : 1968
Theory Of Computer Arithmetic Algorithms And Design Of Digital Arithmetic Processes written by Algirdas Avižienis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Algorithms categories.
Theory Of Computer Arithmetic
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Author :
language : en
Publisher:
Release Date : 1969
Theory Of Computer Arithmetic written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Algorithms categories.
Number Theory For Computing
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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Number Theory For Computing written by Song Y. Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Computers categories.
Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping Ralph Merkle receive the credit he deserves. Diffie, Rivest, Shamir, Adleman and I had the good luck to get expedited review of our papers, so that they appeared before Merkle's seminal contribu tion. Your noting his early submission date and referring to what has come to be called "Diffie-Hellman key exchange" as it should, "Diffie-Hellman-Merkle key exchange", is greatly appreciated. It has been gratifying to see how cryptography and number theory have helped each other over the last twenty-five years. :'-Jumber theory has been the source of numerous clever ideas for implementing cryptographic systems and protocols while cryptography has been helpful in getting funding for this area which has sometimes been called "the queen of mathematics" because of its seeming lack of real world applications. Little did they know! Stanford, 30 July 2001 Martin E. Hellman Preface to the Second Edition Number theory is an experimental science.
Computer Arithmetic
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Author : Behrooz Parhami
language : en
Publisher:
Release Date : 2010
Computer Arithmetic written by Behrooz Parhami and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
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.
Digital Arithmetic
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Author : Miloš D. Ercegovac
language : en
Publisher: Elsevier
Release Date : 2003-09-15
Digital Arithmetic written by Miloš D. Ercegovac and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Mathematics categories.
Digital arithmetic plays an important role in the design of general-purpose digital processors and of embedded systems for signal processing, graphics, and communications. In spite of a mature body of knowledge in digital arithmetic, each new generation of processors or digital systems creates new arithmetic design problems. Designers, researchers, and graduate students will find solid solutions to these problems in this comprehensive, state-of-the-art exposition of digital arithmetic.Ercegovac and Lang, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independent manner. They consistently use an algorithmic approach in defining arithmetic operations, illustrate concepts with examples of designs at the logic level, and discuss cost/performance characteristics throughout. Students and practicing designers alike will find Digital Arithmetic a definitive reference and a consistent teaching tool for developing a deep understanding of the "arithmetic style" of algorithms and designs. - Guides readers to develop sound solutions, avoid known mistakes, and repeat successful design decisions. - Presents comprehensive coverage3⁄4from fundamental theories to current research trends. - Written in a clear and engaging style by two masters of the field. - Concludes each chapter with in-depth discussions of the key literature. - Includes a full set of over 250 exercises
A New Approach To Scientific Computation
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Author : Ulrich W. Kulisch
language : en
Publisher: Elsevier
Release Date : 2014-05-12
A New Approach To Scientific Computation written by Ulrich W. Kulisch and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
A New Approach to Scientific Computation is a collection of papers delivered at a symposium held at the IBM Thomas J. Watson Research Center on August 3, 1982. The symposium provided a forum for reviewing various aspects of an approach to scientific computation based on a systematic theory of computer arithmetic. Computer demonstration packages for standard problems of numerical mathematics are considered. Comprised of 12 chapters, this volume begins by summarizing an extensive research activity in scientific computation as well as the experience gained through various implementations of a new approach to arithmetic on diverse processors, including even microprocessors. A complete listing of the spaces that occur in numerical computations is presented, followed by a discussion of aspects of traditional computer arithmetic and a new definition of computer arithmetic. The properties of semimorphisms are also considered. Subsequent chapters focus on potential applications of programming packages to standard problems in numerical analysis implemented on a Z80 based minicomputer, with a PASCAL extension called PASCAL-SC as the programming language; methods for solving algebraic problems with high accuracy; and the use of a computer with floating-point arithmetic to obtain guaranteed sharp bounds for the value of an arithmetic expression. An extension of FORTRAN which satisfies contemporary requirements of numerical computation is also described. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.