Author: Ulrich W. Kulisch Publisher: Springer Science & Business Media ISBN: 3709105250 Category : Computers Languages : en Pages : 151
Book Description
The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.
Author: Ulrich Kulisch Publisher: Walter de Gruyter ISBN: 3110301792 Category : Mathematics Languages : en Pages : 456
Book Description
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.
Author: Michael J. Flynn Publisher: Wiley-Interscience ISBN: Category : Computers Languages : en Pages : 352
Book Description
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: James E. Stine Publisher: Springer Science & Business Media ISBN: 1441989315 Category : Technology & Engineering Languages : en Pages : 185
Book Description
The role of arithmetic in datapath design in VLSI design has been increasing in importance over the last several years due to the demand for processors that are smaller, faster, and dissipate less power. Unfortunately, this means that many of these datapaths will be complex both algorithmically and circuit wise. As the complexity of the chips increases, less importance will be placed on understanding how a particular arithmetic datapath design is implemented and more importance will be given to when a product will be placed on the market. This is because many tools that are available today, are automated to help the digital system designer maximize their efficiently. Unfortunately, this may lead to problems when implementing particular datapaths. The design of high-performance architectures is becoming more compli cated because the level of integration that is capable for many of these chips is in the billions. Many engineers rely heavily on software tools to optimize their work, therefore, as designs are getting more complex less understanding is going into a particular implementation because it can be generated automati cally. Although software tools are a highly valuable asset to designer, the value of these tools does not diminish the importance of understanding datapath ele ments. Therefore, a digital system designer should be aware of how algorithms can be implemented for datapath elements. Unfortunately, due to the complex ity of some of these algorithms, it is sometimes difficult to understand how a particular algorithm is implemented without seeing the actual code.
Author: Behrooz Parhami Publisher: ISBN: 9780199766932 Category : Computer algorithms Languages : en Pages : 623
Book Description
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.
Author: Ulrich W. Kulisch
Author: Ulrich Kulisch
Author: Ulrich Kulisch
Author: Michael J. Flynn
Author: Ulrich Kulisch
Author: Joseph Cavanagh
Author: Ulrich Kulisch
Author: Joseph Cavanagh
Author: James E. Stine
Author: Behrooz Parhami