Fast and Accurate Vector Operations
Advances in computer technology are now so profound that the arithmetic capability and repertoire of computers can and should be expanded. Nowadays the elementary floating-point operations +,- x,/ give computed results that coincide with the rounded exact
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Ulrich W. Kulisch Advanced Arithmetic for the Digital Computer Design of Arithmetic Units
Springer-Verlag Wien GmbH
Dr.Ulrich W. Kulisch Professor of Mathematics Institut fiir Angewandte Mathematik, Universităt Karlsruhe, Germany
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© 2002 Springer-Verlag Wien Originally published by Springer-Verlag Wien in 2002 Product Liability: The publisher can give no guarantee for all the information contained in this book. This does also refer to information about drug dosage and application thereof. In every individual case the respective user must check its accuracy by consulting other pharmaceuticalliterature. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Cover illustration: Falko SchrMer, University of Applied Science, Zweibriicken Typesetting: Camera ready by editor Printed on acid-free and chlorine-free bleached paper SPIN: 10892255 CIP data applied for
With 32 Figures (1 in colour)
ISBN 978-3-211-83870-9 ISBN 978-3-7091-0525-2 (eBook) DOI 10.1007/978-3-7091-0525-2
Preface
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 programming 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. Vector processing is an important technique used
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