Finite Precision Number Systems and Arithmetic

Finite Precision Number Systems and Arithmetic

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Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.
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Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 155 b/w illus. 70 tables 240 exercises
  • 1139632701
  • 9781139632706

Table of contents

Preface; 1. Radix polynomial representations; 2. Base and digit set conversion; 3. Addition; 4. Multiplication; 5. Division; 6. Square root; 7. Floating point number systems; 8. Modular arithmetic and residue number systems; 9. Rational arithmetic; Author index; Index.
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Review quote

'For researchers and more mathematically oriented readers, this book is a treasure trove of algorithms difficult or impossible to find elsewhere.' Mathematical Reviews
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About Peter Kornerup

Peter Kornerup is a Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark, Odense. David W. Matula is Professor of Computer Science at Southern Methodist University, Dallas.
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