Coverart for item
The Resource Computer arithmetic and validity, by Ulrich Kulisch

Computer arithmetic and validity, by Ulrich Kulisch

Label
Computer arithmetic and validity
Title
Computer arithmetic and validity
Statement of responsibility
by Ulrich Kulisch
Creator
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
YDXCP
http://library.link/vocab/creatorName
Kulisch, Ulrich
Dewey number
005.101/5113
Index
index present
Language note
In English
LC call number
QA76.9.C62
LC item number
K853 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
De Gruyter Studies in Mathematics
Series volume
33
http://library.link/vocab/subjectName
  • Computer arithmetic
  • Computer arithmetic and logic units
  • Floating-point arithmetic
  • Informatik
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • Computer arithmetic
  • Computer arithmetic and logic units
  • Floating-point arithmetic
Label
Computer arithmetic and validity, by Ulrich Kulisch
Link
http://dx.doi.org/10.1515/9783110301793
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Foreword to the second edition; Preface; Introduction; I Theory of computer arithmetic; 1 First concepts; 1.1 Ordered sets; 1.2 Complete lattices and complete subnets; 1.3 Screens and roundings; 1.4 Arithmetic operations and roundings; 2 Ringoids and vectoids; 2.1 Ringoids; 2.2 Vectoids; 3 Definition of computer arithmetic; 3.1 Introduction; 3.2 Preliminaries; 3.3 The traditional definition of computer arithmetic; 3.4 Definition of computer arithmetic by semimorphisms; 3.5 A remark about roundings; 3.6 Uniqueness of the minus operator; 3.7 Rounding near zero; 4 Interval arithmetic
  • 4.1 Interval sets and arithmetic4.2 Interval arithmetic over a linearly ordered set; 4.3 Interval matrices; 4.4 Interval vectors; 4.5 Interval arithmetic on a screen; 4.6 Interval matrices and interval vectors on a screen; 4.7 Complex interval arithmetic; 4.8 Complex interval matrices and interval vectors; 4.9 Extended interval arithmetic; 4.10 Exception-free arithmetic for extended intervals; 4.11 Extended interval arithmetic on the computer; 4.12 Exception-free arithmetic for closed real intervals on the computer; 4.13 Comparison relations and lattice operations
  • 4.14 Algorithmic implementation of interval multiplication and divisionII Implementation of arithmetic on computers; 5 Floating-point arithmetic; 5.1 Definition and properties of the real numbers; 5.2 Floating-point numbers and roundings; 5.3 Floating-point operations; 5.4 Subnormal floating-point numbers; 5.5 On the IEEE floating-point arithmetic standard; 6 Implementation of floating-point arithmetic on a computer; 6.1 A brief review of the realization of integer arithmetic; 6.2 Introductory remarks about the level 1 operations; 6.3 Addition and subtraction; 6.4 Normalization
  • 6.5 Multiplication6.6 Division; 6.7 Rounding; 6.8 A universal rounding unit; 6.9 Overflow and underflow treatment; 6.10 Algorithms using the short accumulator; 6.11 The level 2 operations; 7 Hardware support for interval arithmetic; 7.1 Introduction; 7.2 Arithmetic interval operations; 7.2.1 Algebraic operations; 7.2.2 Comments on the algebraic operations; 7.3 Circuitry for the arithmetic interval operations; 7.4 Comparisons and lattice operations; 7.4.1 Comments on comparisons and lattice operations; 7.4.2 Hardware support for comparisons and lattice operations
  • 7.5 Alternative circuitry for interval operations and comparisons7.5.1 Hardware support for interval arithmetic on x86-processors; 7.5.2 Accurate evaluation of interval scalar products; 8 Scalar products and complete arithmetic; 8.1 Introduction and motivation; 8.2 Historical remarks; 8.3 The ubiquity of the scalar product in numerical analysis; 8.4 Implementation principles; 8.4.1 Long adder and long shift; 8.4.2 Short adder with local memory on the arithmetic unit; 8.4.3 Remarks; 8.4.4 Fast carry resolution; 8.5 Informal sketch for computing an exact dot product
Control code
ocn857276812
Dimensions
unknown
Edition
Second fully rev. and extended edition.
Extent
1 online resource.
Form of item
online
Isbn
9783110301793
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1515/9783110301793
Specific material designation
remote
System control number
  • (Sirsi) o851970604
  • (OCoLC)857276812
Label
Computer arithmetic and validity, by Ulrich Kulisch
Link
http://dx.doi.org/10.1515/9783110301793
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Foreword to the second edition; Preface; Introduction; I Theory of computer arithmetic; 1 First concepts; 1.1 Ordered sets; 1.2 Complete lattices and complete subnets; 1.3 Screens and roundings; 1.4 Arithmetic operations and roundings; 2 Ringoids and vectoids; 2.1 Ringoids; 2.2 Vectoids; 3 Definition of computer arithmetic; 3.1 Introduction; 3.2 Preliminaries; 3.3 The traditional definition of computer arithmetic; 3.4 Definition of computer arithmetic by semimorphisms; 3.5 A remark about roundings; 3.6 Uniqueness of the minus operator; 3.7 Rounding near zero; 4 Interval arithmetic
  • 4.1 Interval sets and arithmetic4.2 Interval arithmetic over a linearly ordered set; 4.3 Interval matrices; 4.4 Interval vectors; 4.5 Interval arithmetic on a screen; 4.6 Interval matrices and interval vectors on a screen; 4.7 Complex interval arithmetic; 4.8 Complex interval matrices and interval vectors; 4.9 Extended interval arithmetic; 4.10 Exception-free arithmetic for extended intervals; 4.11 Extended interval arithmetic on the computer; 4.12 Exception-free arithmetic for closed real intervals on the computer; 4.13 Comparison relations and lattice operations
  • 4.14 Algorithmic implementation of interval multiplication and divisionII Implementation of arithmetic on computers; 5 Floating-point arithmetic; 5.1 Definition and properties of the real numbers; 5.2 Floating-point numbers and roundings; 5.3 Floating-point operations; 5.4 Subnormal floating-point numbers; 5.5 On the IEEE floating-point arithmetic standard; 6 Implementation of floating-point arithmetic on a computer; 6.1 A brief review of the realization of integer arithmetic; 6.2 Introductory remarks about the level 1 operations; 6.3 Addition and subtraction; 6.4 Normalization
  • 6.5 Multiplication6.6 Division; 6.7 Rounding; 6.8 A universal rounding unit; 6.9 Overflow and underflow treatment; 6.10 Algorithms using the short accumulator; 6.11 The level 2 operations; 7 Hardware support for interval arithmetic; 7.1 Introduction; 7.2 Arithmetic interval operations; 7.2.1 Algebraic operations; 7.2.2 Comments on the algebraic operations; 7.3 Circuitry for the arithmetic interval operations; 7.4 Comparisons and lattice operations; 7.4.1 Comments on comparisons and lattice operations; 7.4.2 Hardware support for comparisons and lattice operations
  • 7.5 Alternative circuitry for interval operations and comparisons7.5.1 Hardware support for interval arithmetic on x86-processors; 7.5.2 Accurate evaluation of interval scalar products; 8 Scalar products and complete arithmetic; 8.1 Introduction and motivation; 8.2 Historical remarks; 8.3 The ubiquity of the scalar product in numerical analysis; 8.4 Implementation principles; 8.4.1 Long adder and long shift; 8.4.2 Short adder with local memory on the arithmetic unit; 8.4.3 Remarks; 8.4.4 Fast carry resolution; 8.5 Informal sketch for computing an exact dot product
Control code
ocn857276812
Dimensions
unknown
Edition
Second fully rev. and extended edition.
Extent
1 online resource.
Form of item
online
Isbn
9783110301793
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1515/9783110301793
Specific material designation
remote
System control number
  • (Sirsi) o851970604
  • (OCoLC)857276812

Library Locations

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