| Edition |
[Second fully rev. and extended edition]. |
| Description |
1 online resource. |
|
text file |
| Series |
De Gruyter Studies in Mathematics ; 33
|
|
De Gruyter studies in mathematics ; 33.
|
| Bibliography |
Includes bibliographical references and index. |
| 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. |
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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. |
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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. |
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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. |
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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. |
| 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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Computer arithmetic.
|
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Computer arithmetic. |
|
Computer arithmetic and logic units.
|
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Computer arithmetic and logic units. |
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Floating-point arithmetic.
|
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Floating-point arithmetic. |
| Genre/Form |
Electronic books.
|
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Electronic books.
|
| Other Form: |
Print version: Kulisch, Ulrich. Computer arithmetic and validity. [Second fully rev. and extended edition]. 9783110301731 3110301733 (DLC) 2012050942 |
| ISBN |
3110301792 (electronic book) |
|
9783110301793 (electronic book) |
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9783110301731 (alkaline paper) |
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3110301733 (alkaline paper) |
