Computer arithmetic and validity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
2013
|
| Ausgabe: | [Second fully rev. and extended edition] |
| Schriftenreihe: | De Gruyter studies in mathematics
33 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | Includes bibliographical references and index 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 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 |
| ISBN: | 3110301792 9783110301793 9783110301731 3110301733 |
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
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Datensatz im Suchindex
| _version_ | 1804176604517105664 |
|---|---|
| any_adam_object | |
| author | Kulisch, Ulrich |
| author_facet | Kulisch, Ulrich |
| author_role | aut |
| author_sort | Kulisch, Ulrich |
| author_variant | u k uk |
| building | Verbundindex |
| bvnumber | BV043777178 |
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| ctrlnum | (ZDB-4-EBA)ocn857276812 (ZDB-4-ITC)ocn857276812 (OCoLC)857276812 (DE-599)BVBBV043777178 |
| dewey-full | 005.101/5113 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.101/5113 |
| dewey-search | 005.101/5113 |
| dewey-sort | 15.101 45113 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| edition | [Second fully rev. and extended edition] |
| format | Electronic eBook |
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| id | DE-604.BV043777178 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:34:49Z |
| institution | BVB |
| isbn | 3110301792 9783110301793 9783110301731 3110301733 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029188238 |
| oclc_num | 857276812 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| psigel | ZDB-4-EBA ZDB-4-ITC ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter studies in mathematics |
| spelling | Kulisch, Ulrich Verfasser aut Computer arithmetic and validity by Ulrich Kulisch [Second fully rev. and extended edition] Berlin De Gruyter 2013 txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics 33 Includes bibliographical references and index 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 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 COMPUTERS / Computer Literacy bisacsh COMPUTERS / Computer Science bisacsh COMPUTERS / Data Processing bisacsh COMPUTERS / Hardware / General bisacsh COMPUTERS / Information Technology bisacsh COMPUTERS / Machine Theory bisacsh COMPUTERS / Reference bisacsh Computer arithmetic fast Computer arithmetic and logic units fast Floating-point arithmetic fast Informatik Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Computerarithmetik (DE-588)4135485-0 gnd rswk-swf Intervallalgebra (DE-588)4139152-4 gnd rswk-swf Gleitkommarechnung (DE-588)4157582-9 gnd rswk-swf Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s Richtigkeit von Ergebnissen (DE-588)4127444-1 s 1\p DE-604 Gleitkommarechnung (DE-588)4157582-9 s 2\p DE-604 Intervallalgebra (DE-588)4139152-4 s 3\p DE-604 Computerarithmetik (DE-588)4135485-0 s 4\p DE-604 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kulisch, Ulrich Computer arithmetic and validity COMPUTERS / Computer Literacy bisacsh COMPUTERS / Computer Science bisacsh COMPUTERS / Data Processing bisacsh COMPUTERS / Hardware / General bisacsh COMPUTERS / Information Technology bisacsh COMPUTERS / Machine Theory bisacsh COMPUTERS / Reference bisacsh Computer arithmetic fast Computer arithmetic and logic units fast Floating-point arithmetic fast Informatik Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Computerarithmetik (DE-588)4135485-0 gnd Intervallalgebra (DE-588)4139152-4 gnd Gleitkommarechnung (DE-588)4157582-9 gnd Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4135485-0 (DE-588)4139152-4 (DE-588)4157582-9 (DE-588)4127444-1 (DE-588)4042805-9 |
| title | Computer arithmetic and validity |
| title_auth | Computer arithmetic and validity |
| title_exact_search | Computer arithmetic and validity |
| title_full | Computer arithmetic and validity by Ulrich Kulisch |
| title_fullStr | Computer arithmetic and validity by Ulrich Kulisch |
| title_full_unstemmed | Computer arithmetic and validity by Ulrich Kulisch |
| title_short | Computer arithmetic and validity |
| title_sort | computer arithmetic and validity |
| topic | COMPUTERS / Computer Literacy bisacsh COMPUTERS / Computer Science bisacsh COMPUTERS / Data Processing bisacsh COMPUTERS / Hardware / General bisacsh COMPUTERS / Information Technology bisacsh COMPUTERS / Machine Theory bisacsh COMPUTERS / Reference bisacsh Computer arithmetic fast Computer arithmetic and logic units fast Floating-point arithmetic fast Informatik Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Computerarithmetik (DE-588)4135485-0 gnd Intervallalgebra (DE-588)4139152-4 gnd Gleitkommarechnung (DE-588)4157582-9 gnd Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | COMPUTERS / Computer Literacy COMPUTERS / Computer Science COMPUTERS / Data Processing COMPUTERS / Hardware / General COMPUTERS / Information Technology COMPUTERS / Machine Theory COMPUTERS / Reference Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Informatik Computerarithmetik Intervallalgebra Gleitkommarechnung Richtigkeit von Ergebnissen Numerische Mathematik |
| work_keys_str_mv | AT kulischulrich computerarithmeticandvalidity |